leetcode_gym/_problems/uniquePaths.md

layout, title, last_solved, category, leetcode_url, status

layout	title	last_solved	category	leetcode_url	status
page	Unique Paths	2020-06-29	dp	https://leetcode.com/problems/unique-paths/submissions/	Solved

Problem

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

 

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:

Input: m = 7, n = 3
Output: 28

Solution

{% highlight python %}

def uniquePaths(self, m: int, n: int) -> int:

dp = [[1]*(n) for x in range(m)]

for i in range(1, m):
    for j in range(1, n):
        dp[i][j] = dp[i][j-1] + dp[i-1][j]

print(dp)
return dp[-1][-1]

{% endhighlight %}