Add Intro Sort (TheAlgorithms#538)

Author: cyrixninja

src/sorting/intro_sort.rs

@@ -0,0 +1,107 @@
+// Intro Sort (Also known as Introspective Sort)
+// Introspective Sort is hybrid sort (Quick Sort + Heap Sort + Insertion Sort)
+// https://en.wikipedia.org/wiki/Introsort
+fn insertion_sort<T: Ord>(arr: &mut [T]) {
+    for i in 1..arr.len() {
+        let mut j = i;
+        while j > 0 && arr[j] < arr[j - 1] {
+            arr.swap(j, j - 1);
+            j -= 1;
+        }
+    }
+}
+
+fn heapify<T: Ord>(arr: &mut [T], n: usize, i: usize) {
+    let mut largest = i;
+    let left = 2 * i + 1;
+    let right = 2 * i + 2;
+
+    if left < n && arr[left] > arr[largest] {
+        largest = left;
+    }
+
+    if right < n && arr[right] > arr[largest] {
+        largest = right;
+    }
+
+    if largest != i {
+        arr.swap(i, largest);
+        heapify(arr, n, largest);
+    }
+}
+
+fn heap_sort<T: Ord>(arr: &mut [T]) {
+    let n = arr.len();
+
+    // Build a max-heap
+    for i in (0..n / 2).rev() {
+        heapify(arr, n, i);
+    }
+
+    // Extract elements from the heap one by one
+    for i in (0..n).rev() {
+        arr.swap(0, i);
+        heapify(arr, i, 0);
+    }
+}
+
+fn intro_sort<T: Ord>(arr: &mut [T]) {
+    let len = arr.len();
+    let max_depth = (2.0 * len as f64).log2() as usize + 1;
+
+    fn intro_sort_recursive<T: Ord>(arr: &mut [T], max_depth: usize) {
+        let len = arr.len();
+
+        if len <= 16 {
+            insertion_sort(arr);
+        } else if max_depth == 0 {
+            heap_sort(arr);
+        } else {
+            let pivot = partition(arr);
+            intro_sort_recursive(&mut arr[..pivot], max_depth - 1);
+            intro_sort_recursive(&mut arr[pivot + 1..], max_depth - 1);
+        }
+    }
+
+    fn partition<T: Ord>(arr: &mut [T]) -> usize {
+        let len = arr.len();
+        let pivot_index = len / 2;
+        arr.swap(pivot_index, len - 1);
+
+        let mut i = 0;
+        for j in 0..len - 1 {
+            if arr[j] <= arr[len - 1] {
+                arr.swap(i, j);
+                i += 1;
+            }
+        }
+
+        arr.swap(i, len - 1);
+        i
+    }
+
+    intro_sort_recursive(arr, max_depth);
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_intro_sort() {
+        // Test with integers
+        let mut arr1 = vec![67, 34, 29, 15, 21, 9, 99];
+        intro_sort(&mut arr1);
+        assert_eq!(arr1, vec![9, 15, 21, 29, 34, 67, 99]);
+
+        // Test with strings
+        let mut arr2 = vec!["sydney", "london", "tokyo", "beijing", "mumbai"];
+        intro_sort(&mut arr2);
+        assert_eq!(arr2, vec!["beijing", "london", "mumbai", "sydney", "tokyo"]);
+
+        // Test with an empty array
+        let mut arr3: Vec<i32> = vec![];
+        intro_sort(&mut arr3);
+        assert_eq!(arr3, vec![]);
+    }
+}