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41 lines
1.1 KiB
Plaintext
41 lines
1.1 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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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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row = [1] * n
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for i in range(m - 1):
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newRow = [1] * n
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for j in range(n - 2, -1, -1):
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newRow[j] = newRow[j + 1] + row[j]
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row = newRow
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return row[0]
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```
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