How do you solve Minimize Maximum Component Cost on LeetCode?

Minimize Maximum Component Cost (LeetCode #3613) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(E log E + E α(N)) time complexity and O(N) space complexity. Key insight: Binary search helps narrow down the maximum cost efficiently.

What is the time complexity of Minimize Maximum Component Cost?

The optimal solution for Minimize Maximum Component Cost runs in O(E log E + E α(N)) time and uses O(N) space. Sorting edges takes O(E log E), and union-find operations are nearly constant time due to path compression.

What is the brute force solution for Minimize Maximum Component Cost?

The brute force approach for Minimize Maximum Component Cost is Brute Force, with O(n²) time complexity and O(1) space complexity. Try every possible combination of edge removals to check the resulting maximum component cost. This is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(E log E + E α(N)).

What algorithm or data structure is used to solve Minimize Maximum Component Cost?

Minimize Maximum Component Cost uses the following concepts: Binary Search, Union-Find, Graph Theory, Sorting. The recommended patterns to study are: Binary Search, Union-Find.

What are the interview tips for Minimize Maximum Component Cost?

Explain your thought process clearly. Discuss trade-offs between brute force and optimal solutions. Practice edge cases and their handling.

What are common mistakes when solving Minimize Maximum Component Cost?

Not sorting edges before binary search. Incorrectly implementing union-find operations.

#3613

Minimize Maximum Component Cost

Medium

Binary SearchUnion-FindGraph TheorySortingBinary SearchUnion-Find

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(E log E + E α(N))
Space	O(1)	O(N)

💡

Intuition

Time O(E log E + E α(N))Space O(N)

Use binary search on the maximum edge weight and a union-find structure to efficiently count components.

⚙️

Algorithm

3 steps

1Step 1: Sort edges by weight.
2Step 2: Perform binary search on the edge weights, checking if we can form at most k components with edges <= mid.
3Step 3: Use union-find to track connected components during the check.

solution.py24 lines

1def minMaxCost(n, edges, k):
2    edges.sort(key=lambda x: x[2])
3    def canFormComponents(maxWeight):
4        parent = list(range(n))
5        def find(x):
6            if parent[x] != x:
7                parent[x] = find(parent[x])
8            return parent[x]
9        count = n
10        for u, v, w in edges:
11            if w <= maxWeight:
12                rootU, rootV = find(u), find(v)
13                if rootU != rootV:
14                    parent[rootU] = rootV
15                    count -= 1
16        return count <= k
17    low, high = 0, edges[-1][2]
18    while low < high:
19        mid = (low + high) // 2
20        if canFormComponents(mid):
21            high = mid
22        else:
23            low = mid + 1
24    return low

ℹ

Complexity note: Sorting edges takes O(E log E), and union-find operations are nearly constant time due to path compression.

1Binary search helps narrow down the maximum cost efficiently.
2Union-Find allows quick component counting.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.