offer2-13

给定一个二维矩阵 matrix，以下类型的多个请求：

• 计算其子矩形范围内元素的总和，该子矩阵的左上角为 (row1, col1) ，右下角为 (row2, col2) 。

实现 NumMatrix 类：

• NumMatrix(int[][] matrix) 给定整数矩阵 matrix 进行初始化
• int sumRegion(int row1, int col1, int row2, int col2) 返回左上角 (row1, col1) 、右下角 (row2, col2) 的子矩阵的元素总和。

示例 1：

输入: 
["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]]
输出: 
[null, 8, 11, 12]

解释:
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 (红色矩形框的元素总和)
numMatrix.sumRegion(1, 1, 2, 2); // return 11 (绿色矩形框的元素总和)
numMatrix.sumRegion(1, 2, 2, 4); // return 12 (蓝色矩形框的元素总和)

提示：

• m == matrix.length
• n == matrix[i].length
• 1 <= m, n <= 200
• -105 <= matrix[i][j] <= 105
• 0 <= row1 <= row2 < m
• 0 <= col1 <= col2 < n
• 最多调用 104 次 sumRegion 方法

//leetcode submit region begin(Prohibit modification and deletion)
class NumMatrix {

    private int[][] sum;

    public NumMatrix(int[][] matrix) {
        sum = matrix;

        if (sum != null) {
            for (int i = 1; i < sum.length; i++) {
                sum[i][0] = sum[i - 1][0] + sum[i][0];
            }
            for (int i = 1; i < sum[0].length; i++) {
                sum[0][i] = sum[0][i - 1] + sum[0][i];
            }

            for (int i = 1; i < sum.length; i++) {
                for (int j = 1; j < sum[0].length; j++) {
                    sum[i][j] = sum[i][j] + sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1];
                }
            }
        }
    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        if (sum == null || row1 < 0 || col1 < 0 || row1 > row2 || col1 > col2 || row2 >= sum.length || col2 >= sum[0].length) {
            return 0;
        }

        int result = sum[row2][col2];

        if (row1 > 0) {
            result -=  sum[row1 - 1][col2];
        }
        if (col1 > 0) {
            result -=  sum[row2][col1 - 1];
        }
        if (row1 > 0 && col1 > 0) {
            result += sum[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);
 */
//leetcode submit region end(Prohibit modification and deletion)