Question

Formatted question description: https://leetcode.ca/all/304.html

 304	Range Sum Query 2D - Immutable

 Given a 2D matrix matrix, find the sum of the elements inside the rectangle
 defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

 The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3),
 which contains sum = 8.

 Example:
 Given matrix = [
     [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]
 ]

 sumRegion(2, 1, 4, 3) -> 8
 sumRegion(1, 1, 2, 2) -> 11
 sumRegion(1, 2, 2, 4) -> 12

 Note:
     You may assume that the matrix does not change.
     There are many calls to sumRegion function.
     You may assume that row1 ≤ row2 and col1 ≤ col2.

Algorithm

Maintain a two-dimensional array dp, where dp[i][j] represents the sum of all the numbers in the cumulative interval (0, 0) to (i, j).

Then if we want to quickly find (r1 , c1) to (r2, c2) rectangular interval, only dp[r2][c2]-dp[r2][c1-1]-dp[r1-1][c2] + dp[r1-1 ][c1-1].

Code

Java

public class Range_Sum_Query_2D_Immutable {

    public class NumMatrix {
        private int[][] matrix;
        private int[][] sum;

        public NumMatrix(int[][] matrix) {
            this.matrix = matrix;

            if (matrix == null || matrix.length == 0) {
                return;
            }

            int m = matrix.length;
            int n = matrix[0].length;

            sum = new int[m + 1][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];
                }
            }
        }

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

// Your NumMatrix object will be instantiated and called as such:
// NumMatrix numMatrix = new NumMatrix(matrix);
// numMatrix.sumRegion(0, 1, 2, 3);
// numMatrix.sumRegion(1, 2, 3, 4);

}

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