《算法导论》CLRS算法C++实现（三）P75 堆排序

第六章 堆排序

主要分为三个子算法。算法MAX-HEAPIFY(A, i)为调整堆，算法BUILD-MAX-HEAP(A)为建堆，算法HEAPSORT(A)为堆排序。运行环境Code::Blocks 10.05。

MAX-HEAPIFY(A, i)

 1 l ← LEFT(i)

 2 r ← RIGHT(i)

 3 if l ≤ heap-size[A] and A[l] > A[i]

 4     then largest ← l

 5 else largest ← i

 6 if r ≤ heap-size[A] and A[r] > A[largest]

 7     then largest ← r

 8 if largest ≠ i

 9     then swap(A[i], A[largest])

10     MAX-HEAPIFY(A, largest)

BUILD-MAX-HEAP(A) 

heap-size[A] ← length[A]

for i ← ⌊length[A]/2⌋ down to 1

    do MAX-HEAPIFY(A, i)

 HEAPSORT(A)

1 BUILD-MAX-HEAP(A)

2 for i ← length[A] downto 2

3     do exchange A[1] ↔ A[i]

4     heap-size[A] ← heap-size[A] - 1

5     MAX-HEAPIFY(A, 1)

C++代码实现

 1 #include <iostream>

 2 

 3 using namespace std;

 4 

 5 //交换x和y

 6 

 7 void swap(int* x, int* y)

 8 {

 9     int temp;

10     temp = *x;

11     *x = *y;

12     *y = temp;

13 }

14 

15 //返回左孩子的下标

16 inline int left(int i)

17 {

18     return 2 * i + 1;

19 }

20 

21 //返回右孩子的下标

22 inline int right(int i)

23 {

24     return 2 * i + 2;

25 }

26 

27 //返回父结点

28 inline int parent(int i)

29 {

30     if(i % 2)

31         return (i - 1) / 2;

32     return (i - 2) / 2;

33 }

34 

35 void maxHeapify(int* arr, int i, int heapsize)

36 {

37     int l = left(i);

38     int r = right(i);

39     int largest;

40     if((l < heapsize) && (arr[l] > arr[i]))

41         largest = l;

42     else

43         largest = i;

44     if((r < heapsize) && (arr[r] > arr[largest]))

45         largest = r;

46     if(largest != i)

47     {

48         swap(arr[i], arr[largest]);

49         maxHeapify(arr, largest, heapsize);

50     }

51 }

52 

53 void buildMaxHeap(int* arr, int length)

54 {

55     int i;

56     for(i = length / 2; i >= 0; i--)

57     {

58         maxHeapify(arr, i, length);

59     }

60 }

61 

62 void heapSort(int* arr, int length)

63 {

64     int i, heapsize = length;

65     buildMaxHeap(arr, length);

66     for(i = heapsize - 1; i > 0; i--)

67     {

68         swap(arr[0], arr[i]);

69         heapsize--;

70         maxHeapify(arr, 0, heapsize);

71     }

72 }

73 

74 int main()

75 {

76     int arr[] = {0, 2, 6, 98, 34, -5, 23, 11, 89, 100, 7};

77     heapSort(arr, 11);

78     for(int i = 0; i < 11; i++)

79     {

80         cout << arr[i] << " ";

81     }

82     cout << endl;

83     return 0;

84 }