Leetcode 62. Unique Paths

题目：

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.

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• Total Accepted: 127048
• Total Submissions: 319022
• Difficulty: Medium
• Contributors: Admin

思路：

采用动态规划，路径中，到这个点的方式等于到它左边点的方式加上到右边点的方式

path[i][j] = path[i-1][j] + path[j-1][i]

是一道典型的动态规划题目

代码：

public class Solution {
    public int uniquePaths(int m, int n) {
        int path[][] = new int[m][n];
        for(int i = 0; i < m; ++ i) {
        	path[i][0] = 1;
        }
        for(int j = 0; j < n; ++ j) {
        	path[0][j] = 1;
        }
        for(int i = 1; i < m; ++ i) {
        	for (int j = 1; j < n; ++ j) {
        		path[i][j] = path[i][j-1] + path[i-1][j];
        	}
        }
        return path[m-1][n-1];
    }
}