diff --git a/core/math/big/combinatorics.odin b/core/math/big/combinatorics.odin new file mode 100644 index 000000000..87c76d830 --- /dev/null +++ b/core/math/big/combinatorics.odin @@ -0,0 +1,60 @@ +package math_big + +/* + With `n` items, calculate how many ways that `r` of them can be ordered. +*/ +permutations_with_repetition :: int_pow_int + +/* + With `n` items, calculate how many ways that `r` of them can be ordered without any repeats. +*/ +permutations_without_repetition :: proc(dest: ^Int, n, r: int) -> (error: Error) { + if n == r { + return factorial(dest, n) + } + + tmp := &Int{} + defer internal_destroy(tmp) + + // n! + // -------- + // (n - r)! + factorial(dest, n) or_return + factorial(tmp, n - r) or_return + div(dest, dest, tmp) or_return + + return +} + +/* + With `n` items, calculate how many ways that `r` of them can be chosen. + + Also known as the multiset coefficient or (n multichoose k). +*/ +combinations_with_repetition :: proc(dest: ^Int, n, r: int) -> (error: Error) { + // (n + r - 1)! + // ------------ + // r! (n - 1)! + return combinations_without_repetition(dest, n + r - 1, r) +} + +/* + With `n` items, calculate how many ways that `r` of them can be chosen without any repeats. + + Also known as the binomial coefficient or (n choose k). +*/ +combinations_without_repetition :: proc(dest: ^Int, n, r: int) -> (error: Error) { + tmp_a, tmp_b := &Int{}, &Int{} + defer internal_destroy(tmp_a, tmp_b) + + // n! + // ------------ + // r! (n - r)! + factorial(dest, n) or_return + factorial(tmp_a, r) or_return + factorial(tmp_b, n - r) or_return + mul(tmp_a, tmp_a, tmp_b) or_return + div(dest, dest, tmp_a) or_return + + return +}