path-with-maximum-minimum-value

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1102. Path With Maximum Minimum Value (Medium)

Given a matrix of integers A with R rows and C columns, find the maximum score of a path starting at [0,0] and ending at [R-1,C-1].

The score of a path is the minimum value in that path.  For example, the value of the path 8 →  4 →  5 →  9 is 4.

A path moves some number of times from one visited cell to any neighbouring unvisited cell in one of the 4 cardinal directions (north, east, west, south).

 

Example 1:

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

Example 3:

Input: [[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

 

Note:

1. 1 <= R, C <= 100
2. 0 <= A[i][j] <= 10^9

Related Topics

[Depth-First Search] [Breadth-First Search] [Union Find] [Array] [Matrix] [Heap (Priority Queue)]

Hints

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.