堆排序
算法导论 第六章 堆排序
堆是一个棵完全二叉树，通常用一个数组表示。这样的数组有两个属性：lenght(A)是数组中的元素个数，heap-size(A)是存放在A中的堆的元素个数。
堆排序的时间复杂度为O(nlgn).
给定堆中结点i的下标，其父为i/2,其左孩子为i*2，右孩子为i*2 + 1。
堆分为大根堆和小根堆。小根堆通常在构造优先级队列时使用。
常用的过程有：max-heaplify （堆调整）、build-max-heap （堆构造）、heap-sort （堆排序）。
以下程序根据书中思想而来：
1 /**
2 * Max Heap Sort
3 * It is a in-place sort. Its time is O(nlgn).
4 * An array A[1...n] has the following features:
5 * i is among 1 and n.
6 * its parent is i/2 (i >> 1);
7 * its left child is i*2 (i << 1);
8 * its right child is i*2 + 1 (i << 1 + 1;
9 * parent >= {left child, right child}
10 * ---------------------------------------------
11 */
12 #include<stdio.h>
13
14 void buildmaxheap(int* A, int length);
15 void maxheap(int* A, int i, int length);
16 void maxheapsort(int* A, int length);
17
18 void buildmaxheap(int* A, int length) {
19 int i = 0;
20 for (i = length >> 1; i >= 1; i--) {
21 maxheap(A, i, length);
22 }
23 }
24
25 void maxheap(int* A, int i, int length) {
26 int left = i << 1;
27 int right = left + 1;
28 int largest = i;
29
30 if (left <= length && A[left] > A[largest]) {
31 largest = left;
32 }
33
34 if (right <= length && A[right] > A[largest]) {
35 largest = right;
36 }
37
38 if (largest != i) {
39 A[0] = A[largest];
40 A[largest] = A[i];
41 A[i] = A[0];
42 maxheap(A, largest, length);
43 }
44 }
45
46 void maxheapsort(int* A, int length) {
47 int i = length;
48
49 if (A == NULL) return;
50
51 buildmaxheap(A, length);
52
53 // We need n-1 loop to get the other in order.
54 for(;i >= 2;i--) {
55 A[0] = A[i];
56 A[i] = A[1];
57 A[1] = A[0];
58
59 maxheap(A, 1, i - 1);
60 }
61 }
62
63 int main() {
64 int A[] = {0,2,8,7,1,3,5,6,4};
65 int len = sizeof(A) / sizeof(int) - 1;
66 int i = 1;
67
68 maxheapsort(A, len);
69
70 for (i = 1; i <= len; i++)
71 printf("%d,",A[i]);
72
73 printf("\n");
74 return 0;
75 }
