feat: complete lc-62

work/1/Medium/Math/62.unique-paths.py

@@ -0,0 +1,53 @@
+"""
+62. Unique Paths
+Difficulty: Medium
+https://leetcode.com/problems/unique-paths/
+
+──────────────────────────────────────────────────
+
+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.
+
+Given the two integers m and n, return the number of possible unique
+paths that the robot can take to reach the bottom-right corner.
+
+The test cases are generated so that the answer will be less than or
+equal to 2 * 10^9.
+
+
+
+Example 1:
+
+Input: m = 3, n = 7
+Output: 28
+
+Example 2:
+
+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 -> Down -> Down
+2. Down -> Down -> Right
+3. Down -> Right -> Down
+
+
+
+Constraints:
+
+        • 1 <= m, n <= 100
+"""
+
+
+class Solution:
+    def uniquePaths(self, m: int, n: int) -> int:
+        row = [1] * n
+
+        for i in range(m - 1):
+            newRow = [1] * n
+            for j in range(n - 2, -1, -1):
+                newRow[j] = newRow[j + 1] + row[j]
+            row = newRow
+        return row[0]