Time: 9455 ms (100%), Space: 32.5 MB (100%) - LeetHub

Author: hogan-tech

3986-maximum-path-score-in-a-grid/3986-maximum-path-score-in-a-grid.py

@@ -0,0 +1,49 @@
+# time complexity: O(m*n*k)
+# space complexity: O(m*n*k)
+from typing import List
+
+
+class Solution:
+    def maxPathScore(self, grid: List[List[int]], k: int) -> int:
+        ROW, COL = len(grid), len(grid[0])
+
+        dp = [[[-10**9 for _ in range(k + 1)]
+               for _ in range(COL)] for _ in range(ROW)]
+
+        startVal = grid[0][0]
+        startCost = 1 if startVal in (1, 2) else 0
+        if startCost <= k:
+            dp[0][0][startCost] = startVal
+
+        for r in range(ROW):
+            for c in range(COL):
+                for i in range(k + 1):
+                    if dp[r][c][i] < 0:
+                        continue
+                    if c + 1 < COL:
+                        val = grid[r][c + 1]
+                        newCost = i + (1 if val in (1, 2) else 0)
+                        if newCost <= k:
+                            dp[r][c + 1][newCost] = max(dp[r]
+                                                        [c + 1][newCost], dp[r][c][i] + val)
+                    if r + 1 < ROW:
+                        val = grid[r + 1][c]
+                        newCost = i + (1 if val in (1, 2) else 0)
+                        if newCost <= k:
+                            dp[r + 1][c][newCost] = max(dp[r + 1]
+                                                        [c][newCost], dp[r][c][i] + val)
+
+        result = -1
+        for i in range(k + 1):
+            if dp[ROW - 1][COL - 1][i] >= 0:
+                result = max(result, dp[ROW - 1][COL - 1][i])
+
+        return result if result >= 0 else -1
+
+
+grid = [[0, 1], [2, 0]]
+k = 1
+print(Solution().maxPathScore(grid, k))
+grid = [[0, 1], [1, 2]]
+k = 1
+print(Solution().maxPathScore(grid, k))