对二维区域和检索

暴力法：
private int[][] data;

public NumMatrix(int[][] matrix) {
    data = matrix;
}

public int sumRegion(int row1, int col1, int row2, int col2) {
    int sum = 0;
    for (int r = row1; r <= row2; r++) {
        for (int c = col1; c <= col2; c++) {
            sum += data[r][c];
        }
    }
    return sum;
}

动规：
class NumMatrix {
    
    private int[][] dp;

    public NumMatrix(int[][] matrix) {
        if (matrix.length == 0 || matrix[0].length == 0) return;
        dp = new int[matrix.length][matrix[0].length + 1];
        
        for (int r = 0; r < matrix.length; r++) {
            for (int c = 0; c < matrix[0].length; c++) {
                dp[r][c + 1] = dp[r][c] + matrix[r][c];
            }
        }
    }
    将计算的过程分为两部分：
    public int sumRegion(int row1, int col1, int row2, int col2) {
        int sum = 0;
        for (int row = row1; row <= row2; row++) {
            sum += dp[row][col2 + 1] - dp[row][col1];
        }
        return sum;
    }
}