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MST

25 posts

Number of Critical and Pseudo-Critical edges

Last Updated: 23 July 2025

Given a weighted undirected graph with n vertices numbered from 0 to n - 1, and an array of edges where edges[i] = [u, v, weight] represents a bidirectional and weighted e...read more

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What is Minimum Spanning Tree (MST)

Last Updated: 23 July 2025

A spanning tree is defined as a tree-like subgraph of a connected, undirected graph that includes all the vertices of the graph. Or, to say in Layman's words, it is a subs...read more

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Minimize rope length to connect given points in a 3D plane

Last Updated: 23 July 2025

Given a 2-D array A[][] of size N × 3, where each element of the array is of the form {x, y, z}, where x, y and z are coordinates of a point in 3D space. The task is to co...read more

Check if an edge is a part of any Minimum Spanning Tree

Last Updated: 23 July 2025

Given a connected undirected weighted graph in the form of a 2D array where each row is of the type [start node, end node, weight] describing an edge, and also two integer...read more

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Minimize cost to connect the graph by connecting any pairs of vertices having cost at least 0

Last Updated: 23 July 2025

Given a disconnected graph G with N vertices and M edges and an array cost[] corresponding to each vertex, the task is to find the minimum cost to make the graph by connec...read more

Difference between Minimum Spanning Tree and Shortest Path

Last Updated: 23 July 2025

Spanning tree: A spanning tree (T) of an undirected graph(G) is a subgraph which is a tree that includes all the vertices of a graph (G) and the minimum number of edges re...read more

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Properties of Minimum Spanning Tree (MST)

Last Updated: 23 July 2025

For a connected and undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have multiple s...read more

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Minimum Spanning Tree

Graph Minimum Spanning Tree

Minimum cost to connect all houses in a city

Last Updated: 23 July 2025

Given a 2D array houses[][] consisting of n 2D coordinates {x, y} where each coordinate represents the location of each house, the task is to find the minimum cost to conn...read more

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Kruskal'sAlgorithm

Minimum Spanning Tree

Second Best Minimum Spanning Tree

Last Updated: 15 July 2025

Given an undirected graph represented by the array edges[][], where each edges[i] contains three integers [u, v, w], representing an undirected edge from u to v, having di...read more

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Kruskal'sAlgorithm

Minimum Spanning Tree

Minimum Bottleneck Spanning Tree(MBST)

Last Updated: 12 July 2025

The minimum bottleneck spanning tree in an undirected graph is a tree whose most expensive edge is as minimum as possible. In this article, we will understand more about h...read more

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Advanced Data Structure

Minimum Spanning Tree using Priority Queue and Array List

Last Updated: 12 July 2025

Given a bi-directed weighted (positive) graph without self-loops, the task is to generate the minimum spanning tree of the graph.Examples:Input: N = 9, E = 14, edges = {{0...read more

Difference between Prim's and Kruskal's algorithm for MST

Last Updated: 12 July 2025

Minimum Spanning Tree (MST) is a fundamental concept in graph theory and has various applications in network design, clustering, and optimization problems. Two of the most...read more

Difference Between

Types of Spanning Tree Protocol (STP)

Last Updated: 11 July 2025

In Ethernet networks, switches use frames to forward data between devices. However, if there are multiple active paths between switches (such as when switches are intercon...read more

Computer Networks

Minimum cost to connect all cities

Last Updated: 28 February 2025

There are n cities and there are roads in between some of the cities. Somehow all the roads are damaged simultaneously. We have to repair the roads to connect the cities a...read more

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Problem Solving for Minimum Spanning Trees (Kruskal’s and Prim’s)

Last Updated: 04 October 2018

Minimum spanning Tree (MST) is an important topic for GATE. Therefore, we will discuss how to solve different types of questions based on MST. Before understanding this ar...read more

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