LeetCode 3419: Minimize the Maximum Edge Weight of Graph Solution
Master LeetCode problem 3419 (Minimize the Maximum Edge Weight of Graph), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.
3419. Minimize the Maximum Edge Weight of Graph
Problem Explanation
Explanation
To solve this problem, we can use binary search to find the minimum possible value of the maximum edge weight. We will define a function isPossible that checks if it is possible to remove edges such that node 0 is reachable from all other nodes and the maximum edge weight is less than or equal to a given threshold. If it is possible, we update our binary search range to look for a smaller maximum edge weight. Otherwise, we look for a larger maximum edge weight.
We start by sorting the edges based on their weights in ascending order. Then, we perform binary search over the range of edge weights. For each weight in the binary search, we use a union-find data structure to keep track of the connected components and check if it is possible to satisfy the given conditions.
The time complexity of this approach is O(E log W + E * alpha(V)), where E is the number of edges, W is the maximum edge weight, and alpha(V) is the inverse Ackermann function. The space complexity is O(V), where V is the number of nodes.
Solution Code
class Solution {
public int minimizeTheMaximumEdgeWeight(int n, int[][] edges, int threshold) {
Arrays.sort(edges, (a, b) -> a[2] - b[2]);
int left = 1, right = 1000000;
int result = -1;
while (left <= right) {
int mid = left + (right - left) / 2;
if (isPossible(n, edges, threshold, mid)) {
result = mid;
right = mid - 1;
} else {
left = mid + 1;
}
}
return result;
}
private boolean isPossible(int n, int[][] edges, int threshold, int maxWeight) {
UnionFind uf = new UnionFind(n);
int count = n - 1;
for (int[] edge : edges) {
if (edge[2] <= maxWeight) {
if (uf.union(edge[0], edge[1])) {
count--;
}
}
}
return count <= threshold;
}
class UnionFind {
int[] parent;
public UnionFind(int n) {
parent = new int[n];
for (int i = 0; i < n; i++) {
parent[i] = i;
}
}
public int find(int x) {
if (parent[x] != x) {
parent[x] = find(parent[x]);
}
return parent[x];
}
public boolean union(int x, int y) {
int rootX = find(x);
int rootY = find(y);
if (rootX == rootY) {
return false;
}
parent[rootX] = rootY;
return true;
}
}
}Try It Yourself
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