卖萌的弱渣

I am stupid, I am hungry.

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?

Note

m and n will be at most 100.

Solution

  • Java:
(Unique-Paths.java) download
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public class Solution {
    public int uniquePaths(int m, int n) {
        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];
        }
}
(Unique-Paths.py) download
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class Solution(object):
    def uniquePaths(self, m, n):
        """
        :type m: int
        :type n: int
        :rtype: int
        """
        if m<=0 or n <=0:
            return 0

        dp = [[0] * (n+1) for i in range(m+1)]
        # make the first row as 1
        for i in range(n+1):
            dp[1][i] = 1
        # dp starts from the second row
        for i in range (2,m+1):
            for j in range(1,n+1):
                dp[i][j] = max(dp[i-1][j],dp[i][j-1]
        return dp[m][n]