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How to Solve Maximize Spanning Tree Stability with Upgrades Problem
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LeetCode ProblemMaximize Spanning Tree Stability with Upgrades
You are given an integer n, representing n nodes numbered from 0 to n - 1 and a list of edges, where edges[i] = [ui, vi, si, musti]: You are also given an integer k, the maximum number of upgrades you can perform. Each upgrade doubles the strength of an edge, and each eligible edge (with musti == 0) can be upgraded at most once. The stability of a spanning tree is defined as the minimum strength score among all edges included in it. Return the maximum possible stability of any valid spanning tree. If it is impossible to connect all nodes, return -1. Note: A spanning tree of a graph with n nodes is a subset of the edges that connects all nodes together (i.e. the graph is connected) without forming any cycles, and uses exactly n - 1 edges.
Binary SearchGreedyUnion FindGraphMinimum Spanning Tree
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Problem Breakdown
Understanding the Maximize Spanning Tree Stability with Upgrades Problem
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Problem Statement
You are given an integer n, representing n nodes numbered from 0 to n - 1 and a list of edges, where edges[i] = [ui, vi, si, musti]: You are also given an integer k, the maximum number of upgrades you can perform. Each upgrade doubles the strength of an edge, and each eligible edge (with musti == 0) can be upgraded at most once. The stability of a spanning tree is defined as the minimum strength score among all edges included in it. Return the maximum possible stability of any valid spanning tree. If it is impossible to connect all nodes, return -1. Note: A spanning tree of a graph with n nodes is a subset of the edges that connects all nodes together (i.e. the graph is connected) without forming any cycles, and uses exactly n - 1 edges.
HardProblem #3600
LeetCodeMaximize Spanning Tree Stability with Upgrades
Related Topics
Binary SearchGreedyUnion FindGraphMinimum Spanning Tree
How Phantom Code Helps
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Examples
# Example 1
Input
n = 3, edges = [[0,1,2,1],[1,2,3,0]], k = 1
Output
2
# Example 2
Input
n = 3, edges = [[0,1,4,0],[1,2,3,0],[0,2,1,0]], k = 2
Output
6
# Example 3
Input
n = 3, edges = [[0,1,1,1],[1,2,1,1],[2,0,1,1]], k = 0
Output
-1
Constraints
2 <= n <= 105
1 <= edges.length <= 105
edges[i] = [ui, vi, si, musti]
0 <= ui, vi < n
ui != vi
1 <= si <= 105
musti is either 0 or 1.
0 <= k <= n
There are no duplicate edges.
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Frequently Asked Questions
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Phantom Code catches common mistakes like off-by-one errors, missing edge cases, incorrect base conditions, and suboptimal approaches. It provides clean, well-structured code that handles all edge cases.
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The AI provides structured guidance: first the approach (what algorithm/data structure to use and why), then the implementation with clean code, and finally complexity analysis. This helps you think clearly even under pressure.
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