Two-dimensional prefix and template (DP, tolerance and exclusion principle)

The idea of ​​using DP and the principle of tolerance and exclusion.

• $s\left[i\right]\left[j\right]$ record from$\left[1\right]\left[1\right]$ arrival$\left[i\right]\left[j\right]$ The sum of the rectangular areas formed.
• 状态更新：$s[i][j]=s[i-1][j]+s[i][j-1]-s[i-1][j-1+g[i\left]\right[j]$ The subscript starts from 1
• Find $\left[x1\right]\left[y1\right]$ to$\left[x2\right][y2]\; and$ the rectangular area formed by:
  $area=s[x2][y2]-s[x1-1]\left[y2\right]-s[x2][y1-1]+s[x1-1][y1-1]$

class NumMatrix {
    
    
    vector<vector<int>> s; 
    int m = 0 , n = 0;
public:
    NumMatrix(vector<vector<int>>& g) {
    
    
        m = g.size()a
        if(m) n = g[0].size();
        if(n==0) return;
        s.resize(m+1,vector<int>(n+1,0)); 
        for(int i=1;i<=m;i++){
    
    
            for(int j=1;j<=n;j++){
    
    
                s[i][j] = s[i-1][j]+s[i][j-1]-s[i-1][j-1]+g[i-1][j-1];
            }
        }
    }
    
    int sumRegion(int x1, int y1, int x2, int y2) {
    
    
        if(n==0) return 0;
        x1++, y1++, x2++, y2++; // 下标从1开始
        return s[x2][y2]-s[x1-1][y2]-s[x2][y1-1]+s[x1-1][y1-1];
    }
};

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix* obj = new NumMatrix(matrix);
 * int param_1 = obj->sumRegion(row1,col1,row2,col2);
 */

Template questions: 304. Two-dimensional area and retrieval-matrix is ​​immutable