Is Path With Maximum Minimum Value easy or hard?

The problem is rated Medium because the grid traversal itself is straightforward, but recognizing the max-min optimization requires a greedy insight. Understanding Dijkstra-style traversal or Union-Find threshold activation is the key challenge.

How to solve Path With Maximum Minimum Value in O(mn log(mn))?

Use a priority queue to always process the highest-value cell first. Maintain the minimum value seen along the current path and mark visited cells to avoid revisiting them. When the bottom-right cell is reached, the recorded minimum value is the maximum possible path score.

What is the best approach for Path With Maximum Minimum Value?

The most common approach uses a max heap (priority queue) to perform a Dijkstra-style traversal on the grid. Always expand the cell with the highest value and track the minimum value along the path. This guarantees the optimal answer when the destination is reached, with time complexity O(mn log(mn)) and space complexity O(mn).

Is Path With Maximum Minimum Value asked at Google/Amazon/Meta?

Path With Maximum Minimum Value appears in interview prep lists for companies like Google, Amazon, and Meta because it combines graph traversal with greedy reasoning. It tests understanding of priority queues, grid graphs, and connectivity strategies such as Union-Find.

What data structure is used in Path With Maximum Minimum Value?

The main data structures are a max heap (priority queue) for greedy traversal and Union-Find for connectivity tracking. The grid itself is treated as a graph where each cell connects to its four neighbors.

What is the time complexity of Path With Maximum Minimum Value?

Both common optimal solutions run in O(mn log(mn)) time for an m × n grid. The heap-based search performs priority queue operations for each cell, while the Union-Find approach sorts all cells and performs near-constant union operations.

Path With Maximum Minimum Value Python or Java solution approach?

In Python or Java, the typical implementation uses a priority queue. Python uses heapq with negated values to simulate a max heap, while Java uses PriorityQueue with a custom comparator. Both implementations run in O(mn log(mn)) time and require O(mn) space.

Description Hints 5 Solution Video 11:35

1102. Path With Maximum Minimum Value

Medium54.6% acceptance3 companiesPremium elsewhere, free here

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.

For example, the score of the path 8 → 4 → 5 → 9 is 4.

Example 1:

Input: grid = [[5,4,5],[1,2,6],[7,4,6]]
Output: 4
Explanation: The path with the maximum score is highlighted in yellow.

Example 2:

Input: grid = [[2,2,1,2,2,2],[1,2,2,2,1,2]]
Output: 2

Example 3:

Input: grid = [[3,4,6,3,4],[0,2,1,1,7],[8,8,3,2,7],[3,2,4,9,8],[4,1,2,0,0],[4,6,5,4,3]]
Output: 3

Constraints:

m == grid.length
n == grid[i].length
1 <= m, n <= 100
0 <= grid[i][j] <= 10⁹

Asked at 3 companies

Geico

Google Amazon

Topics

Hints open one at a time

Hint 1

What if we sort each cell of the matrix by the value?

Hint 2

Don't include small values in your path if you can only include large values.

Hint 3

Let's keep adding a possible cell to use in the path incrementally with decreasing values.

Hint 4

If the start and end cells are connected then we don't need to add more cells.

Hint 5

Use union-find data structure to check connectivity and return as answer the value of the given cell that makes start and end cells connected.

11:35

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