Leetcode #1102: Path With Maximum Minimum Value
In this guide, we solve Leetcode #1102 Path With Maximum Minimum Value in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given an m x n integer matrix grid, return the maximum score of a path starting at (0, 0) and ending at (m - 1, n - 1) moving in the 4 cardinal directions. The score of a path is the minimum value in that path.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Depth-First Search, Breadth-First Search, Union Find, Array, Binary Search, Matrix, Heap (Priority Queue)
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: grid = [[5,4,5],[1,2,6],[7,4,6]]
Output: 4
Explanation: The path with the maximum score is highlighted in yellow.
Python Solution
class Solution:
def maximumMinimumPath(self, grid: List[List[int]]) -> int:
def find(x: int) -> int:
if p[x] != x:
p[x] = find(p[x])
return p[x]
m, n = len(grid), len(grid[0])
p = list(range(m * n))
q = [(v, i, j) for i, row in enumerate(grid) for j, v in enumerate(row)]
q.sort()
ans = 0
dirs = (-1, 0, 1, 0, -1)
vis = set()
while find(0) != find(m * n - 1):
v, i, j = q.pop()
ans = v
vis.add((i, j))
for a, b in pairwise(dirs):
x, y = i + a, j + b
if (x, y) in vis:
p[find(i * n + j)] = find(x * n + y)
return ans
Complexity
The time complexity is , where and are the number of rows and columns of the matrix, respectively. The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.