堆排序和优先级队列

  1 // max_heap and priority queue
  2 // the index must be [1,size],not [0,size-1]
  3 #include<iostream>
  4 using namespace std;
  5 int arr[20] = {1,4,2,3,9,7,8,14,10,16};
  6 #define PARENT(i) (i/2)
  7 #define LEFT(i) (i*2)
  8 #define RIGHT(i) (i*2+1)
  9 #define ERROR (-1)
 10 // dump an array
 11 void dump(int arr[],int cnt)
 12 {
 13     for(int i=0;i<cnt;i++){
 14         cout<<arr[i]<<" ";
 15     }
 16     cout<<endl;
 17 }
 18
 19 // ensure the max heap time=O(lg(n))
 20 void max_heapify(int arr[],const int size,const int index)
 21 {
 22     int l=LEFT(index),r=RIGHT(index),largest = index;
 23     if(l<=size && arr[l-1] > arr[index-1])largest=l;
 24     if(r<=size && arr[r-1] > arr[largest-1])largest=r;
 25     if(largest != index)
 26     {
 27         int tmp = arr[largest-1];
 28         arr[largest-1] = arr[index-1];
 29         arr[index-1] = tmp;
 30         max_heapify(arr,size,largest);
 31     }
 32 }
 33
 34 // build max_heap,time=O(n)
 35 // if index>size/2,arr[index] must be a leaf
 36 void build_max_heap(int arr[],const int size)
 37 {
 38     for(int i=size/2;i>0;i--)
 39     {
 40         max_heapify(arr,size,i);
 41     }
 42 }
 43
 44 // heap_sort,time=O(nlg(n))
 45 void heap_sort(int arr[],int size)
 46 {
 47     int tmp;
 48     for(int i=size;i>1;i--)
 49     {
 50         tmp = arr[0];
 51         arr[0] = arr[i-1];
 52         arr[i-1] = tmp;
 53         max_heapify(arr,--size,1);
 54     }
 55 }
 56
 57 // return max key of arr
 58 int top(int arr[],const int size)
 59 {
 60     return arr[0];
 61 }
 62
 63 // return max key of arr and delete it
 64 int pop(int arr[],int &size)
 65 {
 66     if(size < 1)return ERROR;
 67     int max = arr[0];
 68     arr[0] = arr[--size];
 69     max_heapify(arr,size,1);
 70     return max;
 71 }
 72
 73 // increase the key of i
 74 void heap_increase_key(int arr[],int i,int key)
 75 {
 76     if(key < arr[i-1])return;
 77     arr[i-1] = key;
 78     while(i>1 && arr[i-1]>arr[PARENT(i)-1])
 79     {
 80         int tmp = arr[i-1];
 81         arr[i-1] = arr[PARENT(i)-1];
 82         arr[PARENT(i)-1] = tmp;
 83         i = PARENT(i);
 84     }
 85 }
 86
 87 // insert into priority queue
 88 void insert(int arr[],int &size,int key)
 89 {
 90     size++;
 91     arr[size] = key-1;
 92     heap_increase_key(arr,size,key);
 93 }
 94 int main()
 95 {
 96     int n = 10;
 97     build_max_heap(arr,n);
 98     dump(arr,n);
 99     //heap_sort(arr,n);
100     //dump(arr,n);
101     pop(arr,n);
102     dump(arr,n);
103     insert(arr,n,13);
104     dump(arr,n);
105     return 0;
106 }

值得注意的是,堆排序中使用(i/2)表示父节点,(2*i)表示左节点,(2*i+1)表示右节点,所以这里面的 i 是从1开始计数的,而我们常见的数组是从0开始计数的,所以在调用[]取值操作时要记得下标-1