2D prefix sum submatrix
How to calculate prefix and matrix:
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+
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+
How to use the prefix sum matrix to calculate the sum of a certain submatrix:
Such as seeking: [x1y1, x2, y2] sub-matrix sum, Sx2, y2-Sx2, y-1-Sx1-1, y2+Sx1-1, y1-1
Examples and code templates:
sum of submatrices
Input an integer matrix with n rows and m columns, and then input q queries, each query contains four integers x1, y1, x2, y2, representing the coordinates of the upper left corner and the lower right corner of a sub-matrix.
For each query output the sum of all numbers in the submatrix.
Input format
The first line contains three integers n, m, q.
The next n lines, each containing m integers, represent an integer matrix.
Next q lines, each line contains four integers x1, y1, x2, y2, representing a set of queries.
Output format
There are q lines in total, and each line outputs a query result.
Data range
1≤n, m≤1000,
1≤q≤200000,
1≤x1≤x2≤n,
1≤y1≤y2≤m,
−1000≤value of elements in the matrix≤1000
Input sample:
3 4 3
1 7 2 4
3 6 2 8
2 1 2 3
1 1 2 2
2 1 3 4
1 3 3 4
Sample output:
17
27
21
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int N=1007;
int n,m,q;
int a[N][N];
int main(){
scanf("%d%d%d",&n,&m,&q);
for(int i=1;i<=n;i++){
for(int j=1;j<=m;j++){
scanf("%d",&a[i][j]);
a[i][j]=a[i-1][j]+a[i][j-1]+a[i][j]-a[i-1][j-1];
}
}
while(q--){
int x1,x2,y1,y2;
scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
printf("%d\n",a[x2][y2]-a[x2][y1-1]-a[x1-1][y2]+a[x1-1][y1-1]);
}
return 0;
}