[LeetCode]Range Sum Query 2D - Immutable

https://leetcode.com/problems/range-sum-query-2d-immutable/

DP，二维DP记录[0,0]到[i,j]的和，那么[a,b]到[c,d]的和就是dp[c][d] - dp[a - 1][d] - dp[c][b - 1] + dp[a - 1][b - 1]注意dp数组边界加一位，保证不用check边界条件。

初始化DP同样思路。

public class NumMatrix {    private int[][] dp;    public NumMatrix(int[][] matrix) {        if (matrix != null && matrix.length != 0) {            dp = new int[matrix.length + 1][matrix[0].length + 1];            for (int i = 1; i <= matrix.length; i++) {                for (int j = 1; j <= matrix[0].length; j++) {                    dp[i][j] = dp[i][j - 1] + dp[i - 1][j] - dp[i - 1][j - 1] + matrix[i - 1][j - 1];                }            }        }    }    public int sumRegion(int row1, int col1, int row2, int col2) {        return dp[row2 + 1][col2 + 1] - dp[row1][col2 + 1] - dp[row2 + 1][col1] + dp[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);