D Programming Language 2.0

# std.algorithm

Category | Functions
--- | ---
Searching | balancedParens boyerMooreFinder canFind count countUntil endsWith commonPrefix find findAdjacent findAmong findSkip findSplit findSplitAfter findSplitBefore indexOf minCount minPos mismatch skipOver startsWith until
Comparison | cmp equal levenshteinDistance levenshteinDistanceAndPath max min mismatch
Iteration | filter filterBidirectional group joiner map reduce splitter uniq
Sorting | completeSort isPartitioned isSorted makeIndex partialSort partition partition3 schwartzSort sort topN topNCopy nextPermutation nextEvenPermutation
Set operations | cartesianProduct largestPartialIntersection largestPartialIntersectionWeighted nWayUnion setDifference setIntersection setSymmetricDifference setUnion
Mutation | bringToFront copy fill initializeAll move moveAll moveSome remove reverse swap swapRanges uninitializedFill

Implements algorithms oriented mainly towards processing of sequences. Some functions are semantic equivalents or supersets of those found in the <algorithm> header in Alexander Stepanov's Standard Template Library for C++.

Many functions in this module are parameterized with a function or a predicate . The predicate may be passed either as a function name, a delegate name, a functor name, or a compile-time string. The string may consist of any legal D expression that uses the symbol a (for unary functions) or the symbols a and b (for binary functions). These names will NOT interfere with other homonym symbols in user code because they are evaluated in a different context. The default for all binary comparison predicates is "a == b" for unordered operations and "a < b" for ordered operations.

Example:

    int[] a = ...;
    static bool greater(int a, int b)
    {
        return a > b;
    }
    sort!(greater)(a);  // predicate as alias
    sort!("a > b")(a);  // predicate as string
                        // (no ambiguity with array name)
    sort(a);            // no predicate, "a < b" is implicit

Cheat Sheet
Function Name | Description
--- | ---
Searching
balancedParens | balancedParens("((1 + 1) / 2)") returns true because the string has balanced parentheses.
boyerMooreFinder | find("hello world", boyerMooreFinder("or")) returns "orld" using the Boyer-Moore algorithm.
canFind | canFind("hello world", "or") returns true.
count | Counts elements that are equal to a specified value or satisfy a predicate. count([1, 2, 1], 1) returns 2 and count!"a < 0"([1, -3, 0]) returns 1.
countUntil | countUntil(a, b) returns the number of steps taken in a to reach b; for example, countUntil("hello!", "o") returns 4.
endsWith | endsWith("rocks", "ks") returns true.
find | find("hello world", "or") returns "orld" using linear search. (For binary search refer to std.range.sortedRange.)
findAdjacent | findAdjacent([1, 2, 3, 3, 4]) returns the subrange starting with two equal adjacent elements, i.e. [3, 3, 4].
findAmong | findAmong("abcd", "qcx") returns "cd" because 'c' is among "qcx".
findSkip | If a = "abcde", then findSkip(a, "x") returns false and leaves a unchanged, whereas findSkip(a, 'c') advances a to "cde" and returns true.
findSplit | findSplit("abcdefg", "de") returns the three ranges "abc", "de", and "fg".
findSplitAfter | findSplitAfter("abcdefg", "de") returns the two ranges "abcde" and "fg".
findSplitBefore | findSplitBefore("abcdefg", "de") returns the two ranges "abc" and "defg".
minCount | minCount([2, 1, 1, 4, 1]) returns tuple(1, 3).
minPos | minPos([2, 3, 1, 3, 4, 1]) returns the subrange [1, 3, 4, 1], i.e., positions the range at the first occurrence of its minimal element.
skipOver | Assume a = "blah". Then skipOver(a, "bi") leaves a unchanged and returns false, whereas skipOver(a, "bl") advances a to refer to "ah" and returns true.
startsWith | startsWith("hello, world", "hello") returns true.
until | Lazily iterates a range until a specific value is found.
Comparison
cmp | cmp("abc", "abcd") is -1, cmp("abc", "aba") is 1, and cmp("abc", "abc") is 0.
equal | Compares ranges for element-by-element equality, e.g. equal([1, 2, 3], [1.0, 2.0, 3.0]) returns true.
levenshteinDistance | levenshteinDistance("kitten", "sitting") returns 3 by using the Levenshtein distance algorithm.
levenshteinDistanceAndPath | levenshteinDistanceAndPath("kitten", "sitting") returns tuple(3, "snnnsni") by using the Levenshtein distance algorithm.
max | max(3, 4, 2) returns 4.
min | min(3, 4, 2) returns 2.
mismatch | mismatch("oh hi", "ohayo") returns tuple(" hi", "ayo").
Iteration
filter | filter!"a > 0"([1, -1, 2, 0, -3]) iterates over elements 1, 2, and 0.
filterBidirectional | Similar to filter, but also provides back and popBack at a small increase in cost.
group | group([5, 2, 2, 3, 3]) returns a range containing the tuples tuple(5, 1), tuple(2, 2), and tuple(3, 2).
joiner | joiner(["hello", "world!"], ";") returns a range that iterates over the characters "hello; world!". No new string is created - the existing inputs are iterated.
map | map!"2 * a"([1, 2, 3]) lazily returns a range with the numbers 2, 4, 6.
reduce | reduce!"a + b"([1, 2, 3, 4]) returns 10.
splitter | Lazily splits a range by a separator.
uniq | Iterates over the unique elements in a range, which is assumed sorted.
Sorting
completeSort | If a = [10, 20, 30] and b = [40, 6, 15], then completeSort(a, b) leaves a = [6, 10, 15] and b = [20, 30, 40]. The range a must be sorted prior to the call, and as a result the combination std.range.chain(a, b) is sorted.
isPartitioned | isPartitioned!"a < 0"([-1, -2, 1, 0, 2]) returns true because the predicate is true for a portion of the range and false afterwards.
isSorted | isSorted([1, 1, 2, 3]) returns true.
makeIndex | Creates a separate index for a range.
partialSort | If a = [5, 4, 3, 2, 1], then partialSort(a, 3) leaves a[0 .. 3] = [1, 2, 3]. The other elements of a are left in an unspecified order.
partition | Partitions a range according to a predicate.
schwartzSort | Sorts with the help of the Schwartzian transform.
sort | Sorts.
topN | Separates the top elements in a range.
topNCopy | Copies out the top elements of a range.
nextPermutation | Computes the next lexicographically greater permutation of a range in-place.
nextEvenPermutation | Computes the next lexicographically greater even permutation of a range in-place.
Set operations
cartesianProduct | Computes Cartesian product of two ranges.
largestPartialIntersection | Copies out the values that occur most frequently in a range of ranges.
largestPartialIntersectionWeighted | Copies out the values that occur most frequently (multiplied by per-value weights) in a range of ranges.
nWayUnion | Computes the union of a set of sets implemented as a range of sorted ranges.
setDifference | Lazily computes the set difference of two or more sorted ranges.
setIntersection | Lazily computes the intersection of two or more sorted ranges.
setSymmetricDifference | Lazily computes the symmetric set difference of two or more sorted ranges.
setUnion | Lazily computes the set union of two or more sorted ranges.
Mutation
bringToFront | If a = [1, 2, 3] and b = [4, 5, 6, 7], bringToFront(a, b) leaves a = [4, 5, 6] and b = [7, 1, 2, 3].
copy | Copies a range to another. If a = [1, 2, 3] and b = new int[5], then copy(a, b) leaves b = [1, 2, 3, 0, 0] and returns b[3 .. $].
fill | Fills a range with a pattern, e.g., if a = new int[3], then fill(a, 4) leaves a = [4, 4, 4] and fill(a, [3, 4]) leaves a = [3, 4, 3].
initializeAll | If a = [1.2, 3.4], then initializeAll(a) leaves a = [double.init, double.init].
move | move(a, b) moves a into b. move(a) reads a destructively.
moveAll | Moves all elements from one range to another.
moveSome | Moves as many elements as possible from one range to another.
reverse | If a = [1, 2, 3], reverse(a) changes it to [3, 2, 1].
swap | Swaps two values.
swapRanges | Swaps all elements of two ranges.
uninitializedFill | Fills a range (assumed uninitialized) with a value.

License:
Boost License 1.0.

Authors:
Andrei Alexandrescu

Source:
std/algorithm.d

template map(fun...) if (fun.length >= 1)
  auto map(Range)(Range r) if (isInputRange!(Unqual!Range));

  Implements the homonym function (also known as transform) present in many languages of functional flavor. The call map!(fun)(range) returns a range of which elements are obtained by applying fun(x) left to right for all x in range. The original ranges are not changed. Evaluation is done lazily.

  Example:

      int[] arr1 = [ 1, 2, 3, 4 ];
      int[] arr2 = [ 5, 6 ];
      auto squares = map!(a => a * a)(chain(arr1, arr2));
      assert(equal(squares, [ 1, 4, 9, 16, 25, 36 ]));

  Multiple functions can be passed to map. In that case, the element type of map is a tuple containing one element for each function.

  Example:

      auto arr1 = [ 1, 2, 3, 4 ];
      foreach (e; map!("a + a", "a * a")(arr1))
      {
          writeln(e[0], " ", e[1]);
      }

  You may alias map with some function(s) to a symbol and use it separately:

      alias map!(to!string) stringize;
      assert(equal(stringize([ 1, 2, 3, 4 ]), [ "1", "2", "3", "4" ]));

template reduce(fun...) if (fun.length >= 1)
  auto reduce(Args...)(Args args) if (Args.length > 0 && Args.length <= 2 && isIterable!(Args[$ - 1]));

  Implements the homonym function (also known as accumulate, compress, inject, or foldl) present in various programming languages of functional flavor. The call reduce!(fun)(seed, range) first assigns seed to an internal variable result, also called the accumulator. Then, for each element x in range, result = fun(result, x) gets evaluated. Finally, result is returned. The one-argument version reduce!(fun)(range) works similarly, but it uses the first element of the range as the seed (the range must be non-empty).

  Many aggregate range operations turn out to be solved with reduce quickly and easily. The example below illustrates reduce's remarkable power and flexibility.

  Example:

      int[] arr = [ 1, 2, 3, 4, 5 ];
      // Sum all elements
      auto sum = reduce!((a,b) => a + b)(0, arr);
      assert(sum == 15);

      // Sum again, using a string predicate with "a" and "b"
      sum = reduce!"a + b"(0, arr);
      assert(sum == 15);

      // Compute the maximum of all elements
      auto largest = reduce!(max)(arr);
      assert(largest == 5);

      // Max again, but with Uniform Function Call Syntax (UFCS)
      largest = arr.reduce!(max);
      assert(largest == 5);

      // Compute the number of odd elements
      auto odds = reduce!((a,b) => a + (b & 1))(0, arr);
      assert(odds == 3);

      // Compute the sum of squares
      auto ssquares = reduce!((a,b) => a + b * b)(0, arr);
      assert(ssquares == 55);

      // Chain multiple ranges into seed
      int[] a = [ 3, 4 ];
      int[] b = [ 100 ];
      auto r = reduce!("a + b")(chain(a, b));
      assert(r == 107);

      // Mixing convertible types is fair game, too
      double[] c = [ 2.5, 3.0 ];
      auto r1 = reduce!("a + b")(chain(a, b, c));
      assert(approxEqual(r1, 112.5));

      // To minimize nesting of parentheses, Uniform Function Call Syntax can be used
      auto r2 = chain(a, b, c).reduce!("a + b");
      assert(approxEqual(r2, 112.5));

  Multiple functions:
  Sometimes it is very useful to compute multiple aggregates in one pass. One advantage is that the computation is faster because the looping overhead is shared. That's why reduce accepts multiple functions. If two or more functions are passed, reduce returns a std.typecons.Tuple object with one member per passed-in function. The number of seeds must be correspondingly increased.

  Example:

      double[] a = [ 3.0, 4, 7, 11, 3, 2, 5 ];
      // Compute minimum and maximum in one pass
      auto r = reduce!(min, max)(a);
      // The type of r is Tuple!(int, int)
      assert(approxEqual(r[0], 2));  // minimum
      assert(approxEqual(r[1], 11)); // maximum

      // Compute sum and sum of squares in one pass
      r = reduce!("a + b", "a + b * b")(tuple(0.0, 0.0), a);
      assert(approxEqual(r[0], 35));  // sum
      assert(approxEqual(r[1], 233)); // sum of squares
      // Compute average and standard deviation from the above
      auto avg = r[0] / a.length;
      auto stdev = sqrt(r[1] / a.length - avg * avg);

void fill(Range, Value)(Range range, Value filler);
  Fills range with a filler.

  Example:

      int[] a = [ 1, 2, 3, 4 ];
      fill(a, 5);
      assert(a == [ 5, 5, 5, 5 ]);

void fill(Range1, Range2)(Range1 range, Range2 filler);
  Fills range with a pattern copied from filler. The length of range does not have to be a multiple of the length of filler. If filler is empty, an exception is thrown.

  Example:

      int[] a = [ 1, 2, 3, 4, 5 ];
      int[] b = [ 8, 9 ];
      fill(a, b);
      assert(a == [ 8, 9, 8, 9, 8 ]);

void uninitializedFill(Range, Value)(Range range, Value filler);
  Fills a range with a value. Assumes that the range does not currently contain meaningful content. This is of interest for structs that define copy constructors (for all other types, fill and uninitializedFill are equivalent).

  uninitializedFill will only operate on ranges that expose references to its members and have assignable elements.

  Example:

      struct S { ... }
      S[] s = (cast(S*) malloc(5 * S.sizeof))[0 .. 5];
      uninitializedFill(s, 42);
      assert(s == [ 42, 42, 42, 42, 42 ]);

void initializeAll(Range)(Range range);
  Initializes all elements of a range with their .init value. Assumes that the range does not currently contain meaningful content.

  initializeAll will operate on ranges that expose references to its members and have assignable elements, as well as on (mutable) strings.

  Example:

      struct S { ... }
      S[] s = (cast(S*) malloc(5 * S.sizeof))[0 .. 5];
      initializeAll(s);
      assert(s == [ 0, 0, 0, 0, 0 ]);

template filter(alias pred) if (is(typeof(unaryFun!(pred))))
  auto filter(Range)(Range rs) if (isInputRange!(Unqual!Range));

  Implements the homonym function present in various programming languages of functional flavor. The call filter!(predicate)(range) returns a new range only containing elements x in range for which predicate(x) is true.

  Example:

      int[] arr = [ 1, 2, 3, 4, 5 ];

      // Sum all elements
      auto small = filter!(a => a < 3)(arr);
      assert(equal(small, [ 1, 2 ]));

      // Sum again, but with Uniform Function Call Syntax (UFCS)
      auto sum = arr.filter!(a => a < 3);
      assert(equal(sum, [ 1, 2 ]));

      // In combination with chain() to span multiple ranges
      int[] a = [ 3, -2, 400 ];
      int[] b = [ 100, -101, 102 ];
      auto r = chain(a, b).filter!(a => a > 0);
      assert(equal(r, [ 3, 400, 100, 102 ]));

      // Mixing convertible types is fair game, too
      double[] c = [ 2.5, 3.0 ];
      auto r1 = chain(c, a, b).filter!(a => cast(int) a != a);
      assert(approxEqual(r1, [ 2.5 ]));

template filterBidirectional(alias pred)
  auto filterBidirectional(Range)(Range r) if (isBidirectionalRange!(Unqual!Range));

  Similar to filter, except it defines a bidirectional range. There is a speed disadvantage - the constructor spends time finding the last element in the range that satisfies the filtering condition (in addition to finding the first one). The advantage is that the filtered range can be spanned from both directions. Also, std.range.retro can be applied against the filtered range.

  Example:

      int[] arr = [ 1, 2, 3, 4, 5 ];
      auto small = filterBidirectional!("a < 3")(arr);
      assert(small.back == 2);
      assert(equal(small, [ 1, 2 ]));
      assert(equal(retro(small), [ 2, 1 ]));
      // In combination with chain() to span multiple ranges
      int[] a = [ 3, -2, 400 ];
      int[] b = [ 100, -101, 102 ];
      auto r = filterBidirectional!("a > 0")(chain(a, b));
      assert(r.back == 102);

void move(T)(ref T source, ref T target);
T move(T)(ref T source);
  Moves source into target via a destructive copy. Specifically:
  - If hasAliasing!T is true (see std.traits.hasAliasing), then the representation of source is bitwise copied into target and then source = T.init is evaluated.
  - Otherwise, target = source is evaluated.
  See also std.exception.pointsTo.

  Preconditions:
  &source == &target || !pointsTo(source, source)

Range2 moveAll(Range1, Range2)(Range1 src, Range2 tgt);
  For each element a in src and each element b in tgt in lockstep in increasing order, calls move(a, b). Returns the leftover portion of tgt. Throws an exeption if there is not enough room in tgt to acommodate all of src.

  Preconditions:
  walkLength(src) <= walkLength(tgt)

Tuple!(Range1, Range2) moveSome(Range1, Range2)(Range1 src, Range2 tgt);
  For each element a in src and each element b in tgt in lockstep in increasing order, calls move(a, b). Stops when either src or tgt have been exhausted. Returns the leftover portions of the two ranges.

pure nothrow @trusted void swap(T)(ref T lhs, ref T rhs);
  Swaps lhs and rhs. See also std.exception.pointsTo.

  Preconditions:
  !pointsTo(lhs, lhs) && !pointsTo(lhs, rhs) && !pointsTo(rhs, lhs) && !pointsTo(rhs, rhs)

template forward(args...)
  Forwards function arguments with saving ref-ness.

  Example:

      int foo(int n) { return 1; }
      int foo(ref int n) { return 2; }
      int bar()(auto ref int x) { return foo(forward!x); }

      assert(bar(1) == 1);
      int i;
      assert(bar(i) == 2);

      void foo(int n, ref string s) { s = null; foreach (i; 0..n) s ~= "Hello"; }

      // forwards all arguments which are bound to parameter tuple
      void bar(Args...)(auto ref Args args) { return foo(forward!args); }

      // forwards all arguments with swapping order
      void baz(Args...)(auto ref Args args) { return foo(forward!args[$/2..$], forward!args[0..$/2]); }

      string s;
      bar(1, s);
      assert(s == "Hello");
      baz(s, 2);
      assert(s == "HelloHello");

auto splitter(Range, Separator)(Range r, Separator s);
  Splits a range using an element as a separator. This can be used with any narrow string type or sliceable range type, but is most popular with string types.

  Two adjacent separators are considered to surround an empty element in the split range.

  If the empty range is given, the result is a range with one empty element. If a range with one separator is given, the result is a range with two empty elements.

  Example:

      assert(equal(splitter("hello  world", ' '), [ "hello", "", "world" ]));
      int[] a = [ 1, 2, 0, 0, 3, 0, 4, 5, 0 ];
      int[][] w = [ [1, 2], [], [3], [4, 5] ];
      assert(equal(splitter(a, 0), w));
      a = null;
      assert(equal(splitter(a, 0), [ (int[]).init ]));
      a = [ 0 ];
      assert(equal(splitter(a, 0), [ (int[]).init, (int[]).init ]));
      a = [ 0, 1 ];
      assert(equal(splitter(a, 0), [ [], [1] ]));

auto splitter(Range, Separator)(Range r, Separator s);
  Splits a range using another range as a separator. This can be used with any narrow string type or sliceable range type, but is most popular with string types.

auto joiner(RoR, Separator)(RoR r, Separator sep);
auto joiner(RoR)(RoR r);
  Lazily joins a range of ranges with a separator. The separator itself is a range. If you do not provide a separator, then the ranges are joined directly without anything in between them.

  Example:

      assert(equal(joiner([""], "xyz"), ""));
      assert(equal(joiner(["", ""], "xyz"), "xyz"));
      assert(equal(joiner(["", "abc"], "xyz"), "xyzabc"));
      assert(equal(joiner(["abc", ""], "xyz"), "abcxyz"));
      assert(equal(joiner(["abc", "def"], "xyz"), "abcxyzdef"));
      assert(equal(joiner(["Mary", "has", "a", "little", "lamb"], "..."),
        "Mary...has...a...little...lamb"));
      assert(equal(joiner(["abc", "def"]), "abcdef"));

auto uniq(alias pred = "a == b", Range)(Range r);
  Iterates unique consecutive elements of the given range (functionality akin to the uniq system utility). Equivalence of elements is assessed by using the predicate pred, by default "a == b". If the given range is bidirectional, uniq also yields a bidirectional range.

  Example:

      int[] arr = [ 1, 2, 2, 2, 2, 3, 4, 4, 4, 5 ];
      assert(equal(uniq(arr), [ 1, 2, 3, 4, 5 ][]));

struct Group(alias pred, R) if (isInputRange!(R));
Group!(pred, Range) group(alias pred = "a == b", Range)(Range r);
  Similarly to uniq, group iterates unique consecutive elements of the given range. The element type is Tuple!(ElementType!R, uint) because it includes the count of equivalent elements seen. Equivalence of elements is assessed by using the predicate pred, by default "a == b".

  Group is an input range if R is an input range, and a forward range in all other cases.

  Example:

      int[] arr = [ 1, 2, 2, 2, 2, 3, 4, 4, 4, 5 ];
      assert(equal(group(arr), [ tuple(1, 1u), tuple(2, 4u), tuple(3, 1u),
          tuple(4, 3u), tuple(5, 1u) ][]));

R find(alias pred = "a == b", R, E)(R haystack, E needle);
  Finds an individual element in an input range. Elements of haystack are compared with needle by using predicate pred. Performs Ο(walkLength(haystack)) evaluations of pred. See also STL's find.

  To find the last occurence of needle in haystack, call find(retro(haystack), needle). See also std.range.retro.

  Parameters:

  haystack | The range searched in.
  needle | The element searched for.

  Constraints:
  isInputRange!R && is(typeof(binaryFun!pred(haystack.front, needle) : bool))

  Returns:
  haystack advanced such that binaryFun!pred(haystack.front, needle) is true (if no such position exists, returns haystack after exhaustion).

  Example:

      assert(find("hello, world", ',') == ", world");
      assert(find([1, 2, 3, 5], 4) == []);
      assert(find(SList!int(1, 2, 3, 4, 5)[], 4) == SList!int(4, 5)[]);
      assert(find!"a > b"([1, 2, 3, 5], 2) == [3, 5]);

      auto a = [ 1, 2, 3 ];
      assert(find(a, 5).empty);       // not found
      assert(!find(a, 2).empty);      // found

      // Case-insensitive find of a string
      string[] s = [ "Hello", "world", "!" ];
      assert(!find!("toLower(a) == b")(s, "hello").empty);

R1 find(alias pred = "a == b", R1, R2)(R1 haystack, R2 needle);
  Finds a forward range in another. Elements are compared for equality. Performs Ο(walkLength(haystack) * walkLength(needle)) comparisons in the worst case. Specializations taking advantage of bidirectional or random access (where present) may accelerate search depending on the statistics of the two ranges' content.

  Parameters:

  haystack | The range searched in.
  needle | The range searched for.

  Constraints:
  isForwardRange!R1 && isForwardRange!R2 && is(typeof(binaryFun!pred(haystack.front, needle.front) : bool))

  Returns:
  haystack advanced such that needle is a prefix of it (if no such position exists, returns haystack advanced to termination).

      assert(find("hello, world", "World").empty);
      assert(find("hello, world", "wo") == "world");
      assert(find([1, 2, 3, 4], SList!(2, 3)[]) == [2, 3, 4]);

Tuple!(Range, size_t) find(alias pred = "a == b", Range, Ranges...)(Range haystack, Ranges needles);
struct BoyerMooreFinder(alias pred, Range);
BoyerMooreFinder!(binaryFun!(pred), Range) boyerMooreFinder(alias pred = "a == b", Range)(Range needle);
  Finds two or more needles into a haystack. The predicate pred is used throughout to compare elements. By default, elements are compared for equality.

  Parameters:

  haystack | The target of the search. Must be an input range . If any of needles is a range with elements comparable to elements in haystack, then haystack must be a forward range such that the search can backtrack.
  needles | One or more items to search for. Each of needles must be either comparable to one element in haystack, or be itself a forward range with elements comparable with elements in haystack.

  Returns:
  A tuple containing haystack positioned to match one of the needles and also the 1-based index of the matching element in needles (0 if none of needles matched, 1 if needles[0] matched, 2 if needles[1] matched...). The first needle to be found will be the one that matches. If multiple needles are found at the same spot in the range, then the shortest one is the one which matches (if multiple needles of the same length are found at the same spot (e.g "a" and 'a'), then the left-most of them in the argument list matches).

  The relationship between haystack and needles simply means that one can e.g. search for individual ints or arrays of ints in an array of ints. In addition, if elements are individually comparable, searches of heterogeneous types are allowed as well: a double[] can be searched for an int or a short[], and conversely a long can be searched for a float or a double[]. This makes for efficient searches without the need to coerce one side of the comparison into the other's side type.

  Example:

      int[] a = [ 1, 4, 2, 3 ];
      assert(find(a, 4) == [ 4, 2, 3 ]);
      assert(find(a, [ 1, 4 ]) == [ 1, 4, 2, 3 ]);
      assert(find(a, [ 1, 3 ], 4) == tuple([ 4, 2, 3 ], 2));
      // Mixed types allowed if comparable
      assert(find(a, 5, [ 1.2, 3.5 ], 2.0, [ 1 ]) == tuple([ 2, 3 ], 3));

  The complexity of the search is Ο(haystack.length * max(needles.length)). (For needles that are individual items, length is considered to be 1.) The strategy used in searching several subranges at once maximizes cache usage by moving in haystack as few times as possible.

Range find(alias pred, Range)(Range haystack);
  Advances the input range haystack by calling haystack.popFront until either pred(haystack.front), or haystack.empty. Performs Ο(haystack.length) evaluations of pred. See also STL's find_if.

  To find the last element of a bidirectional haystack satisfying pred, call find!(pred)(retro(haystack)). See also std.range.retro.

  Example:

      auto arr = [ 1, 2, 3, 4, 1 ];
      assert(find!("a > 2")(arr) == [ 3, 4, 1 ]);

      // with predicate alias
      bool pred(int x) { return x + 1 > 1.5; }
      assert(find!(pred)(arr) == arr);

bool findSkip(alias pred = "a == b", R1, R2)(ref R1 haystack, R2 needle);
  If needle occurs in haystack, positions haystack right after the first occurrence of needle and returns true. Otherwise, leaves haystack as is and returns false.

  Example:

      string s = "abcdef";
      assert(findSkip(s, "cd") && s == "ef");
      s = "abcdef";
      assert(!findSkip(s, "cxd") && s == "abcdef");
      assert(findSkip(s, "def") && s.empty);

auto findSplit(alias pred = "a == b", R1, R2)(R1 haystack, R2 needle);
auto findSplitBefore(alias pred = "a == b", R1, R2)(R1 haystack, R2 needle);
auto findSplitAfter(alias pred = "a == b", R1, R2)(R1 haystack, R2 needle);
  These functions find the first occurrence of needle in haystack and then split haystack as follows.

  findSplit returns a tuple result containing three ranges. result[0] is the portion of haystack before needle, result[1] is the portion of haystack that matches needle, and result[2] is the portion of haystack after the match. If needle was not found, result[0] comprehends haystack entirely and result[1] and result[2] are empty.

  findSplitBefore returns a tuple result containing two ranges. result[0] is the portion of haystack before needle, and result[1] is the balance of haystack starting with the match. If needle was not found, result[0] comprehends haystack entirely and result[1] is empty.

  findSplitAfter returns a tuple result containing two ranges. result[0] is the portion of haystack up to and including the match, and result[1] is the balance of haystack starting after the match. If needle was not found, result[0] is empty and result[1] is haystack.

  In all cases, the concatenation of the returned ranges spans the entire haystack.

  If haystack is a random-access range, all three components of the tuple have the same type as haystack. Otherwise, haystack must be a forward range and the type of result[0] and result[1] is the same as std.range.takeExactly.

  Example:

      auto a = "Carl Sagan Memorial Station";
      auto r = findSplit(a, "Velikovsky");
      assert(r[0] == a);
      assert(r[1].empty);
      assert(r[2].empty);
      r = findSplit(a, " ");
      assert(r[0] == "Carl");
      assert(r[1] == " ");
      assert(r[2] == "Sagan Memorial Station");
      auto r1 = findSplitBefore(a, "Sagan");
      assert(r1[0] == "Carl ", r1[0]);
      assert(r1[1] == "Sagan Memorial Station");
      auto r2 = findSplitAfter(a, "Sagan");
      assert(r2[0] == "Carl Sagan");
      assert(r2[1] == " Memorial Station");

ptrdiff_t countUntil(alias pred = "a == b", R, Rs...)(R haystack, Rs needles);
ptrdiff_t countUntil(alias pred = "a == b", R, N)(R haystack, N needle);
  Returns the number of elements which must be popped from the front of haystack before reaching an element for which startsWith!pred(haystack, needles) is true. If startsWith!pred(haystack, needles) is not true for any element in haystack, then -1 is returned.

  needles may be either an element or a range.

  Examples:

      assert(countUntil("hello world", "world") == 6);
      assert(countUntil("hello world", 'r') == 8);
      assert(countUntil("hello world", "programming") == -1);
      assert(countUntil("日本語", "本語") == 1);
      assert(countUntil("日本語", '語')   == 2);
      assert(countUntil("日本語", "五") == -1);
      assert(countUntil("日本語", '五') == -1);
      assert(countUntil([0, 7, 12, 22, 9], [12, 22]) == 2);
      assert(countUntil([0, 7, 12, 22, 9], 9) == 4);
      assert(countUntil!"a > b"([0, 7, 12, 22, 9], 20) == 3);

ptrdiff_t countUntil(alias pred, R)(R haystack);
  Returns the number of elements which must be popped from haystack before pred(haystack.front) is true.

  Examples:

      assert(countUntil!(std.uni.isWhite)("hello world") == 5);
      assert(countUntil!(std.ascii.isDigit)("hello world") == -1);
      assert(countUntil!"a > 20"([0, 7, 12, 22, 9]) == 3);

enum OpenRight;
  Interval option specifier for until (below) and others.

  no
    Interval is closed to the right (last element included)

  yes
    Interval is open to the right (last element is not included)

struct Until(alias pred, Range, Sentinel) if (isInputRange!(Range));
Until!(pred, Range, Sentinel) until(alias pred = "a == b", Range, Sentinel)(Range range, Sentinel sentinel, OpenRight openRight = OpenRight.yes);
Until!(pred, Range, void) until(alias pred, Range)(Range range, OpenRight openRight = OpenRight.yes);
  Lazily iterates range until value sentinel is found, at which point it stops.

  Example:

      int[] a = [ 1, 2, 4, 7, 7, 2, 4, 7, 3, 5];
      assert(equal(a.until(7), [1, 2, 4][]));
      assert(equal(a.until(7, OpenRight.no), [1, 2, 4, 7][]));

uint startsWith(alias pred = "a == b", Range, Needles...)(Range doesThisStart, Needles withOneOfThese);
bool startsWith(alias pred = "a == b", R1, R2)(R1 doesThisStart, R2 withThis);
bool startsWith(alias pred = "a == b", R, E)(R doesThisStart, E withThis);
  If the range doesThisStart starts with any of the withOneOfThese ranges or elements, returns 1 if it starts with withOneOfThese[0], 2 if it starts with withOneOfThese[1], and so on. If none match, returns 0. In the case where doesThisStart starts with multiple of the ranges or elements in withOneOfThese, then the shortest one matches (if there are two which match which are of the same length (e.g. "a" and 'a'), then the left-most of them in the argument list matches).

  Example:

      assert(startsWith("abc", ""));
      assert(startsWith("abc", "a"));
      assert(!startsWith("abc", "b"));
      assert(startsWith("abc", 'a', "b") == 1);
      assert(startsWith("abc", "b", "a") == 2);
      assert(startsWith("abc", "a", "a") == 1);
      assert(startsWith("abc", "ab", "a") == 2);
      assert(startsWith("abc", "x", "a", "b") == 2);
      assert(startsWith("abc", "x", "aa", "ab") == 3);
      assert(startsWith("abc", "x", "aaa", "sab") == 0);
      assert(startsWith("abc", "x", "aaa", "a", "sab") == 3);

bool skipOver(alias pred = "a == b", R1, R2)(ref R1 r1, R2 r2);
  If startsWith(r1, r2), consume the corresponding elements off r1 and return true. Otherwise, leave r1 unchanged and return false.

bool skipOver(alias pred = "a == b", R, E)(ref R r, E e);
  Checks whether a range starts with an element, and if so, consume that element off r and return true. Otherwise, leave r unchanged and return false.

uint endsWith(alias pred = "a == b", Range, Needles...)(Range doesThisEnd, Needles withOneOfThese);
bool endsWith(alias pred = "a == b", R1, R2)(R1 doesThisEnd, R2 withThis);
bool endsWith(alias pred = "a == b", R, E)(R doesThisEnd, E withThis);
  The reciprocal of startsWith.

  Example:

      assert(endsWith("abc", ""));
      assert(!endsWith("abc", "b"));
      assert(endsWith("abc", "a", 'c') == 2);
      assert(endsWith("abc", "c", "a") == 1);
      assert(endsWith("abc", "c", "c") == 1);
      assert(endsWith("abc", "bc", "c") == 2);
      assert(endsWith("abc", "x", "c", "b") == 2);
      assert(endsWith("abc", "x", "aa", "bc") == 3);
      assert(endsWith("abc", "x", "aaa", "sab") == 0);
      assert(endsWith("abc", "x", "aaa", 'c', "sab") == 3);

auto commonPrefix(alias pred = "a == b", R1, R2)(R1 r1, R2 r2);
  Returns the common prefix of two ranges. Example:

      assert(commonPrefix("hello, world", "hello, there") == "hello, ");

  If the first argument is a string, then the result is a slice of r1 which contains the characters that both ranges start with. For all other types, the type of the result is the same as the result of takeExactly(r1, n), where n is the number of elements that both ranges start with.

  See Also:
  std.range.takeExactly

Range findAdjacent(alias pred = "a == b", Range)(Range r);
  Advances r until it finds the first two adjacent elements a, b that satisfy pred(a, b). Performs Ο(r.length) evaluations of pred. See also STL's adjacent_find.

  Example:

      int[] a = [ 11, 10, 10, 9, 8, 8, 7, 8, 9 ];
      auto r = findAdjacent(a);
      assert(r == [ 10, 10, 9, 8, 8, 7, 8, 9 ]);
      p = findAdjacent!("a < b")(a);
      assert(p == [ 7, 8, 9 ]);

Range1 findAmong(alias pred = "a == b", Range1, Range2)(Range1 seq, Range2 choices);
  Advances seq by calling seq.popFront until either find!(pred)(choices, seq.front) is true, or seq becomes empty. Performs Ο(seq.length * choices.length) evaluations of pred. See also STL's find_first_of.

  Example:

      int[] a = [ -1, 0, 1, 2, 3, 4, 5 ];
      int[] b = [ 3, 1, 2 ];
      assert(findAmong(a, b) == a[2 .. $]);

size_t count(alias pred = "a == b", Range, E)(Range haystack, E needle);
size_t count(alias pred = "a == b", R1, R2)(R1 haystack, R2 needle);
size_t count(alias pred = "true", R)(R haystack);
  The first version counts the number of elements x in r for which pred(x, value) is true. pred defaults to equality. Performs Ο(r.length) evaluations of pred.

  The second version returns the number of times needle occurs in haystack. Throws an exception if needle.empty, as the count of the empty range in any range would be infinite. Overlapped counts are not considered, for example count("aaa", "aa") is 1, not 2.

  The third version counts the elements for which pred(x) is true. Performs Ο(r.length) evaluations of pred.

  Note:
  Regardless of the overload, count will not accept infinite ranges for haystack.

  Example:

      // count elements in range
      int[] a = [ 1, 2, 4, 3, 2, 5, 3, 2, 4 ];
      assert(count(a, 2) == 3);
      assert(count!("a > b")(a, 2) == 5);
      // count range in range
      assert(count("abcadfabf", "ab") == 2);
      assert(count("ababab", "abab") == 1);
      assert(count("ababab", "abx") == 0);
      // fuzzy count range in range
      assert(count!"std.uni.toLower(a) == std.uni.toLower(b)"("AbcAdFaBf", "ab") == 2);
      // count predicate in range
      assert(count!("a > 1")(a) == 8);

bool balancedParens(Range, E)(Range r, E lPar, E rPar, size_t maxNestingLevel = size_t.max);
  Checks whether r has "balanced parentheses", i.e. all instances of lPar are closed by corresponding instances of rPar. The parameter maxNestingLevel controls the nesting level allowed. The most common uses are the default or 0. In the latter case, no nesting is allowed.

  Example:

      auto s = "1 + (2 * (3 + 1 / 2)";
      assert(!balancedParens(s, '(', ')'));
      s = "1 + (2 * (3 + 1) / 2)";
      assert(balancedParens(s, '(', ')'));
      s = "1 + (2 * (3 + 1) / 2)";
      assert(!balancedParens(s, '(', ')', 1));
      s = "1 + (2 * 3 + 1) / (2 - 5)";
      assert(balancedParens(s, '(', ')', 1));

bool equal(Range1, Range2)(Range1 r1, Range2 r2);
bool equal(alias pred, Range1, Range2)(Range1 r1, Range2 r2);
  Returns true if and only if the two ranges compare equal element for element, according to binary predicate pred. The ranges may have different element types, as long as pred(a, b) evaluates to bool for a in r1 and b in r2. Performs Ο(min(r1.length, r2.length)) evaluations of pred. See also STL's equal.

  Example:

      int[] a = [ 1, 2, 4, 3 ];
      assert(!equal(a, a[1..$]));
      assert(equal(a, a));

      // different types
      double[] b = [ 1.0, 2, 4, 3];
      assert(!equal(a, b[1..$]));
      assert(equal(a, b));

      // predicated: ensure that two vectors are approximately equal
      double[] c = [ 1.005, 2, 4, 3];
      assert(equal!(approxEqual)(b, c));

int cmp(alias pred = "a < b", R1, R2)(R1 r1, R2 r2);
  Performs three-way lexicographical comparison on two input ranges according to predicate pred. Iterating r1 and r2 in lockstep, cmp compares each element e1 of r1 with the corresponding element e2 in r2. If binaryFun!pred(e1, e2), cmp returns a negative value. If binaryFun!pred(e2, e1), cmp returns a positive value. If one of the ranges has been finished, cmp returns a negative value if r1 has fewer elements than r2, a positive value if r1 has more elements than r2, and 0 if the ranges have the same number of elements.

  If the ranges are strings, cmp performs UTF decoding appropriately and compares the ranges one code point at a time.

MinType!(T1, T2, T) min(T1, T2, T...)(T1 a, T2 b, T xs);
  Returns the minimum of the passed-in values. The type of the result is computed by using std.traits.CommonType.

MaxType!(T1, T2, T) max(T1, T2, T...)(T1 a, T2 b, T xs);
  Returns the maximum of the passed-in values. The type of the result is computed by using std.traits.CommonType.

  Example:

      int a = 5;
      short b = 6;
      double c = 2;
      auto d = max(a, b);
      assert(is(typeof(d) == int));
      assert(d == 6);
      auto e = min(a, b, c);
      assert(is(typeof(e) == double));
      assert(e == 2);

Tuple!(ElementType!(Range), size_t) minCount(alias pred = "a < b", Range)(Range range);
  Returns the minimum element of a range together with the number of occurrences. The function can actually be used for counting the maximum or any other ordering predicate (that's why maxCount is not provided).

  Example:

      int[] a = [ 2, 3, 4, 1, 2, 4, 1, 1, 2 ];
      // Minimum is 1 and occurs 3 times
      assert(minCount(a) == tuple(1, 3));
      // Maximum is 4 and occurs 2 times
      assert(minCount!("a > b")(a) == tuple(4, 2));

Range minPos(alias pred = "a < b", Range)(Range range);
  Returns the position of the minimum element of forward range range, i.e. a subrange of range starting at the position of its smallest element and with the same ending as range. The function can actually be used for counting the maximum or any other ordering predicate (that's why maxPos is not provided).

  Example:

      int[] a = [ 2, 3, 4, 1, 2, 4, 1, 1, 2 ];
      // Minimum is 1 and first occurs in position 3
      assert(minPos(a) == [ 1, 2, 4, 1, 1, 2 ]);
      // Maximum is 4 and first occurs in position 2
      assert(minPos!("a > b")(a) == [ 4, 1, 2, 4, 1, 1, 2 ]);

Tuple!(Range1, Range2) mismatch(alias pred = "a == b", Range1, Range2)(Range1 r1, Range2 r2);
  Sequentially compares elements in r1 and r2 in lockstep, and stops at the first mismatch (according to pred, by default equality). Returns a tuple with the reduced ranges that start with the two mismatched values. Performs Ο(min(r1.length, r2.length)) evaluations of pred. See also STL's mismatch.

  Example:

      int[]    x = [ 1,  5, 2, 7,   4, 3 ];
      double[] y = [ 1.0, 5, 2, 7.3, 4, 8 ];
      auto m = mismatch(x, y);
      assert(m[0] == x[3 .. $]);
      assert(m[1] == y[3 .. $]);

enum EditOp;
  Encodes edit operations necessary to transform one sequence into another. Given sequences s (source) and t (target), a sequence of EditOp encodes the steps that need to be taken to convert s into t. For example, if s = "cat" and "cars", the minimal sequence that transforms s into t is: skip two characters, replace 't' with 'r', and insert an 's'. Working with edit operations is useful in applications such as spell-checkers (to find the closest word to a given misspelled word), approximate searches, diff-style programs that compute the difference between files, efficient encoding of patches, DNA sequence analysis, and plagiarism detection.

  none
    Current items are equal; no editing is necessary.

  substitute
    Substitute current item in target with current item in source.

  insert
    Insert current item from the source into the target.

  remove
    Remove current item from the target.

size_t levenshteinDistance(alias equals = "a == b", Range1, Range2)(Range1 s, Range2 t);
  Returns the Levenshtein distance between s and t. The Levenshtein distance computes the minimal amount of edit operations necessary to transform s into t. Performs Ο(s.length * t.length) evaluations of equals and occupies Ο(s.length * t.length) storage.

  Example:

      assert(levenshteinDistance("cat", "rat") == 1);
      assert(levenshteinDistance("parks", "spark") == 2);
      assert(levenshteinDistance("kitten", "sitting") == 3);
      // ignore case
      assert(levenshteinDistance!("std.uni.toUpper(a) == std.uni.toUpper(b)")
          ("parks", "SPARK") == 2);

Tuple!(size_t, EditOp[]) levenshteinDistanceAndPath(alias equals = "a == b", Range1, Range2)(Range1 s, Range2 t);
  Returns the Levenshtein distance and the edit path between s and t.

  Example:

      string a = "Saturday", b = "Sunday";
      auto p = levenshteinDistanceAndPath(a, b);
      assert(p[0] == 3);
      assert(equal(p[1], "nrrnsnnn"));

Range2 copy(Range1, Range2)(Range1 source, Range2 target);
  Copies the content of source into target and returns the remaining (unfilled) part of target. See also STL's copy. If a behavior similar to STL's copy_backward is needed, use copy(retro(source), retro(target)). See also std.range.retro.

  Example:

      int[] a = [ 1, 5 ];
      int[] b = [ 9, 8 ];
      int[] c = new int[a.length + b.length + 10];
      auto d = copy(b, copy(a, c));
      assert(c[0 .. a.length + b.length] == a ~ b);
      assert(d.length == 10);

  As long as the target range elements support assignment from source range elements, different types of ranges are accepted.

  Example:

      float[] a = [ 1.0f, 5 ];
      double[] b = new double[a.length];
      auto d = copy(a, b);

  To copy at most n elements from range a to range b, you may want to use copy(take(a, n), b). To copy those elements from range a that satisfy predicate pred to range b, you may want to use copy(filter!(pred)(a), b).

  Example:

      int[] a = [ 1, 5, 8, 9, 10, 1, 2, 0 ];
      auto b = new int[a.length];
      auto c = copy(filter!("(a & 1) == 1")(a), b);
      assert(b[0 .. $ - c.length] == [ 1, 5, 9, 1 ]);

Tuple!(Range1, Range2) swapRanges(Range1, Range2)(Range1 r1, Range2 r2);
  Swaps all elements of r1 with successive elements in r2. Returns a tuple containing the remainder portions of r1 and r2 that were not swapped (one of them will be empty). The ranges may be of different types but must have the same element type and support swapping.

  Example:

      int[] a = [ 100, 101, 102, 103 ];
      int[] b = [ 0, 1, 2, 3 ];
      auto c = swapRanges(a[1 .. 3], b[2 .. 4]);
      assert(c[0].empty && c[1].empty);
      assert(a == [ 100, 2, 3, 103 ]);
      assert(b == [ 0, 1, 101, 102 ]);

void reverse(Range)(Range r);
void reverse(Range)(Range r);
  Reverses r in-place. Performs r.length / 2 evaluations of swap. See also STL's reverse.

  Example:

      int[] arr = [ 1, 2, 3 ];
      reverse(arr);
      assert(arr == [ 3, 2, 1 ]);

void reverse(Char)(Char[] s);
  Reverses r in-place, where r is a narrow string (having elements of type char or wchar). UTF sequences consisting of multiple code units are preserved properly.

  Example:

      char[] arr = "hello\U00010143\u0100\U00010143".dup;
      reverse(arr);
      assert(arr == "\U00010143\u0100\U00010143olleh");

size_t bringToFront(Range1, Range2)(Range1 front, Range2 back);
  The bringToFront function has considerable flexibility and usefulness. It can rotate elements in one buffer left or right, swap buffers of equal length, and even move elements across disjoint buffers of different types and different lengths.

  bringToFront takes two ranges front and back, which may be of different types. Considering the concatenation of front and back one unified range, bringToFront rotates that unified range such that all elements in back are brought to the beginning of the unified range. The relative ordering of elements in front and back, respectively, remains unchanged.

  The simplest use of bringToFront is for rotating elements in a buffer. For example:

      auto arr = [4, 5, 6, 7, 1, 2, 3];
      bringToFront(arr[0 .. 4], arr[4 .. $]);
      assert(arr == [ 1, 2, 3, 4, 5, 6, 7 ]);

  The front range may actually "step over" the back range. This is very useful with forward ranges that cannot compute comfortably right-bounded subranges like arr[0 .. 4] above. In the example below, r2 is a right subrange of r1.

      auto list = SList!(int)(4, 5, 6, 7, 1, 2, 3);
      auto r1 = list[];
      auto r2 = list[]; popFrontN(r2, 4);
      assert(equal(r2, [ 1, 2, 3 ]));
      bringToFront(r1, r2);
      assert(equal(list[], [ 1, 2, 3, 4, 5, 6, 7 ]));

  Elements can be swapped across ranges of different types:

      auto list = SList!(int)(4, 5, 6, 7);
      auto vec = [ 1, 2, 3 ];
      bringToFront(list[], vec);
      assert(equal(list[], [ 1, 2, 3, 4 ]));
      assert(equal(vec, [ 5, 6, 7 ]));

  Performs Ο(max(front.length, back.length)) evaluations of swap. See also STL's rotate.

  Preconditions:
  Either front and back are disjoint, or back is reachable from front and front is not reachable from back.

  Returns:
  The number of elements brought to the front, i.e., the length of back.

enum SwapStrategy;
  Defines the swapping strategy for algorithms that need to swap elements in a range (such as partition and sort). The strategy concerns the swapping of elements that are not the core concern of the algorithm. For example, consider an algorithm that sorts [ "abc", "b", "aBc" ] according to toUpper(a) < toUpper(b). That algorithm might choose to swap the two equivalent strings "abc" and "aBc". That does not affect the sorting since both [ "abc", "aBc", "b" ] and [ "aBc", "abc", "b" ] are valid outcomes.

  Some situations require that the algorithm must NOT ever change the relative ordering of equivalent elements (in the example above, only [ "abc", "aBc", "b" ] would be the correct result). Such algorithms are called stable. If the ordering algorithm may swap equivalent elements discretionarily, the ordering is called unstable.

  Yet another class of algorithms may choose an intermediate tradeoff by being stable only on a well-defined subrange of the range. There is no established terminology for such behavior; this library calls it semistable.

  Generally, the stable ordering strategy may be more costly in time and/or space than the other two because it imposes additional constraints. Similarly, semistable may be costlier than unstable. As (semi-)stability is not needed very often, the ordering algorithms in this module parameterized by SwapStrategy all choose SwapStrategy.unstable as the default.

  unstable
    Allows freely swapping of elements as long as the output satisfies the algorithm's requirements.

  semistable
    In algorithms partitioning ranges in two, preserve relative ordering of elements only to the left of the partition point.

  stable
    Preserve the relative ordering of elements to the largest extent allowed by the algorithm's requirements.

Range remove(SwapStrategy s = SwapStrategy.stable, Range, Offset...)(Range range, Offset offset);
  Eliminates elements at given offsets from range and returns the shortened range. In the simplest call, one element is removed.

      int[] a = [ 3, 5, 7, 8 ];
      assert(remove(a, 1) == [ 3, 7, 8 ]);
      assert(a == [ 3, 7, 8, 8 ]);

  In the case above the element at offset 1 is removed and remove returns the range smaller by one element. The original array has remained of the same length because all functions in std.algorithm only change content, not topology. The value 8 is repeated because std.algorithm.move was invoked to move elements around and on integers move simply copies the source to the destination. To replace a with the effect of the removal, simply assign a = remove(a, 1). The slice will be rebound to the shorter array and the operation completes with maximal efficiency.

  Multiple indices can be passed into remove. In that case, elements at the respective indices are all removed. The indices must be passed in increasing order, otherwise an exception occurs.

      int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
      assert(remove(a, 1, 3, 5) ==
          [ 0, 2, 4, 6, 7, 8, 9, 10 ]);

  (Note how all indices refer to slots in the original array, not in the array as it is being progressively shortened.) Finally, any combination of integral offsets and tuples composed of two integral offsets can be passed in.

      int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
      assert(remove(a, 1, tuple(3, 5), 9) == [ 0, 2, 6, 7, 8, 10 ]);

  In this case, the slots at positions 1, 3, 4, and 9 are removed from the array. The tuple passes in a range closed to the left and open to the right (consistent with built-in slices), e.g. tuple(3, 5) means indices 3 and 4 but not 5.

  If the need is to remove some elements in the range but the order of the remaining elements does not have to be preserved, you may want to pass SwapStrategy.unstable to remove.

      int[] a = [ 0, 1, 2, 3 ];
      assert(remove!(SwapStrategy.unstable)(a, 1) == [ 0, 3, 2 ]);

  In the case above, the element at slot 1 is removed, but replaced with the last element of the range. Taking advantage of the relaxation of the stability requirement, remove moved elements from the end of the array over the slots to be removed. This way there is less data movement to be done which improves the execution time of the function.

  The function remove works on any forward range. The moving strategy is (listed from fastest to slowest):
  - If s == SwapStrategy.unstable && isRandomAccessRange!Range && hasLength!Range, then elements are moved from the end of the range into the slots to be filled. In this case, the absolute minimum of moves is performed.
  - Otherwise, if s == SwapStrategy.unstable && isBidirectionalRange!Range && hasLength!Range, then elements are still moved from the end of the range, but time is spent on advancing between slots by repeated calls to range.popFront.
  - Otherwise, elements are moved incrementally towards the front of range; a given element is never moved several times, but more elements are moved than in the previous cases.

Range remove(alias pred, SwapStrategy s = SwapStrategy.stable, Range)(Range range);
  Reduces the length of the bidirectional range range by removing elements that satisfy pred. If s = SwapStrategy.unstable, elements are moved from the right end of the range over the elements to eliminate. If s = SwapStrategy.stable (the default), elements are moved progressively to front such that their relative order is preserved. Returns the filtered range.

  Example:

      int[] a = [ 1, 2, 3, 2, 3, 4, 5, 2, 5, 6 ];
      assert(remove!("a == 2")(a) == [ 1, 3, 3, 4, 5, 5, 6 ]);

Range partition(alias predicate, SwapStrategy ss = SwapStrategy.unstable, Range)(Range r);
  Partitions a range in two using pred as a predicate. Specifically, reorders the range r = [left, right) using swap such that all elements i for which pred(i) is true come before all elements j for which pred(j) returns false.

  Performs Ο(r.length) (if unstable or semistable) or Ο(r.length * log(r.length)) (if stable) evaluations of less and swap. The unstable version computes the minimum possible evaluations of swap (roughly half of those performed by the semistable version).

  See also STL's partition and stable_partition.

  Returns:
  The right part of r after partitioning.

  If ss == SwapStrategy.stable, partition preserves the relative ordering of all elements a, b in r for which pred(a) == pred(b). If ss == SwapStrategy.semistable, partition preserves the relative ordering of all elements a, b in the left part of r for which pred(a) == pred(b).

  Example:

      auto Arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
      auto arr = Arr.dup;
      static bool even(int a) { return (a & 1) == 0; }
      // Partition arr such that even numbers come first
      auto r = partition!(even)(arr);
      // Now arr is separated in evens and odds.
      // Numbers may have become shuffled due to instability
      assert(r == arr[5 .. $]);
      assert(count!(even)(arr[0 .. 5]) == 5);
      assert(find!(even)(r).empty);

      // Can also specify the predicate as a string.
      // Use 'a' as the predicate argument name
      arr[] = Arr[];
      r = partition!(q{(a & 1) == 0})(arr);
      assert(r == arr[5 .. $]);

      // Now for a stable partition:
      arr[] = Arr[];
      r = partition!(q{(a & 1) == 0}, SwapStrategy.stable)(arr);
      // Now arr is [2 4 6 8 10 1 3 5 7 9], and r points to 1
      assert(arr == [2, 4, 6, 8, 10, 1, 3, 5, 7, 9] && r == arr[5 .. $]);

      // In case the predicate needs to hold its own state, use a delegate:
      arr[] = Arr[];
      int x = 3;
      // Put stuff greater than 3 on the left
      bool fun(int a) { return a > x; }
      r = partition!(fun, SwapStrategy.semistable)(arr);
      // Now arr is [4 5 6 7 8 9 10 2 3 1] and r points to 2
      assert(arr == [4, 5, 6, 7, 8, 9, 10, 2, 3, 1] && r == arr[7 .. $]);

bool isPartitioned(alias pred, Range)(Range r);
  Returns true if r is partitioned according to predicate pred.

  Example:

      int[] r = [ 1, 3, 5, 7, 8, 2, 4, ];
      assert(isPartitioned!("a & 1")(r));

auto partition3(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range, E)(Range r, E pivot);
  Rearranges elements in r in three adjacent ranges and returns them. The first and leftmost range only contains elements in r less than pivot. The second and middle range only contains elements in r that are equal to pivot. Finally, the third and rightmost range only contains elements in r that are greater than pivot. The less-than test is defined by the binary function less.

  Example:

      auto a = [ 8, 3, 4, 1, 4, 7, 4 ];
      auto pieces = partition3(a, 4);
      assert(a == [ 1, 3, 4, 4, 4, 7, 8 ]);
      assert(pieces[0] == [ 1, 3 ]);
      assert(pieces[1] == [ 4, 4, 4 ]);
      assert(pieces[2] == [ 7, 8 ]);

  BUGS:
  stable partition3 has not been implemented yet.

void topN(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range)(Range r, size_t nth);
  Reorders the range r using swap such that r[nth] refers to the element that would fall there if the range were fully sorted. In addition, it also partitions r such that all elements e1 from r[0] to r[nth] satisfy !less(r[nth], e1), and all elements e2 from r[nth] to r[r.length] satisfy !less(e2, r[nth]). Effectively, it finds the nth smallest (according to less) elements in r. Performs an expected Ο(r.length) (if unstable) or Ο(r.length * log(r.length)) (if stable) evaluations of less and swap. See also STL's nth_element.

  If n >= r.length, the algorithm has no effect.

  Examples:

      int[] v = [ 25, 7, 9, 2, 0, 5, 21 ];
      auto n = 4;
      topN!(less)(v, n);
      assert(v[n] == 9);
      // Equivalent form:
      topN!("a < b")(v, n);
      assert(v[n] == 9);

  BUGS:
  Stable topN has not been implemented yet.

void topN(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range1, Range2)(Range1 r1, Range2 r2);
  Stores the smallest elements of the two ranges in the left-hand range.

  Examples:
  Ditto

      int[] a = [ 5, 7, 2, 6, 7 ];
      int[] b = [ 2, 1, 5, 6, 7, 3, 0 ];
      topN(a, b);
      sort(a);
      assert(a == [0, 1, 2, 2, 3]);

SortedRange!(Range, less) sort(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range)(Range r);
  Sorts a random-access range according to the predicate less. Performs Ο(r.length * log(r.length)) (if unstable) or Ο(r.length * log(r.length) * log(r.length)) (if stable) evaluations of less and swap. See also STL's sort and stable_sort.

  sort returns a std.range.SortedRange over the original range, which functions that can take advantage of sorted data can then use to know that the range is sorted and adjust accordingly. The std.range.SortedRange is a wrapper around the original range, so both it and the original range are sorted, but other functions won't know that the original range has been sorted, whereas they can know that std.range.SortedRange has been sorted.

  See Also:
  std.range.assumeSorted

  Remark:
  Stable sort is implementated as Timsort, the original code at XSort by Xinok, public domain.

  Example:

      int[] array = [ 1, 2, 3, 4 ];
      // sort in descending order
      sort!("a > b")(array);
      assert(array == [ 4, 3, 2, 1 ]);
      // sort in ascending order
      sort(array);
      assert(array == [ 1, 2, 3, 4 ]);
      // sort with a delegate
      bool myComp(int x, int y) { return x > y; }
      sort!(myComp)(array);
      assert(array == [ 4, 3, 2, 1 ]);
      // Showcase stable sorting
      string[] words = [ "aBc", "a", "abc", "b", "ABC", "c" ];
      sort!("toUpper(a) < toUpper(b)", SwapStrategy.stable)(words);
      assert(words == [ "a", "aBc", "abc", "ABC", "b", "c" ]);

template multiSort(less...)
  void multiSort(Range)(Range r) if (validPredicates!(ElementType!Range, less));

  Sorts a range by multiple keys. The call multiSort!("a.id < b.id", "a.date > b.date")(r) sorts the range r by id ascending, and sorts elements that have the same id by date descending. Such a call is equivalent to sort!"a.id != b.id ? a.id < b.id : a.date > b.date"(r), but multiSort is faster because it does fewer comparisons (in addition to being more convenient).

  Example:

      static struct Point { int x, y; }
      auto pts1 = [ Point(0, 0), Point(5, 5), Point(0, 1), Point(0, 2) ];
      auto pts2 = [ Point(0, 0), Point(0, 1), Point(0, 2), Point(5, 5) ];
      multiSort!("a.x < b.x", "a.y < b.y", SwapStrategy.unstable)(pts1);
      assert(pts1 == pts2);

SortedRange!(R, (a, b) => binaryFun!(less)(unaryFun!(transform)(a), unaryFun!(transform)(b))) schwartzSort(alias transform, alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, R)(R r);
  Sorts a range using an algorithm akin to the Schwartzian transform, also known as the decorate-sort-undecorate pattern in Python and Lisp. (Not to be confused with the other Schwartz.) This function is helpful when the sort comparison includes an expensive computation. The complexity is the same as that of the corresponding sort, but schwartzSort evaluates transform only r.length times (less than half when compared to regular sorting). The usage can be best illustrated with an example.

  Examples:

      uint hashFun(string) { ... expensive computation ... }
      string[] array = ...;
      // Sort strings by hash, slow
      sort!((a, b) => hashFun(a) < hashFun(b))(array);
      // Sort strings by hash, fast (only computes arr.length hashes):
      schwartzSort!(hashFun, "a < b")(array);

  The schwartzSort function might require less temporary data and be faster than the Perl idiom or the decorate-sort-undecorate idiom present in Python and Lisp. This is because sorting is done in-place and only minimal extra data (one array of transformed elements) is created.

  To check whether an array was sorted and benefit of the speedup of Schwartz sorting, a function schwartzIsSorted is not provided because the effect can be achieved by calling isSorted!less(map!transform(r)).

  Returns:
  The initial range wrapped as a SortedRange with the predicate (a, b) => binaryFun!less(transform(a), transform(b)).

void partialSort(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range)(Range r, size_t n);
  Reorders the random-access range r such that the range r[0 .. mid] is the same as if the entire r were sorted, and leaves the range r[mid .. r.length] in no particular order. Performs Ο(r.length * log(mid)) evaluations of pred. The implementation simply calls topN!(less, ss)(r, n) and then sort!(less, ss)(r[0 .. n]).

  Example:

      int[] a = [ 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 ];
      partialSort(a, 5);
      assert(a[0 .. 5] == [ 0, 1, 2, 3, 4 ]);

void completeSort(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range1, Range2)(SortedRange!(Range1, less) lhs, Range2 rhs);
  Sorts the random-access range chain(lhs, rhs) according to predicate less. The left-hand side of the range lhs is assumed to be already sorted; rhs is assumed to be unsorted. The exact strategy chosen depends on the relative sizes of lhs and rhs. Performs Ο(lhs.length + rhs.length * log(rhs.length)) (best case) to Ο((lhs.length + rhs.length) * log(lhs.length + rhs.length)) (worst-case) evaluations of swap.

  Example:

      int[] a = [ 1, 2, 3 ];
      int[] b = [ 4, 0, 6, 5 ];
      completeSort(assumeSorted(a), b);
      assert(a == [ 0, 1, 2 ]);
      assert(b == [ 3, 4, 5, 6 ]);

bool isSorted(alias less = "a < b", Range)(Range r);
  Checks whether a forward range is sorted according to the comparison operation less. Performs Ο(r.length) evaluations of less.

  Example:

      int[] arr = [4, 3, 2, 1];
      assert(!isSorted(arr));
      sort(arr);
      assert(isSorted(arr));
      sort!("a > b")(arr);
      assert(isSorted!("a > b")(arr));

SortedRange!(RangeIndex, (a, b) => binaryFun!(less)(*a, *b)) makeIndex(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range, RangeIndex)(Range r, RangeIndex index);
void makeIndex(alias less = "a < b", SwapStrategy ss = SwapStrategy.unstable, Range, RangeIndex)(Range r, RangeIndex index);
  Computes an index for r based on the comparison less. The index is a sorted array of pointers or indices into the original range. This technique is similar to sorting, but it is more flexible because (1) it allows "sorting" of immutable collections, (2) allows binary search even if the original collection does not offer random access, (3) allows multiple indexes, each on a different predicate, and (4) may be faster when dealing with large objects. However, using an index may also be slower under certain circumstances due to the extra indirection, and is always larger than a sorting-based solution because it needs space for the index in addition to the original collection. The complexity is the same as sort's.

  The first overload of makeIndex writes to a range containing pointers, and the second writes to a range containing offsets. The first overload requires Range to be a forward range, and the latter requires it to be a random-access range.

  makeIndex overwrites its second argument with the result, but never reallocates it.

  Returns:
  The pointer-based version returns a SortedRange wrapper over index, of type SortedRange!(RangeIndex, (a, b) => binaryFun!less(*a, *b)) thus reflecting the ordering of the index. The index-based version returns void because the ordering relation involves not only index but also r.

  Throws:
  If the second argument's length is less than that of the range indexed, an exception is thrown.

  Example:

      immutable(int[]) arr = [ 2, 3, 1, 5, 0 ];
      // index using pointers
      auto index1 = new immutable(int)*[arr.length];
      makeIndex!("a < b")(arr, index1);
      assert(isSorted!("*a < *b")(index1));
      // index using offsets
      auto index2 = new size_t[arr.length];
      makeIndex!("a < b")(arr, index2);
      assert(isSorted!
          ((size_t a, size_t b){ return arr[a] < arr[b];})
          (index2));

enum SortOutput;
  Specifies whether the output of certain algorithm is desired in sorted format.

  no
    Don't sort output

  yes
    Sort output

bool canFind(alias pred = "a == b", R, E)(R haystack, E needle);
  Returns true if and only if value can be found in range. Performs Ο(needle.length) evaluations of pred.

size_t canFind(alias pred = "a == b", Range, Ranges...)(Range haystack, Ranges needles);
  Returns the 1-based index of the first needle found in haystack. If no needle is found, then 0 is returned.

  So, if used directly in the condition of an if statement or loop, the result will be true if one of the needles is found and false if none are found, whereas if the result is used elsewhere, it can either be cast to bool for the same effect or used to get which needle was found first without having to deal with the tuple that LREF find returns for the same operation.

bool any(alias pred, Range)(Range range);
  Returns true if and only if a value v satisfying the predicate pred can be found in the forward range range. Performs Ο(r.length) evaluations of pred.

bool all(alias pred, R)(R range);
  Returns true if and only if all values in range satisfy the predicate pred. Performs Ο(r.length) evaluations of pred.

  Examples:

      assert(all!"a & 1"([1, 3, 5, 7, 9]));
      assert(!all!"a & 1"([1, 2, 3, 5, 7, 9]));

TRange topNCopy(alias less = "a < b", SRange, TRange)(SRange source, TRange target, SortOutput sorted = SortOutput.no);
  Copies the top n elements of the input range source into the random-access range target, where n = target.length. Elements of source are not touched. If sorted is true, the target is sorted. Otherwise, the target respects the heap property.

  Example:

      int[] a = [ 10, 16, 2, 3, 1, 5, 0 ];
      int[] b = new int[3];
      topNCopy(a, b, true);
      assert(b == [ 0, 1, 2 ]);

struct SetUnion(alias less = "a < b", Rs...) if (allSatisfy!(isInputRange, Rs));
SetUnion!(less, Rs) setUnion(alias less = "a < b", Rs...)(Rs rs);
  Lazily computes the union of two or more ranges rs. The ranges are assumed to be sorted by less. Elements in the output are not unique; the length of the output is the sum of the lengths of the inputs. (The length member is offered if all ranges also have length.) The element types of all ranges must have a common type.

  Example:

      int[] a = [ 1, 2, 4, 5, 7, 9 ];
      int[] b = [ 0, 1, 2, 4, 7, 8 ];
      int[] c = [ 10 ];
      assert(setUnion(a, b).length == a.length + b.length);
      assert(equal(setUnion(a, b), [0, 1, 1, 2, 2, 4, 4, 5, 7, 7, 8, 9][]));
      assert(equal(setUnion(a, c, b),
          [0, 1, 1, 2, 2, 4, 4, 5, 7, 7, 8, 9, 10][]));

struct SetIntersection(alias less = "a < b", Rs...) if (allSatisfy!(isInputRange, Rs));
SetIntersection!(less, Rs) setIntersection(alias less = "a < b", Rs...)(Rs ranges);
  Lazily computes the intersection of two or more input ranges rs. The ranges are assumed to be sorted by less. The element types of all ranges must have a common type.

  Example:

      int[] a = [ 1, 2, 4, 5, 7, 9 ];
      int[] b = [ 0, 1, 2, 4, 7, 8 ];
      int[] c = [ 0, 1, 4, 5, 7, 8 ];
      assert(equal(setIntersection(a, a), a));
      assert(equal(setIntersection(a, b), [1, 2, 4, 7][]));
      assert(equal(setIntersection(a, b, c), [1, 4, 7][]));

struct SetDifference(alias less = "a < b", R1, R2) if (isInputRange!(R1) && isInputRange!(R2));
SetDifference!(less, R1, R2) setDifference(alias less = "a < b", R1, R2)(R1 r1, R2 r2);
  Lazily computes the difference of r1 and r2. The two ranges are assumed to be sorted by less. The element types of the two ranges must have a common type.

  Example:

      int[] a = [ 1, 2, 4, 5, 7, 9 ];
      int[] b = [ 0, 1, 2, 4, 7, 8 ];
      assert(equal(setDifference(a, b), [5, 9][]));

struct SetSymmetricDifference(alias less = "a < b", R1, R2) if (isInputRange!(R1) && isInputRange!(R2));
SetSymmetricDifference!(less, R1, R2) setSymmetricDifference(alias less = "a < b", R1, R2)(R1 r1, R2 r2);
  Lazily computes the symmetric difference of r1 and r2, i.e. the elements that are present in exactly one of r1 and r2. The two ranges are assumed to be sorted by less, and the output is also sorted by less. The element types of the two ranges must have a common type.

  Example:

      int[] a = [ 1, 2, 4, 5, 7, 9 ];
      int[] b = [ 0, 1, 2, 4, 7, 8 ];
      assert(equal(setSymmetricDifference(a, b), [0, 5, 8, 9][]));

struct NWayUnion(alias less, RangeOfRanges);
NWayUnion!(less, RangeOfRanges) nWayUnion(alias less = "a < b", RangeOfRanges)(RangeOfRanges ror);
  Computes the union of multiple sets. The input sets are passed as a range of ranges and each is assumed to be sorted by less. Computation is done lazily, one union element at a time. The complexity of one popFront operation is Ο(log(ror.length)). However, the length of ror decreases as ranges in it are exhausted, so the complexity of a full pass through NWayUnion is dependent on the distribution of the lengths of ranges contained within ror. If all ranges have the same length n (worst case scenario), the complexity of a full pass through NWayUnion is Ο(n * ror.length * log(ror.length)), i.e., log(ror.length) times worse than just spanning all ranges in turn. The output comes sorted (unstably) by less.

  Warning:
  Because NWayUnion does not allocate extra memory, it will leave ror modified. Namely, NWayUnion assumes ownership of ror and discretionarily swaps and advances elements of it. If you want ror to preserve its contents after the call, you may want to pass a duplicate to NWayUnion (and perhaps cache the duplicate in between calls).

  Example:

      double[][] a =
      [
          [ 1, 4, 7, 8 ],
          [ 1, 7 ],
          [ 1, 7, 8],
          [ 4 ],
          [ 7 ],
      ];
      auto witness = [
          1, 1, 1, 4, 4, 7, 7, 7, 7, 8, 8
      ];
      assert(equal(nWayUnion(a), witness[]));

void largestPartialIntersection(alias less = "a < b", RangeOfRanges, Range)(RangeOfRanges ror, Range tgt, SortOutput sorted = SortOutput.no);
  Given a range of sorted forward ranges ror, copies to tgt the elements that are common to most ranges, along with their number of occurrences. All ranges in ror are assumed to be sorted by less. Only the most frequent tgt.length elements are returned.

  Example:

      // Figure which number can be found in most arrays of the set of
      // arrays below.
      double[][] a =
      [
          [ 1, 4, 7, 8 ],
          [ 1, 7 ],
          [ 1, 7, 8],
          [ 4 ],
          [ 7 ],
      ];
      auto b = new Tuple!(double, uint)[1];
      largestPartialIntersection(a, b);
      // First member is the item, second is the occurrence count
      assert(b[0] == tuple(7.0, 4u));

  7.0 is the correct answer because it occurs in 4 out of the 5 inputs, more than any other number. The second member of the resulting tuple is indeed 4 (recording the number of occurrences of 7.0). If more of the top-frequent numbers are needed, just create a larger tgt range. In the axample above, creating b with length 2 yields tuple(1.0, 3u) in the second position.

  The function largestPartialIntersection is useful for e.g. searching an inverted index for the documents most likely to contain some terms of interest. The complexity of the search is Ο(n * log(tgt.length)), where n is the sum of lengths of all input ranges. This approach is faster than keeping an associative array of the occurrences and then selecting its top items, and also requires less memory (largestPartialIntersection builds its result directly in tgt and requires no extra memory).

  Warning:
  Because largestPartialIntersection does not allocate extra memory, it will leave ror modified. Namely, largestPartialIntersection assumes ownership of ror and discretionarily swaps and advances elements of it. If you want ror to preserve its contents after the call, you may want to pass a duplicate to largestPartialIntersection (and perhaps cache the duplicate in between calls).

void largestPartialIntersectionWeighted(alias less = "a < b", RangeOfRanges, Range, WeightsAA)(RangeOfRanges ror, Range tgt, WeightsAA weights, SortOutput sorted = SortOutput.no);
  Similar to largestPartialIntersection, but associates a weight with each distinct element in the intersection.

  Example:

      // Figure which number can be found in most arrays of the set of
      // arrays below, with specific per-element weights
      double[][] a =
      [
          [ 1, 4, 7, 8 ],
          [ 1, 7 ],
          [ 1, 7, 8],
          [ 4 ],
          [ 7 ],
      ];
      auto b = new Tuple!(double, uint)[1];
      double[double] weights = [ 1:1.2, 4:2.3, 7:1.1, 8:1.1 ];
      largestPartialIntersectionWeighted(a, b, weights);
      // First member is the item, second is the occurrence count
      assert(b[0] == tuple(4.0, 2u));

  The correct answer in this case is 4.0, which, although only appears two times, has a total weight 4.6 (three times its weight 2.3). The value 7 is weighted with 1.1 and occurs four times for a total weight 4.4.

bool nextPermutation(alias less = "a<b", BidirectionalRange)(ref BidirectionalRange range);
  Permutes range in-place to the next lexicographically greater permutation.

  The predicate less defines the lexicographical ordering to be used on the range.

  If the range is currently the lexicographically greatest permutation, it is permuted back to the least permutation and false is returned. Otherwise, true is returned. One can thus generate all permutations of a range by sorting it according to less, which produces the lexicographically least permutation, and then calling nextPermutation until it returns false. This is guaranteed to generate all distinct permutations of the range exactly once. If there are N elements in the range and all of them are unique, then N! permutations will be generated. Otherwise, if there are some duplicated elements, fewer permutations will be produced.

      // Enumerate all permutations
      int[] a = [1,2,3,4,5];
      while (nextPermutation(a))
      {
          // a now contains the next permutation of the array.
      }

  Returns:
  false if the range was lexicographically the greatest, in which case the range is reversed back to the lexicographically smallest permutation; otherwise returns true.

  Example:

      // Step through all permutations of a sorted array in lexicographic order
      int[] a = [1,2,3];
      assert(nextPermutation(a) == true);
      assert(a == [1,3,2]);
      assert(nextPermutation(a) == true);
      assert(a == [2,1,3]);
      assert(nextPermutation(a) == true);
      assert(a == [2,3,1]);
      assert(nextPermutation(a) == true);
      assert(a == [3,1,2]);
      assert(nextPermutation(a) == true);
      assert(a == [3,2,1]);
      assert(nextPermutation(a) == false);
      assert(a == [1,2,3]);

      // Step through permutations of an array containing duplicate elements:
      int[] a = [1,1,2];
      assert(nextPermutation(a) == true);
      assert(a == [1,2,1]);
      assert(nextPermutation(a) == true);
      assert(a == [2,1,1]);
      assert(nextPermutation(a) == false);
      assert(a == [1,1,2]);

bool nextEvenPermutation(alias less = "a<b", BidirectionalRange)(ref BidirectionalRange range);
  Permutes range in-place to the next lexicographically greater even permutation.

  The predicate less defines the lexicographical ordering to be used on the range.

  An even permutation is one which is produced by swapping an even number of pairs of elements in the original range. The set of even permutations is distinct from the set of all permutations only when there are no duplicate elements in the range. If the range has N unique elements, then there are exactly N!/2 even permutations.

  If the range is already the lexicographically greatest even permutation, it is permuted back to the least even permutation and false is returned. Otherwise, true is returned, and the range is modified in-place to be the lexicographically next even permutation.

  One can thus generate the even permutations of a range with unique elements by starting with the lexicographically smallest permutation, and repeatedly calling nextEvenPermutation until it returns false.

      // Enumerate even permutations
      int[] a = [1,2,3,4,5];
      while (nextEvenPermutation(a))
      {
          // a now contains the next even permutation of the array.
      }

  One can also generate the odd permutations of a range by noting that permutations obey the rule that even + even = even, and odd + even = odd. Thus, by swapping the last two elements of a lexicographically least range, it is turned into the first odd permutation. Then calling nextEvenPermutation on this first odd permutation will generate the next even permutation relative to this odd permutation, which is actually the next odd permutation of the original range. Thus, by repeatedly calling nextEvenPermutation until it returns false, one enumerates the odd permutations of the original range.

      // Enumerate odd permutations
      int[] a = [1,2,3,4,5];
      swap(a[$-2], a[$-1]);    // a is now the first odd permutation of [1,2,3,4,5]
      while (nextEvenPermutation(a))
      {
          // a now contains the next odd permutation of the original array
          // (which is an even permutation of the first odd permutation).
      }

  Warning:
  Since even permutations are only distinct from all permutations when the range elements are unique, this function assumes that there are no duplicate elements under the specified ordering. If this is not true, some permutations may fail to be generated. When the range has non-unique elements, you should use nextPermutation instead.

  Returns:
  false if the range was lexicographically the greatest, in which case the range is reversed back to the lexicographically smallest permutation; otherwise returns true.

  Examples:

      // Step through even permutations of a sorted array in lexicographic order
      int[] a = [1,2,3];
      assert(nextEvenPermutation(a) == true);
      assert(a == [2,3,1]);
      assert(nextEvenPermutation(a) == true);
      assert(a == [3,1,2]);
      assert(nextEvenPermutation(a) == false);
      assert(a == [1,2,3]);

  Even permutations are useful for generating coordinates of certain geometric shapes. Here's a non-trivial example:

      // Print the 60 vertices of a uniform truncated icosahedron (soccer ball)
      import std.math, std.stdio;
      enum real Phi = (1.0 + sqrt(5.0)) / 2.0;    // Golden ratio
      real[][] seeds = [
          [0.0, 1.0, 3.0*Phi],
          [1.0, 2.0+Phi, 2.0*Phi],
          [Phi, 2.0, Phi^^3]
      ];
      foreach (seed; seeds)
      {
          // Loop over even permutations of each seed
          do
          {
              // Loop over all sign changes of each permutation
              size_t i;
              do
              {
                  // Generate all possible sign changes
                  for (i=0; i < seed.length; i++)
                  {
                      if (seed[i] != 0.0)
                      {
                          seed[i] = -seed[i];
                          if (seed[i] < 0.0)
                              break;
                      }
                  }
                  writeln(seed);
              } while (i < seed.length);
          } while (nextEvenPermutation(seed));
      }

auto cartesianProduct(R1, R2)(R1 range1, R2 range2);
auto cartesianProduct(R1, R2, RR...)(R1 range1, R2 range2, RR otherRanges);
  Lazily computes the Cartesian product of two or more ranges. The product is a range of tuples of elements from each respective range.

  The conditions for the two-range case are as follows:

  If both ranges are finite, then one must be (at least) a forward range and the other an input range.

  If one range is infinite and the other finite, then the finite range must be a forward range, and the infinite range can be an input range.

  If both ranges are infinite, then both must be forward ranges.

  When there are more than two ranges, the above conditions apply to each adjacent pair of ranges.

  Examples:

      auto N = sequence!"n"(0);         // the range of natural numbers
      auto N2 = cartesianProduct(N, N); // the range of all pairs of natural numbers

      // Various arbitrary number pairs can be found in the range in finite time.
      assert(canFind(N2, tuple(0, 0)));
      assert(canFind(N2, tuple(123, 321)));
      assert(canFind(N2, tuple(11, 35)));
      assert(canFind(N2, tuple(279, 172)));

      auto B = [ 1, 2, 3 ];
      auto C = [ 4, 5, 6 ];
      auto BC = cartesianProduct(B, C);

      foreach (n; [[1, 4], [2, 4], [3, 4], [1, 5], [2, 5], [3, 5], [1, 6],
                   [2, 6], [3, 6]])
      {
          assert(canFind(BC, tuple(n[0], n[1])));
      }

      auto A = [ 1, 2, 3 ];
      auto B = [ 'a', 'b', 'c' ];
      auto C = [ "x", "y", "z" ];
      auto ABC = cartesianProduct(A, B, C);

      assert(ABC.equal([
          tuple(1, 'a', "x"), tuple(2, 'a', "x"), tuple(3, 'a', "x"),
          tuple(1, 'b', "x"), tuple(2, 'b', "x"), tuple(3, 'b', "x"),
          tuple(1, 'c', "x"), tuple(2, 'c', "x"), tuple(3, 'c', "x"),
          tuple(1, 'a', "y"), tuple(2, 'a', "y"), tuple(3, 'a', "y"),
          tuple(1, 'b', "y"), tuple(2, 'b', "y"), tuple(3, 'b', "y"),
          tuple(1, 'c', "y"), tuple(2, 'c', "y"), tuple(3, 'c', "y"),
          tuple(1, 'a', "z"), tuple(2, 'a', "z"), tuple(3, 'a', "z"),
          tuple(1, 'b', "z"), tuple(2, 'b', "z"), tuple(3, 'b', "z"),
          tuple(1, 'c', "z"), tuple(2, 'c', "z"), tuple(3, 'c', "z")
      ]));

Andrei Alexandrescu 2008-. | Page generated by Ddoc.