304. Range Sum Query 2D - Immutable

class NumMatrix {
 private int[][] prefixSum;

    public NumMatrix(int[][] matrix) {
        int m = matrix.length;
        int n = matrix[0].length;
        prefixSum = new int[m + 1][n + 1];

        
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                prefixSum[i][j] = matrix[i - 1][j - 1] 
                                + prefixSum[i - 1][j] 
                                + prefixSum[i][j - 1] 
                                - prefixSum[i - 1][j - 1];
            }
        }
    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        return prefixSum[row2 + 1][col2 + 1] 
             - prefixSum[row1][col2 + 1] 
             - prefixSum[row2 + 1][col1] 
             + prefixSum[row1][col1];
    }
}