304-range-sum-query-2d-immutable.cpp

class NumMatrix {
public:
    vector<vector<int>> sum;
    NumMatrix(vector<vector<int>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        
        sum =  vector<vector<int>>(m + 1, vector<int>(n + 1)); 
        
        for(int i=1;i<=m;i++){
            for(int j=1;j<=n;j++){
                sum[i][j]=sum[i][j-1]+sum[i-1][j]-sum[i-1][j-1]+matrix[i-1][j-1];
            }
        }
    }
    
    int sumRegion(int row1, int col1, int row2, int col2) {
        row1++;
        col1++;
        row2++;
        col2++;
        
        return sum[row2][col2]-sum[row2][col1-1]-sum[row1-1][col2]+sum[row1-1][col1-1];
    }
};

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