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use std::{cmp, mem};
use std::cmp::Ordering;
pub fn median_of_medians<T: Ord>(array: &mut [T]) -> (usize, &mut T) {
median_of_medians_by(array, Ord::cmp)
}
pub fn median_of_medians_by<T, F>(array: &mut [T], mut cmp: F) -> (usize, &mut T)
where F: FnMut(&T, &T) -> Ordering
{
if array.len() < 5 {
let median = array.len() / 2;
return (median, super::kth_by(array, median, cmp))
}
let num_medians = (array.len() - 1 + 4) / 5;
for i in 0..num_medians {
let start = 5 * i;
let trailing = array.len() - start;
let idx = if trailing < 5 {
let elem = super::kth_by(&mut array[start..], trailing / 2, &mut cmp) as *mut _ as usize;
let start = array.as_ptr() as usize;
(elem - start) / cmp::max(1, mem::size_of::<T>())
} else {
start + median5(&array[start..start+5], &mut cmp)
};
array.swap(i, idx);
}
let idx = (array.len() - 1) / 10;
(idx, super::kth_by(&mut array[..num_medians], idx, cmp))
}
fn median5<T, F>(array: &[T], cmp: &mut F) -> usize
where F: FnMut(&T, &T) -> Ordering
{
use std::mem;
let array = array;
debug_assert!(array.len() == 5);
let mut a4 = (4, &array[4]);
let mut a3 = (3, &array[3]);
let mut a2 = (2, &array[2]);
let mut a1 = (1, &array[1]);
let mut a0 = (0, &array[0]);
macro_rules! cmp {
($($a: ident, $b: ident;)*) => {
$(
if cmp($a.1, $b.1) == Ordering::Less {
mem::swap(&mut $a, &mut $b)
}
)*
}
}
cmp! {
a3, a4; a0, a1;
a2, a4;
a2, a3; a1, a4;
a0, a3;
a0, a2; a1, a3;
a1, a2;
}
a2.0
}
#[cfg(test)]
mod tests {
use std::cmp;
use super::median_of_medians;
use quickcheck::{self, TestResult};
#[test]
fn qc() {
fn run(mut x: Vec<i32>) -> TestResult {
if x.is_empty() { return TestResult::discard() }
let (_, &mut median) = median_of_medians(&mut x);
x.sort();
let thirty = (x.len() * 3 / 10).saturating_sub(1);
let seventy = cmp::min((x.len() * 7 + 9) / 10, x.len() - 1);
TestResult::from_bool(x[thirty] <= median && median <= x[seventy])
}
quickcheck::quickcheck(run as fn(Vec<i32>) -> TestResult)
}
#[test]
fn smoke() {
let mut x = (0..101).rev().collect::<Vec<_>>();
let (_, &mut median) = median_of_medians(&mut x);
assert!(30 <= median);
assert!(median <= 70);
}
#[test]
fn include_trailing() {
let mut v = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0];
assert_eq!(*median_of_medians(&mut v).1, 0)
}
#[test]
fn correct_sortings() {
let mut v = [0, 0, 0, 0, 0, -1];
assert_eq!(*median_of_medians(&mut v).1, 0);
}
}
#[cfg(all(test, feature = "unstable"))]
mod benches {
use super::median_of_medians;
make_benches!(|_, mut v| median_of_medians(&mut v).0);
mod exact {
make_benches!(|_, mut v| {
let n = v.len() / 2;
::kth(&mut v, n) as *mut _
});
}
}