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Address binomial review feedback 

* Use substraction instead of division in comparison.
* More tests.
* Add comment.
This commit is contained in:
Vinzent Steinberg 2017-03-12 10:08:26 +01:00
parent 2f6eb31903
commit 07df43b034
1 changed files with 15 additions and 2 deletions
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17
integer/src/lib.rs
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@ -668,6 +668,9 @@ impl_integer_for_usize!(usize, test_integer_usize);
/// Calculate r * a / b, avoiding overflows and fractions. /// Calculate r * a / b, avoiding overflows and fractions.
fn multiply_and_divide<T: Integer + Clone>(r: T, a: T, b: T) -> T { fn multiply_and_divide<T: Integer + Clone>(r: T, a: T, b: T) -> T {
// See http://blog.plover.com/math/choose-2.html for the idea. // See http://blog.plover.com/math/choose-2.html for the idea.
//
// This depends on the fact that `b` must evenly divide `r*a`, as that's
// what lets you know that `b/gcd(r, b)` divides `a` evenly.
let g = gcd(r.clone(), b.clone()); let g = gcd(r.clone(), b.clone());
(r/g.clone()) * (a / (b/g)) (r/g.clone()) * (a / (b/g))
} }
@ -678,8 +681,7 @@ pub fn binomial<T: Integer + Clone>(mut n: T, k: T) -> T {
if k > n { if k > n {
return T::zero(); return T::zero();
} }
let two = T::one() + T::one(); if k > n.clone() - k.clone() {
if k > n.clone()/two {
return binomial(n.clone(), n - k); return binomial(n.clone(), n - k);
} }
let mut r = T::one(); let mut r = T::one();
@ -731,39 +733,50 @@ fn test_binomial() {
let y: $t = $y; let y: $t = $y;
let expected: $t = $r; let expected: $t = $r;
assert_eq!(binomial(x, y), expected); assert_eq!(binomial(x, y), expected);
if y <= x {
assert_eq!(binomial(x, x - y), expected);
}
} } } }
} }
check!(u8, 9, 4, 126); check!(u8, 9, 4, 126);
check!(u8, 0, 0, 1); check!(u8, 0, 0, 1);
check!(u8, 2, 3, 0);
check!(i8, 9, 4, 126); check!(i8, 9, 4, 126);
check!(i8, 0, 0, 1); check!(i8, 0, 0, 1);
check!(i8, 2, 3, 0);
check!(u16, 100, 2, 4950); check!(u16, 100, 2, 4950);
check!(u16, 14, 4, 1001); check!(u16, 14, 4, 1001);
check!(u16, 0, 0, 1); check!(u16, 0, 0, 1);
check!(u16, 2, 3, 0);
check!(i16, 100, 2, 4950); check!(i16, 100, 2, 4950);
check!(i16, 14, 4, 1001); check!(i16, 14, 4, 1001);
check!(i16, 0, 0, 1); check!(i16, 0, 0, 1);
check!(i16, 2, 3, 0);
check!(u32, 100, 2, 4950); check!(u32, 100, 2, 4950);
check!(u32, 35, 11, 417225900); check!(u32, 35, 11, 417225900);
check!(u32, 14, 4, 1001); check!(u32, 14, 4, 1001);
check!(u32, 0, 0, 1); check!(u32, 0, 0, 1);
check!(u32, 2, 3, 0);
check!(i32, 100, 2, 4950); check!(i32, 100, 2, 4950);
check!(i32, 35, 11, 417225900); check!(i32, 35, 11, 417225900);
check!(i32, 14, 4, 1001); check!(i32, 14, 4, 1001);
check!(i32, 0, 0, 1); check!(i32, 0, 0, 1);
check!(i32, 2, 3, 0);
check!(u64, 100, 2, 4950); check!(u64, 100, 2, 4950);
check!(u64, 35, 11, 417225900); check!(u64, 35, 11, 417225900);
check!(u64, 14, 4, 1001); check!(u64, 14, 4, 1001);
check!(u64, 0, 0, 1); check!(u64, 0, 0, 1);
check!(u64, 2, 3, 0);
check!(i64, 100, 2, 4950); check!(i64, 100, 2, 4950);
check!(i64, 35, 11, 417225900); check!(i64, 35, 11, 417225900);
check!(i64, 14, 4, 1001); check!(i64, 14, 4, 1001);
check!(i64, 0, 0, 1); check!(i64, 0, 0, 1);
check!(i64, 2, 3, 0);
} }