Program work 13. Heap Sort in Java

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关键在于最大堆的建立和重构 (其实两个过程是一样的)

因为堆是平衡二叉树, 所以数组可以直接用下标表示父子的节点关系, 数组要从下标1开始.

将最大值移到数组只需要O(n)

重构堆需要O(lgn)

所以upper bound is O(n*logn)

事实上, lower bound is Ω(n*logn)

最好最坏最差都是O(n*logn)

Pseudocode

heapSort (arr, len){    buildMaxHeap()    for () {        remove the root element(the max) to the end of array        reconstructHeap();    }}reconsturctHeap(arr, len){    tmp = arr[root]    get the children of root    while () {        get the bigger child between left and right child        if the element of that child is larger than root            replace its parent element with is        move to next children    }    place the tmp to the apporpriate pos}

Java

package ncku.cdc.sorting;import java.util.Random;public class HeapSort {  private int[] sequence;  public HeapSort(int size, int range) {    sequence = new int[size + 1];    Random rand = new Random();    for (int i = 1; i <= size; i++) {      sequence[i] = rand.nextInt(range);    }  }  public static void main(String[] args) {    int size = Integer.valueOf(args[0]);    int range = Integer.valueOf(args[1]);    HeapSort heap = new HeapSort(size, range);    System.out.println("before heapSort:");    SortingTools.validation(heap.getSequence(), 1);        heap.heapSort(heap.getSequence(), size);    System.out.println("after heapSort:");    SortingTools.validation(heap.getSequence(), 1);  }    public void heapSort(int[] arr, int len) {    for (int i = len / 2; i > 0; i--) {      retifyHeap(arr, i, len);    }    for (int j = len - 1; j > 0; j--) {      swap(arr, 1, j + 1);      retifyHeap(arr, 1, j);    }  }  private void retifyHeap(int[] arr, int root, int len) {    int tmp = arr[root];    int child = root * 2;    while (child <= len) {      if ((child < len) && (arr[child] < arr[child + 1])) { child++; }      if (tmp > arr[child]) { break; }       else {        arr[child / 2] = arr[child];        child *= 2;      }    }    arr[child / 2] = tmp;  }    private void swap(int[] arr, int i, int j) {    int t = arr[i];    arr[i] = arr[j];    arr[j] = t;  }  public int[] getSequence() {    return sequence;  }}

程序输入: 35 200. 表示随机生成一个长度为35, 数字范围在[0, 200)的数组

程序输出:

before heapSort:
67 18 192 142 136 30 144 6 158 11 123 34 36 155 97 12 7 159 81 135 160 102 48 42 0 155 77 114 139 146 186 32 42 144 100
after heapSort:
0 6 7 11 12 18 30 32 34 36 42 42 48 67 77 81 97 100 102 114 123 135 136 139 142 144 144 146 155 155 158 159 160 186 192

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