堆的初识

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堆的一个最大特点就是，它的每个节点的值都比它的子节点的值小，但是左右子节点值的大小不分。所以给定一个堆，我们能直接找出最小的值，但是我们无法直接找出所有值的从小到大序列。
3个操作:插入，删除，更新
1.插入
与父节点比较，进行dfs
2.删除，把heap[0]与最后一个元素交换以后，更新
3.更新，把该节点和其字节点比较尽心DFS

1. #include <iostream>
2. #include <string>
3. using namespace std;
4. int heap[1000000],hsize=0;
5. //root is 0
6. string o;
7. void dfs(int x)
8. {
9.     if(x>=hsize)return;
10.     if(2*x+1<hsize)cout<<heap[2*x+1]<<' ';
11.     if(2*x+2<hsize)cout<<heap[2*x+2]<<' ';
12.     dfs(2*x+1);
13.     dfs(2*x+2);
14. }
15. void insert(int n)
16. {
17.     int p,c=hsize;
18.     heap[hsize++]=n;
19.     p=(c-1)/2;
20.     while(c)
21.         {
22.             if(heap[p]>heap[c])
23.                 {
24.                     swap(heap[p],heap[c]);
25.                     c=p;
26.                     p=(c-1)/2;
27.                 }
28.             else return;
29.         }
30. }
31. void update(int p)
32. {
33.     if(2*p+1<hsize)//左节点
34.         {
35.             if(heap[p]>heap[2*p+1])
36.                 {
37.                     swap(heap[p],heap[2*p+1]);
38.                     update(2*p+1);
39.                 }
40.         }
41.     if(2*p+2<hsize)//右节点
42.         {
43.             if(heap[p]>heap[2*p+2])
44.                 {
45.                     swap(heap[p],heap[2*p+2]);
46.                     update(2*p+2);
47.                 }
48.         }
49.     if((p-1)/2>=0&&heap[(p-1)/2]>heap[p])//比父节点还小
50.         {
51.             swap(heap[(p-1)/2],heap[p]);
52.             update((p-1)/2);
53.         }
54. }
55. int del()
56. {
57.     int p=0,c,ret=heap[0];
58.     swap(heap[0],heap[--hsize]);
59.     update(0);
60.     return ret;
61. }
62. int main()
63. {
64.     int n,i,t,tmp;
65.     //freopen("D://in.txt","r",stdin);
66.     while(cin>>o)
67.         {
68.             //cout<<o<<':'<<endl;
69.             if(o=="add")cin>>n,insert(n);
70.             if(o=="display")cout<<heap[0]<<' ',dfs(0),cout<<endl;
71.             if(o=="delete")cout<<del()<<endl;
72.             if(o=="update")cin>>n,update(n);
73.             if(o=="heap")cin>>n>>tmp,heap[n]=tmp;
74.         }
75.     return 0;
76. }
77. /*
78. add 2
    add 10
    add 4
    add -7
    add 5
    add -9
    display
    delete
    display
    heap 3 -100000
    update 3
    display
    heap 2 1000000
    update 2
    display
    heap 5 -10000000
    update 5
    display
    
79. */