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Function std.algorithm.setops.cartesianProduct

Lazily computes the Cartesian product of two or more ranges. The product is a range of tuples of elements from each respective range.

auto cartesianProduct(R1, R2) (
  R1 range1,
  R2 range2
)
if (!allSatisfy!(isForwardRange, R1, R2) || anySatisfy!(isInfinite, R1, R2));

auto cartesianProduct(RR...) (
  RR ranges
)
if (ranges.length >= 2 && allSatisfy!(isForwardRange, RR) && !anySatisfy!(isInfinite, RR));

auto cartesianProduct(R1, R2, RR...) (
  R1 range1,
  R2 range2,
  RR otherRanges
)
if (!allSatisfy!(isForwardRange, R1, R2, RR) || anySatisfy!(isInfinite, R1, R2, RR));

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.

Parameters

NameDescription
range1 The first range
range2 The second range
ranges Two or more non-infinite forward ranges
otherRanges Zero or more non-infinite forward ranges

Returns

A forward range of Tuple representing elements of the cartesian product of the given ranges.

Example

import std.algorithm.searching : canFind;
import std.range;
import std.typecons : tuple;

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)));

Example

import std.algorithm.searching : canFind;
import std.typecons : tuple;

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])));
}

Example

import std.algorithm.comparison : equal;
import std.typecons : tuple;

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(1, 'a', "y"), tuple(1, 'a', "z"),
    tuple(1, 'b', "x"), tuple(1, 'b', "y"), tuple(1, 'b', "z"),
    tuple(1, 'c', "x"), tuple(1, 'c', "y"), tuple(1, 'c', "z"),
    tuple(2, 'a', "x"), tuple(2, 'a', "y"), tuple(2, 'a', "z"),
    tuple(2, 'b', "x"), tuple(2, 'b', "y"), tuple(2, 'b', "z"),
    tuple(2, 'c', "x"), tuple(2, 'c', "y"), tuple(2, 'c', "z"),
    tuple(3, 'a', "x"), tuple(3, 'a', "y"), tuple(3, 'a', "z"),
    tuple(3, 'b', "x"), tuple(3, 'b', "y"), tuple(3, 'b', "z"),
    tuple(3, 'c', "x"), tuple(3, 'c', "y"), tuple(3, 'c', "z")
]));

Authors

Andrei Alexandrescu

License

Boost License 1.0.