堆排序——HeapSort

基本思想：

 

圖示： （88,85,83,73,72,60,57,48,42,6）

 

平均時間複雜度：

O(NlogN)因爲每次從新恢復堆的時間複雜度爲O(logN)，共N - 1次從新恢復堆操做，再加上前面創建堆時N / 2次向下調整，每次調整時間複雜度也爲O(logN)。二次操做時間相加仍是O(N * logN)。

Java代碼實現：

public class HeapSortTest {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[] arr = new int[] { 10, 3, 2, 5, 6, 1, -2, 3, 14, 12, 3, 8, 55, 44,
                -10 };
        print(arr);
        heapSort(arr);
        System.out.println("排序後的數組：");
        print(arr);
    }

    private static void print(int[] a) {
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + "\t");
        }
        System.out.println();
    }

    private static void swap(int[] a, int i, int j) {
        a[i] = a[i] + a[j];
        a[j] = a[i] - a[j];
        a[i] = a[i] - a[j];
    }

    private static void heapSort(int[] a) {
        for (int i = a.length - 1; i >= 0; i--) {
            createMaxHeap(a, i);
            swap(a, 0, i);
            print(a);
        }
    }

    private static void createMaxHeap(int[] a, int lastIndex) {
        for (int i = (lastIndex - 1) / 2; i >= 0; i--) {
            int k = i;
            while ((2 * k + 1) <= lastIndex) {
                int biggerIndex = 2 * k + 1;
                if (biggerIndex < lastIndex) {
                    if (a[biggerIndex] < a[biggerIndex + 1]) {
                        biggerIndex++;
                    }
                }
                if (a[k] < a[biggerIndex]) {
                    swap(a, k, biggerIndex);
                    k = biggerIndex;
                } else {
                    break;
                }
            }
        }
    }
}