算法导论：堆排序

 1 //goal: heap sort

 2 //time: 9/7/2014

 3 //author: zrss

 4 //reference: introduction to algorithms

 5 

 6 #include <cstdio>

 7 #include <cstring>

 8 

 9 #define MAX_DATA 10

10 

11 class MaxHeap {

12 public:

13     MaxHeap(int *data, int size);

14 

15     void heap_sort(void); //堆排序，升序

16 

17     void output(void);

18 

19 private:

20     void max_heapify(int i, int size); //使以i为根的子树成为最大堆，假设i左右子树均为最大堆

21     void build_maxheap(int size); //自底向上使用max_heapify调整，建堆

22 

23 private:

24     int size;

25     int array[MAX_DATA]; //从下标0开始存储

26 };

27 

28 MaxHeap::MaxHeap(int *data, int size):size(size) {

29     if (size > MAX_DATA)

30         return;

31 

32     memcpy(array, data, sizeof(int) * size);

33 }

34 

35 void MaxHeap::max_heapify(int i, int size) {

36     bool check = true;

37 

38     while (check) {

39         int l = (i << 1) + 1;

40         int r = l + 1;

41 

42         int largest = i;

43 

44         //与子节点比较

45         if (l < size && array[l] > array[i])

46             largest = l;

47 

48         if (r < size && array[r] > array[largest])

49             largest = r;

50 

51         if (largest != i) {

52             int temp = array[largest];

53             array[largest] = array[i];

54             array[i] = temp;

55 

56             i = largest; //从被交换的子节点位置继续调整

57         }

58         else

59             check = false; //父节点不小于子节点，满足最大堆性质，停止调整

60     }

61 }

62 

63 void MaxHeap::build_maxheap(int size) {

64     int leaf_start_index = size >> 1; //后续元素为叶子节点

65 

66     //从第一个父节点开始调整

67     for (int i = leaf_start_index - 1; i >= 0; --i)

68         max_heapify(i, size);

69 }

70 

71 void MaxHeap::heap_sort(void) {

72     int cur_size = size;

73 

74     while (cur_size > 1) {

75         //调整成堆

76         build_maxheap(cur_size);

77 

78         //将最大值与堆末尾元素交换

79         int temp = array[cur_size - 1];

80         array[cur_size - 1] = array[0];

81         array[0] = temp;

82 

83         --cur_size;

84     }

85 }

86 

87 void MaxHeap::output(void) {

88     for (int i = 0; i < size; ++i)

89         printf("%d ", array[i]);

90 }