---
id: mst
title: "Minimum Spanning Trees"
author: Benjamin Qi
prerequisites: 
 - 
     - Gold - Shortest Paths
 - 
     - Gold - Disjoint Set Union
description: A subset of the edges of a connected, undirected, edge-weighted graph that connects all the vertices to each other of minimum total weight, where no cycles are allowed.
---

## Standard

 - [Kattis Minimum Spanning Tree](https://open.kattis.com/problems/minspantree)
   - same as [CSES Road Reparation](https://cses.fi/problemset/task/1675)

## Tutorial

 - CPH 15 (Spanning Trees)
 - Prim's Algorithm
   - [cp-algo](https://cp-algorithms.com/graph/mst_prim.html)
   - Similar to Dijkstra
 - Kruskal's Algorithm
   - [cp-algo 1](https://cp-algorithms.com/graph/mst_kruskal.html)
   - [cp-algo 2](https://cp-algorithms.com/graph/mst_kruskal_with_dsu.html)

## USACO Gold Problems

 - [Old Silver - SuperBull](http://www.usaco.org/index.php?page=viewproblem2&cpid=531)
 - [Walk](http://usaco.org/index.php?page=viewproblem2&cpid=946)
   - Prim's is applicable, but the edge weights are special so you don't actually need to use an MST algo ...
 - [Fencedin](http://www.usaco.org/index.php?page=viewproblem2&cpid=623)
   - also special ...

## Other Problems

  - [Birthday Gifts](https://www.hackerearth.com/practice/math/combinatorics/inclusion-exclusion/practice-problems/algorithm/mancunian-and-birthday-gifts-d44faa15/) [](73)
  - [Spanning Tree Fraction](https://www.hackerrank.com/contests/w31/challenges/spanning-tree-fraction) [](78)