feat(work): add Minimum Path Sum & Longest Common Subsequence solutions; refactor Unique Paths DP implementation

work/1/Medium/Array/64.minimum-path-sum.py

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+"""
+64. Minimum Path Sum
+Difficulty: Medium
+https://leetcode.com/problems/minimum-path-sum/
+
+──────────────────────────────────────────────────
+
+Given a m x n grid filled with non-negative numbers, find a path from
+top left to bottom right, which minimizes the sum of all numbers along
+its path.
+
+Note: You can only move either down or right at any point in time.
+
+
+
+Example 1:
+
+Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
+Output: 7
+Explanation: Because the path 1 → 3 → 1 → 1 → 1
+minimizes the sum.
+
+Example 2:
+
+Input: grid = [[1,2,3],[4,5,6]]
+Output: 12
+
+
+
+Constraints:
+
+        • m == grid.length
+
+        • n == grid[i].length
+
+        • 1 <= m, n <= 200
+
+        • 0 <= grid[i][j] <= 200
+"""
+
+
+class Solution:
+    def minPathSum(self, grid: list[list[int]]) -> int:
+        if not grid or not grid[0]:
+            return 0
+
+        m = len(grid)
+        n = len(grid[0])
+        dp = [[0 for _ in range(n)] for _ in range(m)]
+
+        for c in range(n):
+            dp[0][c] = dp[0][c - 1] + grid[0][c] if c else grid[0][c]
+
+        for r in range(m):
+            dp[r][0] = dp[r - 1][0] + grid[r][0] if r else grid[r][0]
+
+        for r in range(1, m):
+            for c in range(1, n):
+                dp[r][c] = min(dp[r - 1][c], dp[r][c - 1]) + grid[r][c]
+
+        return dp[-1][-1]