Given a connected undirected weighted graph with N nodes and M edges. The task is to perform given queries and find the weight of the minimum spanning tree. Queries are of three types:
- query(1) -> Find the weight of the minimum spanning tree.
- query(2, x, y) -> Change the weight of the edge between the nodes x and y to 0.
- query(3, x, y) -> Restore the weight of the edge between the nodes x and y to its original weight.
query(2, 1, 2),
query(3, 1, 2),
query(2, 3, 4),
Approach: Let’s first compute MST of the initial graph before performing any queries and let T be this MST. The crucial observation is that at any point while handling the queries, the weight of the MST of the current graph can be computed by running Kruskal’s algorithm on edges with zero weight at this point and edges of T. So, keep edges with weight zero in a data structure and after query of type 2 and type 3 compute weight of minimum spanning tree.
Below is the implementation of the above approach:
- Find the minimum spanning tree with alternating colored edges
- Minimum Product Spanning Tree
- Kruskal's Minimum Spanning Tree using STL in C++
- Applications of Minimum Spanning Tree Problem
- Boruvka's algorithm for Minimum Spanning Tree
- Minimum spanning tree cost of given Graphs
- Reverse Delete Algorithm for Minimum Spanning Tree
- Prim’s Minimum Spanning Tree (MST) | Greedy Algo-5
- Kruskal’s Minimum Spanning Tree Algorithm | Greedy Algo-2
- Product of minimum edge weight between all pairs of a Tree
- Find minimum weight cycle in an undirected graph
- Count the nodes in the given tree whose weight is even
- Number of Paths of Weight W in a K-ary tree
- Spanning Tree With Maximum Degree (Using Kruskal's Algorithm)
- Count the nodes of the given tree whose weight has X as a factor
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