Add tim sort (rust-lang#273)

Co-authored-by: hossein.dindar <hossein.dindar@arvancloud.com>
Co-authored-by: Andrii Siriak <siryaka@gmail.com>

Author: 3 people

src/sorting/README.md

@@ -158,6 +158,15 @@ From [Wikipedia][stooge-wiki]:  Stooge sort is a recursive sorting algorithm. It
 __Properties__
 * Worst case performance O(n^(log(3) / log(1.5)))
 
+### [Tim](./tim_sort.rs)
+![alt text][tim-image]
+
+From [Wikipedia][tim-wiki]:  Timsort is a hybrid stable sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data. It was implemented by Tim Peters in 2002 for use in the Python programming language. The algorithm finds subsequences of the data that are already ordered (runs) and uses them to sort the remainder more efficiently. This is done by merging runs until certain criteria are fulfilled. Timsort has been Python's standard sorting algorithm since version 2.3. It is also used to sort arrays of non-primitive type in Java SE 7, on the Android platform, in GNU Octave, on V8, Swift, and Rust.
+
+__Properties__
+* Worst-case performance O(n log n)
+* Best-case performance	O(n)
+
 [bubble-toptal]: https://www.toptal.com/developers/sorting-algorithms/bubble-sort
 [bubble-wiki]: https://en.wikipedia.org/wiki/Bubble_sort
 [bubble-image]: https://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Bubblesort-edited-color.svg/220px-Bubblesort-edited-color.svg.png "Bubble Sort"
@@ -199,5 +208,8 @@ __Properties__
 [stooge-image]: https://upload.wikimedia.org/wikipedia/commons/f/f8/Sorting_stoogesort_anim.gif
 [stooge-wiki]: https://en.wikipedia.org/wiki/Stooge_sort
 
+[tim-image]: https://thumbs.gfycat.com/BruisedFrigidBlackrhino-size_restricted.gif
+[tim-wiki]: https://en.wikipedia.org/wiki/Timsort
+
 [comb-sort]: https://upload.wikimedia.org/wikipedia/commons/4/46/Comb_sort_demo.gif
 [comb-sort-wiki]: https://en.wikipedia.org/wiki/Comb_sort

src/sorting/mod.rs

@@ -13,6 +13,7 @@ mod radix_sort;
 mod selection_sort;
 mod shell_sort;
 mod stooge_sort;
+mod tim_sort;
 
 pub use self::bubble_sort::bubble_sort;
 pub use self::bucket_sort::bucket_sort;
@@ -30,6 +31,7 @@ pub use self::radix_sort::radix_sort;
 pub use self::selection_sort::selection_sort;
 pub use self::shell_sort::shell_sort;
 pub use self::stooge_sort::stooge_sort;
+pub use self::tim_sort::tim_sort;
 
 use std::cmp;
 

src/sorting/tim_sort.rs

@@ -0,0 +1,131 @@
+use std::cmp;
+
+static MIN_MERGE: usize = 32;
+
+fn min_run_length(mut n: usize) -> usize {
+    let mut r = 0;
+    while n >= MIN_MERGE {
+        r |= n & 1;
+        n >>= 1;
+    }
+    n + r
+}
+
+fn insertion_sort(arr: &mut Vec<i32>, left: usize, right: usize) -> &Vec<i32> {
+    for i in (left + 1)..(right + 1) {
+        let temp = arr[i];
+        let mut j = (i - 1) as i32;
+
+        while j >= (left as i32) && arr[j as usize] > temp {
+            arr[(j + 1) as usize] = arr[j as usize];
+            j -= 1;
+        }
+        arr[(j + 1) as usize] = temp;
+    }
+    arr
+}
+
+fn merge(arr: &mut Vec<i32>, l: usize, m: usize, r: usize) -> &Vec<i32> {
+    let len1 = m - l + 1;
+    let len2 = r - m;
+    let mut left = vec![0; len1 as usize];
+    let mut right = vec![0; len2 as usize];
+
+    left[..len1].clone_from_slice(&arr[l..(len1 + l)]);
+
+    for x in 0..len2 {
+        right[x] = arr[m + 1 + x];
+    }
+
+    let mut i = 0;
+    let mut j = 0;
+    let mut k = l;
+
+    while i < len1 && j < len2 {
+        if left[i] <= right[j] {
+            arr[k] = left[i];
+            i += 1;
+        } else {
+            arr[k] = right[j];
+            j += 1;
+        }
+        k += 1;
+    }
+
+    while i < len1 {
+        arr[k] = left[i];
+        k += 1;
+        i += 1;
+    }
+
+    while j < len2 {
+        arr[k] = right[j];
+        k += 1;
+        j += 1;
+    }
+    arr
+}
+
+pub fn tim_sort(arr: &mut Vec<i32>, n: usize) {
+    let min_run = min_run_length(MIN_MERGE) as usize;
+
+    let mut i = 0;
+    while i < n {
+        insertion_sort(arr, i, cmp::min(i + MIN_MERGE - 1, n - 1));
+        i += min_run;
+    }
+
+    let mut size = min_run;
+    while size < n {
+        let mut left = 0;
+        while left < n {
+            let mid = left + size - 1;
+            let right = cmp::min(left + 2 * size - 1, n - 1);
+            if mid < right {
+                merge(arr, left, mid, right);
+            }
+
+            left += 2 * size;
+        }
+        size *= 2;
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn basic() {
+        let mut array = vec![-2, 7, 15, -14, 0, 15, 0, 7, -7, -4, -13, 5, 8, -14, 12];
+        let arr_len = array.len();
+        tim_sort(&mut array, arr_len);
+        for i in 0..array.len() - 1 {
+            assert!(array[i] <= array[i + 1]);
+        }
+    }
+
+    #[test]
+    fn empty() {
+        let mut array = Vec::<i32>::new();
+        let arr_len = array.len();
+        tim_sort(&mut array, arr_len);
+        assert_eq!(array, vec![]);
+    }
+
+    #[test]
+    fn one_element() {
+        let mut array = vec![3];
+        let arr_len = array.len();
+        tim_sort(&mut array, arr_len);
+        assert_eq!(array, vec![3]);
+    }
+
+    #[test]
+    fn pre_sorted() {
+        let mut array = vec![0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
+        let arr_len = array.len();
+        tim_sort(&mut array, arr_len);
+        assert_eq!(array, vec![0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
+    }
+}