path-with-minimum-effort py3

1753_path-with-minimum-effort/python3/bfs_binary_search.py

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+# Time: O(M · N)
+# Space: O(M · N)
+from collections import deque
+
+class Solution:
+    def minimumEffortPath(self, heights: List[List[int]]) -> int:
+        '''
+        BFS + Binary Search
+        
+        Give attention to definition of minimum effort in the problem.
+        It's not the total across the path, but just between two 
+        adjacent allowed cells.
+        '''
+        nrows, ncols = len(heights), len(heights[0])
+        
+        def can_reach_destination(mid):
+            '''
+            Do BFS traversing min paths
+            '''
+            visited = set()
+            q = deque([(0, 0)])
+            destination = (nrows - 1, ncols - 1)
+            
+            while q:
+                x, y = q.popleft()
+                
+                # See if we reached the destination
+                if (x, y) == destination:
+                    return True
+                
+                visited.add((x, y))
+                
+                dirs = [
+                    (0, 1),    # Right
+                    (0, -1),  # Left
+                    (1, 0),   # Bottom
+                    (-1, 0)   # Top
+                ]
+                
+                for dx, dy in dirs:
+                    adj_x = x + dx
+                    adj_y = y + dy
+                    
+                    if 0 <= adj_x < nrows and 0 <= adj_y < ncols and (adj_x, adj_y) not in visited:
+                        if abs(heights[x][y] - heights[adj_x][adj_y]) <= mid:
+                            visited.add((adj_x, adj_y))
+                            q.append((adj_x, adj_y))
+            
+            return False
+        
+        left = 0
+        right = 1e6  # As provided in the problem statement
+        
+        # Perform binary search
+        while left < right:
+            mid = (left + right) // 2
+            
+            # The answer could either be mid or an effort value
+            # lower than mid
+            if can_reach_destination(mid):
+                right = mid
+            else:
+                left = mid + 1
+        
+        return int(left)