Leetcode Unique Paths

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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解题思路： 

Dynamic Programming

就是570 discussion7 的第3题。

dp[i][j] = dp[i-1][j] + dp[i][j-1]

初始化第一行和第一列，dp[0][j] = dp[i][0] = 1

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Java code:

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

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Reference:

1. http://bangbingsyb.blogspot.com/2014/11/leetcode-unique-paths-i-ii.html