Leetcode #2371: Minimize Maximum Value in a Grid
In this guide, we solve Leetcode #2371 Minimize Maximum Value in a Grid 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
You are given an m x n integer matrix grid containing distinct positive integers. You have to replace each integer in the matrix with a positive integer satisfying the following conditions: The relative order of every two elements that are in the same row or column should stay the same after the replacements.
Quick Facts
- Difficulty: Hard
- Premium: Yes
- Tags: Union Find, Graph, Topological Sort, Array, Matrix, Sorting
Intuition
The data forms a graph, so we should explore nodes and edges systematically.
A traversal ensures we visit each node once while maintaining the needed state.
Approach
Build an adjacency list and traverse with BFS or DFS.
Aggregate results as you visit nodes.
Steps:
- Build the graph.
- Traverse with BFS/DFS.
- Accumulate the required output.
Example
Input: grid = [[3,1],[2,5]]
Output: [[2,1],[1,2]]
Explanation: The above diagram shows a valid replacement.
The maximum number in the matrix is 2. It can be shown that no smaller value can be obtained.
Python Solution
class Solution:
def minScore(self, grid: List[List[int]]) -> List[List[int]]:
m, n = len(grid), len(grid[0])
nums = [(v, i, j) for i, row in enumerate(grid) for j, v in enumerate(row)]
nums.sort()
row_max = [0] * m
col_max = [0] * n
ans = [[0] * n for _ in range(m)]
for _, i, j in nums:
ans[i][j] = max(row_max[i], col_max[j]) + 1
row_max[i] = col_max[j] = ans[i][j]
return ans
Complexity
The time complexity is O(V+E). The space complexity is O(V).
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.