数据结构与算法(Java) 15：堆排序[含对数器]

思路 ：（1）将原数组建立大根堆；（2）每次将根节点与最后一个叶节点交换位置；（3）有效堆大小减1；（4）将修改后的有效堆进行调整[heapify操作]。最终得到的数组就是从小到大排好序的了。

时间复杂度：    因为每操作一个数的复杂度是logN，所以N个数是N*logN

额外空间复杂度：

package section1;

import java.util.Arrays;

public class HeapSort {
    public static void heapSort(int[] arr){
        if (arr == null || arr.length < 2) return;

        int heapSize = arr.length;
        heapInsert(arr, heapSize);

        while (heapSize > 1){
            swap(arr, 0, --heapSize);
            heapify(arr, 0, heapSize);
        }
    }

    public static void heapInsert(int[] arr, int heapSize){
        for (int i = 0; i < heapSize; i++)
            insert(arr, i);
    }

    public static void insert(int[] arr, int index){
        while (arr[index] > arr[(index - 1) / 2]){
            swap(arr, index, (index - 1) / 2);
            index = (index - 1) / 2;
        }
    }

    public static void swap(int[] arr, int a, int b){
        int f = arr[a];
        arr[a] = arr[b];
        arr[b] = f;
    }

    public static void heapify(int[] arr, int index, int heapSize){
        int L = 2 * index + 1;
        while (L < heapSize){
            int large = arr[L] < arr[L + 1] && L + 1 < heapSize ? L + 1 : L;
            if (arr[large] > arr[index]){
                swap(arr, index, large);
                index = large;
                L = 2 * index + 1;
            }
            else break;
        }
    }

    // for test
    public static void comparator(int[] arr) {
        Arrays.sort(arr);
    }

    // for test
    public static int[] generateRandomArray(int maxSize, int maxValue) {
        int[] arr = new int[(int) ((maxSize + 1) * Math.random())];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = (int) ((maxValue + 1) * Math.random()) - (int) (maxValue * Math.random());
        }
        return arr;
    }

    // for test
    public static int[] copyArray(int[] arr) {
        if (arr == null) {
            return null;
        }
        int[] res = new int[arr.length];
        for (int i = 0; i < arr.length; i++) {
            res[i] = arr[i];
        }
        return res;
    }

    // for test
    public static boolean isEqual(int[] arr1, int[] arr2) {
        if ((arr1 == null && arr2 != null) || (arr1 != null && arr2 == null)) {
            return false;
        }
        if (arr1 == null && arr2 == null) {
            return true;
        }
        if (arr1.length != arr2.length) {
            return false;
        }
        for (int i = 0; i < arr1.length; i++) {
            if (arr1[i] != arr2[i]) {
                return false;
            }
        }
        return true;
    }

    // for test
    public static void printArray(int[] arr) {
        if (arr == null) {
            return;
        }
        for (int i = 0; i < arr.length; i++) {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }

    // for test
    public static void main(String[] args) {
        int testTime = 500000;
        int maxSize = 100;
        int maxValue = 100;
        boolean succeed = true;
        for (int i = 0; i < testTime; i++) {
            int[] arr1 = generateRandomArray(maxSize, maxValue);
            int[] arr2 = copyArray(arr1);
            heapSort(arr1);
            comparator(arr2);
            if (!isEqual(arr1, arr2)) {
                succeed = false;
                break;
            }
        }
        System.out.println(succeed ? "Nice!" : "Fucking fucked!");

        int[] arr = generateRandomArray(maxSize, maxValue);
        printArray(arr);
        heapSort(arr);
        printArray(arr);
    }
}