Auto merge of #270 - vks:binomial, r=cuviper
Implement binomial The implementation avoids overflows and fractions.
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commit
2adf018aa6
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@ -665,6 +665,35 @@ impl_integer_for_usize!(u32, test_integer_u32);
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impl_integer_for_usize!(u64, test_integer_u64);
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impl_integer_for_usize!(usize, test_integer_usize);
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/// Calculate r * a / b, avoiding overflows and fractions.
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fn multiply_and_divide<T: Integer + Clone>(r: T, a: T, b: T) -> T {
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// See http://blog.plover.com/math/choose-2.html for the idea.
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let g = gcd(r.clone(), b.clone());
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(r/g.clone() * a) / (b/g)
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}
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/// Calculate the binomial coefficient.
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pub fn binomial<T: Integer + Clone>(mut n: T, k: T) -> T {
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// See http://blog.plover.com/math/choose.html for the idea.
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if k > n {
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return T::zero();
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}
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if k > n.clone() - k.clone() {
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return binomial(n.clone(), n - k);
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}
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let mut r = T::one();
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let mut d = T::one();
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loop {
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if d > k {
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break;
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}
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r = multiply_and_divide(r, n.clone(), d.clone());
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n = n - T::one();
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d = d + T::one();
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}
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r
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}
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#[test]
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fn test_lcm_overflow() {
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macro_rules! check {
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@ -692,3 +721,59 @@ fn test_lcm_overflow() {
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check!(i64, 0x4000_0000_0000_0000, 0x04, 0x4000_0000_0000_0000);
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check!(u64, 0x8000_0000_0000_0000, 0x02, 0x8000_0000_0000_0000);
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}
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#[test]
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fn test_binomial() {
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macro_rules! check {
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($t:ty, $x:expr, $y:expr, $r:expr) => { {
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let x: $t = $x;
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let y: $t = $y;
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let expected: $t = $r;
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assert_eq!(binomial(x, y), expected);
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if y <= x {
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assert_eq!(binomial(x, x - y), expected);
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}
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} }
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}
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check!(u8, 9, 4, 126);
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check!(u8, 0, 0, 1);
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check!(u8, 2, 3, 0);
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check!(i8, 9, 4, 126);
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check!(i8, 0, 0, 1);
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check!(i8, 2, 3, 0);
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check!(u16, 100, 2, 4950);
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check!(u16, 14, 4, 1001);
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check!(u16, 0, 0, 1);
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check!(u16, 2, 3, 0);
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check!(i16, 100, 2, 4950);
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check!(i16, 14, 4, 1001);
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check!(i16, 0, 0, 1);
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check!(i16, 2, 3, 0);
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check!(u32, 100, 2, 4950);
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check!(u32, 35, 11, 417225900);
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check!(u32, 14, 4, 1001);
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check!(u32, 0, 0, 1);
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check!(u32, 2, 3, 0);
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check!(i32, 100, 2, 4950);
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check!(i32, 35, 11, 417225900);
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check!(i32, 14, 4, 1001);
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check!(i32, 0, 0, 1);
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check!(i32, 2, 3, 0);
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check!(u64, 100, 2, 4950);
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check!(u64, 35, 11, 417225900);
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check!(u64, 14, 4, 1001);
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check!(u64, 0, 0, 1);
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check!(u64, 2, 3, 0);
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check!(i64, 100, 2, 4950);
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check!(i64, 35, 11, 417225900);
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check!(i64, 14, 4, 1001);
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check!(i64, 0, 0, 1);
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check!(i64, 2, 3, 0);
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}
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