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47 lines
1.3 KiB
Plaintext
47 lines
1.3 KiB
Plaintext
---
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title: '62. Unique Paths'
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description: There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time
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icon: dot
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topics:
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- { name: "Math", slug: "math" }
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- { name: "Dynamic Programming", slug: "dynamic-programming" }
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- { name: "Combinatorics", slug: "combinatorics" }
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issue: "https://github.com/prdlk/leetcode/issues/166"
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sidebar:
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label: 'Unique Paths'
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badge: 'Medium'
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---
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### Example 1:
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- Input: `m = 3, n = 7`
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- Output: `28`
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### Example 2:
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- Input: `m = 3, n = 2`
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- Output: `3`
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- Explanation: From the top-left corner, there are a total of `3` ways to reach the bottom-right corner: `1`. Right -> Down -> Down `2`. Down -> Down -> Right `3`. Down -> Right -> Down
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### Constraints:
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- `1 <= m, n <= 100`
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## Solution
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```py
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class Solution:
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def uniquePaths(self, m: int, n: int) -> int:
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dp = [[0 for _ in range(n)] for _ in range(m)]
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for c in range(n):
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dp[0][c] = 1
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for r in range(m):
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dp[r][0] = 1
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for r in range(1, m):
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for c in range(1, n):
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dp[r][c] = dp[r - 1][c] + dp[r][c - 1]
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return dp[-1][-1]
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```
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