Create minimum-cost-to-make-at-least-one-valid-path-in-a-grid.py

Author: kamyu104

Python/minimum-cost-to-make-at-least-one-valid-path-in-a-grid.py

@@ -0,0 +1,32 @@
+# Time:  O(m * n)
+# Space: O(m * n)
+
+import collections
+
+
+class Solution(object):
+    def minCost(self, grid):
+        """
+        :type grid: List[List[int]]
+        :rtype: int
+        """
+        directions = [(0, 1), (0, -1), (1, 0), (-1, 0)]
+        R, C = len(grid), len(grid[0])
+        dq = collections.deque([(0, 0, 0)])
+        lookup = {(0, 0): 0}
+        while dq:
+            d, r, c = dq.popleft()
+            if r == R-1 and c == C-1:
+                return d
+            for nd, (dr, dc) in enumerate(directions, 1):
+                nr, nc = r+dr, c+dc
+                cost = 1-(nd == grid[r][c])
+                if not (0 <= nr < R and 0 <= nc < C and
+                        ((nr, nc) not in lookup or d+cost < lookup[nr, nc])):
+                    continue
+                lookup[nr, nc] = d+cost
+                if cost:
+                    dq.append((d+cost, nr, nc))
+                else:
+                    dq.appendleft((d, nr, nc))
+        return -1  # never reach here