详细解释见小结。http://blog.csdn.net/zmx354/article/details/31740985

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <queue>
#include <cmath>
#include <stack>
#include <map>#pragma comment(linker, "/STACK:1024000000");
#define EPS (1e-8)
#define LL long long
#define ULL unsigned long long
#define _LL __int64
#define _INF 0x3f3f3f3f
#define Mod 9999991
#define lowbit(x) (x&(-x))using namespace std;const int N = 2049;int a[N][N];
int ax[N][N];
int ay[N][N];
int axy[N][N];void Updata(int a[N][N],int x,int y,int n,int m,int data)
{for(; x <= n; x += lowbit(x)){for(int t = y; t <= m; t += lowbit(t)){a[x][t] += data;}}
}int Query(int a[N][N],int x,int y)
{int sum = 0;while(x > 0){for(int t = y; t > 0; t -= lowbit(t)){sum += a[x][t];}x -= lowbit(x);}return sum;
}int sum(int x,int y)
{return Query(a,x,y)*(x+1)*(y+1) - (y+1)*Query(ax,x,y) - (x+1)*Query(ay,x,y) + Query(axy,x,y);
}void Add(int x1,int y1,int x2,int y2,int n,int m,int data)
{Updata(a,x1,y1,n,m,data);Updata(a,x2+1,y1,n,m,-data);Updata(a,x1,y2+1,n,m,-data);Updata(a,x2+1,y2+1,n,m,data);Updata(ax,x1,y1,n,m,x1*data);Updata(ax,x2+1,y1,n,m,-(x2+1)*data);Updata(ax,x1,y2+1,n,m,-x1*data);Updata(ax,x2+1,y2+1,n,m,(x2+1)*data);Updata(ay,x1,y1,n,m,y1*data);Updata(ay,x2+1,y1,n,m,-y1*data);Updata(ay,x1,y2+1,n,m,-(y2+1)*data);Updata(ay,x2+1,y2+1,n,m,(y2+1)*data);Updata(axy,x1,y1,n,m,x1*y1*data);Updata(axy,x2+1,y1,n,m,-(x2+1)*y1*data);Updata(axy,x1,y2+1,n,m,-x1*(y2+1)*data);Updata(axy,x2+1,y2+1,n,m,(x2+1)*(y2+1)*data);
}int main()
{int n,m;char order[10];int x1,x2,y1,y2,data;memset(a,0,sizeof(a));memset(ax,0,sizeof(ax));memset(ay,0,sizeof(ay));memset(axy,0,sizeof(axy));while(scanf("%s",order) != EOF){if(order[0] == 'L'){scanf("%d %d %d %d %d",&x1,&y1,&x2,&y2,&data);Add(x1,y1,x2,y2,n,m,data);}else if(order[0] == 'k'){scanf("%d %d %d %d",&x1,&y1,&x2,&y2);printf("%d\n",sum(x2,y2) - sum(x1-1,y2) - sum(x2,y1-1) + sum(x1-1,y1-1));}else{scanf("%d %d",&n,&m);}}return 0;
}