Problem Statement

Given a 2D matrix matrix, handle multiple queries of the following type:

1. Calculate the sum of the elements of matrix inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

Implement the NumMatrix class:

• NumMatrix(int[][] matrix) Initializes the object with the integer matrix matrix.
• int sumRegion(int row1, int col1, int row2, int col2) Returns the sum of the elements of matrix inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

Example 1:

Input
["NumMatrix", "sumRegion", "sumRegion", "sumRegion"]
[[[[3, 0, 1, 4, 2], [5, 6, 3, 2, 1], [1, 2, 0, 1, 5], [4, 1, 0, 1, 7], [1, 0, 3, 0, 5]]], [2, 1, 4, 3], [1, 1, 2, 2], [1, 2, 2, 4]]
Output
[null, 8, 11, 12]

Explanation
NumMatrix numMatrix = new NumMatrix([[3, 0, 1, 4, 2], [5, 6, 3, 2, 1], [1, 2, 0, 1, 5], [4, 1, 0, 1, 7], [1, 0, 3, 0, 5]]);
numMatrix.sumRegion(2, 1, 4, 3); // return 8 (i.e sum of the red rectangle)
numMatrix.sumRegion(1, 1, 2, 2); // return 11 (i.e sum of the green rectangle)
numMatrix.sumRegion(1, 2, 2, 4); // return 12 (i.e sum of the blue rectangle)

Problem Link

Range Sum Query 2D - Immutable - LeetCode

Reference Video

https://www.youtube.com/watch?v=PwDqpOMwg6U&list=PLrmLmBdmIlpsHaNTPP_jHHDx_os9ItYXr&index=41&t=1s&ab_channel=TusharRoy-CodingMadeSimple

Code

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