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