algos 0.2.0

/**************************************************************************************************
* Copyright 2017 Eric Shimizu Karbstein
* All rights reserved.
*
* This Source Code Form is subject to the terms of the BSD 3-Clause License.
**************************************************************************************************/

//! A module for using sorting algorithms.
//!
//! It contains all major sorting algorithms.

use std::cmp::*;
use rand::prelude::*;

/// Selection Sort: Sort a slice according to the way you define the cmp parameter.
///
/// |           | Time complexity | Space complexity |
/// |:----------|:---------------:|:----------------:|
/// | Best:     | Ω(n^2)          |                  |
/// | Avrg:     | θ(n^2)          |                  |
/// | Worst:    | O(n^2)          | O(1)             |
///
/// #Examples
/// ```rust
/// use algos::sort;
///
/// let mut v = [9, 3, 5, 7, 8, 7];
/// // Crescent sorting
/// sort::selection(&mut v, &|a,b| a<b);
/// ```
pub fn selection<T: Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C) {
    for i in 0..=a.len() {
        let mut i_min = i;
        for j in i+1..a.len() {
            if cmp(&a[j],&a[i_min]) {
                i_min = j;
            }
        }
        if i_min!=i {
            a.swap(i_min, i);
        }
    }
}

/// Bubble Sort: Sort a slice according to the way you define the cmp parameter.
///
/// |           | Time complexity | Space complexity |
/// |:----------|:---------------:|:----------------:|
/// | Best:     | Ω(n)            |                  |
/// | Avrg:     | θ(n^2)          |                  |
/// | Worst:    | O(n^2)          | O(1)             |
///
/// #Examples
/// ```rust
/// use algos::sort;
///
/// let mut v = [9, 3, 5, 7, 8, 7];
/// // Crescent sorting
/// sort::bubble(&mut v, &|a,b| a<b);
/// ```
pub fn bubble<T: Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C) {
    for i in (0..a.len()).rev() {
        for j in 0..i {
            if cmp(&a[j+1],&a[j]) {
                a.swap(j,j+1);
            }
        }
    }
}

/// Cocktail Sort: Sort a slice according to the way you define the cmp parameter.
/// It's a variation of Bubble Sort.
///
/// |           | Time complexity | Space complexity |
/// |:----------|:---------------:|:----------------:|
/// | Best:     | Ω(n)            |                  |
/// | Avrg:     | θ(n^2)          |                  |
/// | Worst:    | O(n^2)          | O(1)             |
///
/// #Examples
/// ```rust
/// use algos::sort;
///
/// let mut v = [9, 3, 5, 7, 8, 7];
/// // Crescent sorting
/// sort::cocktail(&mut v, &|a,b| a<b);
/// ```
pub fn cocktail<T: Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C) {
    let mut changed: bool = true;
    let mut start = 0;
    let mut end = a.len()-1;
    while changed {
        changed = false;
        for i in start..end {
            if cmp(&a[i+1],&a[i]) {
                a.swap(i, i+1);
                changed = true;
            }
        }
        end -= 1;

        if !changed {
            break;
        }

        changed = true;
        for i in (start..end-1).rev() {
            if cmp(&a[i+1],&a[i]) {
                a.swap(i, i+1);
                changed = true;
            }
        }
        start += 1;
    }
}

/// Insection Sort: Sort a slice according to the way you define the cmp parameter.
///
/// |           | Time complexity | Space complexity |
/// |:----------|:---------------:|:----------------:|
/// | Best:     | Ω(n)            |                  |
/// | Avrg:     | θ(n^2)          |                  |
/// | Worst:    | O(n^2)          | O(1)             |
///
/// #Examples
/// ```rust
/// use algos::sort;
///
/// let mut v = [9, 3, 5, 7, 8, 7];
/// // Crescent sorting
/// sort::insection(&mut v, &|a,b| a<b);
/// ```
pub fn insection<T: Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C) {
    for i in 1..a.len() {
        for j in (0..i).rev() {
            if cmp(&a[j+1],&a[j]) {
                a.swap(j, j+1);
            }
        }
    }
}

/// Merge Sort: Sort a slice according to the way you define the cmp parameter.
///
/// |           | Time complexity | Space complexity |
/// |:----------|:---------------:|:----------------:|
/// | Best:     | Ω(nlog(n))      |                  |
/// | Avrg:     | θ(nlog(n))      |                  |
/// | Worst:    | O(nlog(n))      | O(n)             |
///
/// #Examples
/// ```rust
/// use algos::sort;
///
/// let mut v = [9, 3, 5, 7, 8, 7];
/// // Crescent sorting
/// sort::merge(&mut v, &|a,b| a<b);
/// ```
pub fn merge<T: Copy + Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C) {
    let (start, mid, end) = (0, a.len()/2, a.len());
    if end<=1 {
        return;
    }
    merge(&mut a[start..mid], cmp);
    merge(&mut a[mid..end], cmp);
    // Copy array "a" to auxiliar array "o"
    let mut o: Vec<T> = a.to_vec();
    combine(&a[start..mid], &a[mid..end], &mut o[..], cmp);
    // Copy itens of "o" into "a"
    a.copy_from_slice(&o);
}
fn combine<T: Copy + PartialOrd, C: Fn(&T, &T) -> bool>(l: &[T], r: &[T], o: &mut [T], cmp: &C) {
    assert_eq!(r.len()+l.len(), o.len());
    let (mut i, mut j, mut k) = (0, 0, 0);
    while i<l.len() && j<r.len() {
        if cmp(&l[i],&r[j]) {
            o[k] = l[i];
            k += 1;
            i += 1;
        }
        else {
            o[k] = r[j];
            k += 1;
            j += 1;
        }
    }
    if i<l.len() {
        o[k..].copy_from_slice(&l[i..]);
    }
    if j<r.len() {
        o[k..].copy_from_slice(&r[j..]);
    }
}


/// Quick Sort: Sort a slice according to the way you define the cmp parameter.
///
/// |           | Time complexity | Space complexity |
/// |:----------|:---------------:|:----------------:|
/// | Best:     | Ω(nlog(n))      |                  |
/// | Avrg:     | θ(nlog(n))      |                  |
/// | Worst:    | O(n^2)          | O(log(n))        |
///
/// #Examples
/// ```rust
/// use algos::sort;
///
/// let mut v = [9, 3, 5, 7, 8, 7];
/// // Crescent sorting
/// sort::quick(&mut v, &|a,b| a<b);
/// ```
pub fn quick<T: Copy+Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C) {
    let (start, end) = (0, a.len());
    if end<=1 {
        return;
    }
    let mid = partition(a, cmp);
    quick(&mut a[start..mid-1], cmp);
    quick(&mut a[mid..end], cmp);
}
fn partition<T: Copy+Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C) -> usize {
    let (start, end) = (0, a.len()-1);
    // We randomize the choice of the pivot so we have less probability to have Worst case.
    // Then we swap the random element to the end of the array.
    let rand = thread_rng().gen_range(start, end);
    let pivot = a[rand];
    a.swap(rand, end);

    let mut i = start;
    for j in start..end {
        if cmp(&a[j],&pivot) {
            a.swap(i, j);
            i += 1;
        }
    }
    a.swap(i, end);
    i+1
}

///Heap Sort: Sort a slice according to the way you define the cmp parameter.
///
/// |           | Time complexity | Space complexity |
/// |:----------|:---------------:|:----------------:|
/// | Best:     | Ω(nlog(n))      |                  |
/// | Avrg:     | θ(nlog(n))      |                  |
/// | Worst:    | O(nlog(n))      | O(1)             |
///
/// #Examples
/// ```rust
/// use algos::sort;
///
/// let mut v = [9, 3, 5, 7, 8, 7];
/// // Crescent sorting
/// sort::heap(&mut v, &|a,b| a<b);
/// ```
pub fn heap<T: Copy+Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C) {
    let (start, end) = (0, a.len());
    for i in (start..end/2).rev() {
        heapify(&mut a[..], cmp, i);
    }
    for i in (0..end).rev() {
        a.swap(0, i);
        heapify(&mut a[..i], cmp, 0);
    }
}
fn heapify<T: Copy+Ord, C: Fn(&T, &T) -> bool>(a: &mut [T], cmp: &C, aux: usize) {
    let end = a.len();
    let mut root = aux;
    let (left_child, right_child) = (2*aux, 2*aux+1);
    if left_child < end && cmp(&a[root], &a[left_child]) {
        root = left_child;
    }
    if right_child < end && cmp(&a[root], &a[right_child]) {
        root = right_child;
    }
    if root != aux {
        a.swap(aux, root);
        heapify(a, cmp, root);
    }
}


#[cfg(test)]
pub mod test {
    use sort::*;

    #[test]
    pub fn selection_test() {
        let p = [3, 5, 7, 7, 8, 9, 12, 15, 23, 30, 99];
        let mut v = [9, 3, 5, 7, 8, 7, 99, 30, 23, 15, 12];

        selection(&mut v, &|a,b| a<b);
        assert_eq!(v, p);
    }
    #[test]
    pub fn bubble_test() {
        let p = [3, 5, 7, 7, 8, 9, 12, 15, 23, 30, 99];
        let mut v = [9, 3, 5, 7, 8, 7, 99, 30, 23, 15, 12];

        bubble(&mut v, &|a,b| a<b);
        assert_eq!(v, p);
    }
    #[test]
    pub fn cocktail_test() {
        let p = [3, 5, 7, 7, 8, 9, 12, 15, 23, 30, 99];
        let mut v = [9, 3, 5, 7, 8, 7, 99, 30, 23, 15, 12];

        cocktail(&mut v, &|a,b| a<b);
        assert_eq!(v, p);
    }
    #[test]
    pub fn insection_test() {
        let p = [3, 5, 7, 7, 8, 9, 12, 15, 23, 30, 99];
        let mut v = [9, 3, 5, 7, 8, 7, 99, 30, 23, 15, 12];

        insection(&mut v, &|a,b| a<b);
        assert_eq!(v, p);
    }
    #[test]
    pub fn merge_test() {
        let p = [3, 5, 7, 7, 8, 9, 12, 15, 23, 30, 99];
        let mut v = [9, 3, 5, 7, 8, 7, 99, 30, 23, 15, 12];

        merge(&mut v, &|a,b| a<b);
        assert_eq!(v, p);
    }
    #[test]
    pub fn quick_test() {
        let p = [3, 5, 7, 7, 8, 9, 12, 15, 23, 30, 99];
        let mut v = [9, 3, 5, 7, 8, 7, 99, 30, 23, 15, 12];

        quick(&mut v, &|a,b| a<b);
        assert_eq!(v, p);
    }
    #[test]
    pub fn heap_test() {
        let p = [3, 5, 7, 7, 8, 9, 12, 15, 23, 30, 99];
        let mut v = [9, 3, 5, 7, 8, 7, 99, 30, 23, 15, 12];

        heap(&mut v, &|a,b| a<b);
        assert_eq!(v, p);
    }
}