树状数组基础

Posted 2020-09-02 wolf940509

关于树状数组的讲解推荐《算法竞赛入门经典训练指南》

一维版本：

洛谷3374

分析：树状数组裸的模板题

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 using namespace std;
 5 const int maxn=500000+10;
 6 int c[maxn];
 7 int n,m;
 8 int lowbit(int x){
 9     return x&(-x);
10 }
11 void add(int x,int d){
12     while(x<=n){
13         c[x]+=d; x+=lowbit(x);
14     }
15 }
16 int sum(int x){
17     int ret=0;
18     while(x>0){
19         ret+=c[x]; x-=lowbit(x);
20     }
21     return ret;
22 }
23 int main()
24 {
25     cin>>n>>m;
26     memset(c,0,sizeof(c));
27     for(int i=1;i<=n;i++){
28         int x;
29         scanf("%d",&x);
30         add(i,x);
31     }
32     while(m--){
33         int num,a,b;
34         scanf("%d%d%d",&num,&a,&b);
35         if(num==1){
36             add(a,b);
37         }else{
38             printf("%d\\n",sum(b)-sum(a-1));
39         }
40     }
41     return 0;
42 }

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 二维版本：

vijos1512

分析：二维树状数组的裸题，注意面积的计算

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<string>
 5 #include<cmath>
 6 using namespace std;
 7 const int maxn=2000;
 8 int c[maxn][maxn];
 9 int n,m;
10 int lowbit(int x){
11     return x&(-x);
12 }
13 void add(int x,int y,int d){
14     for(int i=x;i<=n;i+=lowbit(i))
15         for(int j=y;j<=n;j+=lowbit(j))
16             c[i][j]+=d;
17 }
18 int sum(int x,int y){
19     int ret=0;
20     for(int i=x;i>0;i-=lowbit(i))
21         for(int j=y;j>0;j-=lowbit(j))
22             ret+=c[i][j];
23     return ret;
24 }
25 int main()
26 {
27     scanf("%d",&n);
28     memset(c,0,sizeof(c));
29     while(scanf("%d",&m)!=EOF){
30         if(m==3) break;
31         if(m==1){
32             int x,y,k;
33             scanf("%d%d%d",&x,&y,&k);
34             add(x+1,y+1,k);
35         }else{
36             int x1,y1,x2,y2;
37             scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
38             int cnt=sum(x2+1,y2+1)-sum(x1,y2+1)-sum(x2+1,y1)+sum(x1,y1);
39             printf("%d\\n",cnt);
40         }
41     }
42     return 0;
43 }

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