RangeSumQuery2DImmutable.java

package medium;
/**
 * ClassName: RangeSumQuery2DImmutable.java
 * Author: chenyiAlone
 * Create Time: 2019/5/21 14:46
 * Description: No.304
 * 思路:
 *
 *
 * 1. 状态转移 sum[i + 1][j + 1] = sum[i + 1][j] + matrix[i][j] + sum[i][j + 1] - sum[i][j];
 *
 * +-------------+x
 * |             |x
 * |             |x
 * +-------------+o
 * ps: 用 o 的 2D 前缀和减去前面的 + 的前缀和就能得到这一列的和
 *
 * 2. 结果 sum[row2 + 1][col2 + 1] - sum[row1][col2 + 1] - sum[row2 + 1][col1] + sum[row1][col1]
 *
 * +---------+----------+
 * |         |          |
 * |  area   |  area1   |
 * |         |          |
 * |         |          |
 * +--------------------+
 * |         |xxxxxxxxxx|
 * |         |xxxxxxxxxx|
 * |  area2  |xxxxxxxxxx|
 * |         |xxxxxxxxxx|
 * |         |xxxxxxxxxx|
 * +--------------------+
 *
 *
 * 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).
 *
 * Range Sum Query 2D
 * 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.
 *
 */
public class RangeSumQuery2DImmutable {
    private int[][] sum;

    public RangeSumQuery2DImmutable(int[][] matrix) {
        if (matrix.length == 0 || matrix[0].length == 0)
            return;
        int m = matrix.length;
        int n = matrix[0].length;
        sum = new int[m + 1][n + 1];
        for (int i = 0; i < m; i++)
            for (int j = 0; j < n; j++)
                sum[i + 1][j + 1] = sum[i + 1][j] + matrix[i][j] + sum[i][j + 1] - sum[i][j];
    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        if (sum == null)
            return 0;
        return sum[row2 + 1][col2 + 1] - sum[row1][col2 + 1] - sum[row2 + 1][col1] + sum[row1][col1];
    }
}

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