题目描述

A robot is located at the top-left corner of a m x n grid (marked ‘Start’ in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked ‘Finish’ in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

分析

构造二维数组dp[m][n]，其中

dp[i][j]={dp[i−1][j]+dp[i][j−1],1,i≠1且j≠1i=1或j=1

其中dp[m-1][n-1]就是结果。

代码

    public static int uniquePaths(int m, int n) {

        if (m <= 0 || n <= 0) {
            return 0;
        }

        int[][] dp = new int[m][n];

        for (int y = 0; y < n; y++) {
            dp[0][y] = 1;
        }

        for (int x = 0; x < m; x++) {
            dp[x][0] = 1;
        }

        for (int y = 1; y < n; y++) {
            for (int x = 1; x < m; x++) {
                dp[x][y] = dp[x - 1][y] + dp[x][y - 1];
            }
        }

        return dp[m - 1][n - 1];
    }