304. Range Sum Query 2D - Immutable

You can extend the previous problem

3070. Count Submatrices with Top-Left Element and Sum Less Than k

and use the same concept to arrive at

class NumMatrix {
public:
    vector<vector<int>>dp;
    NumMatrix(vector<vector<int>>& matrix) {
        int n = matrix.size();
        int m = matrix[0].size();
        dp = vector<vector<int>>(n, vector<int>(m,0));
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(i==0 && j==0) dp[i][j] = matrix[i][j];
                else if(i==0) dp[i][j] = dp[i][j-1] + matrix[i][j];
                else if(j==0) dp[i][j] = dp[i-1][j] + matrix[i][j];
                else dp[i][j] = dp[i-1][j] + dp[i][j-1] - dp[i-1][j-1] + matrix[i][j];
            }
        }
 
    }
    
    int sumRegion(int row1, int col1, int row2, int col2) {
        int result = dp[row2][col2];
        if(row1>0) result-= dp[row1-1][col2];
        if(col1>0) result-=dp[row2][col1-1];
        if(row1>0 && col1>0) result += dp[row1-1][col1-1];
        return result;
    }
};
 
/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix* obj = new NumMatrix(matrix);
 * int param_1 = obj->sumRegion(row1,col1,row2,col2);
 */

or if you do not want to handle the edge cases

class NumMatrix {
public:
    vector<vector<int>> sum;
    NumMatrix(vector<vector<int>>& matrix) {
        int m = matrix.size(), 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 - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1] + matrix[i - 1][j - 1];
            }
        }
    }
    int sumRegion(int r1, int c1, int r2, int c2) {
        r1++; c1++; r2++; c2++;
        return sum[r2][c2] -  sum[r1 - 1][c2] - sum[r2][c1 - 1]  + sum[r1 - 1][c1 - 1];
    }
};