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---
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id: mst
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title: "Minimum Spanning Trees"
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author: Benjamin Qi
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prerequisites:
-
- Gold - Shortest Paths
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-
- Gold - Disjoint Set Union
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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.
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---
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## Standard
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- [Kattis Minimum Spanning Tree ](https://open.kattis.com/problems/minspantree )
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- same as [CSES Road Reparation ](https://cses.fi/problemset/task/1675 )
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## Tutorial
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- CPH 15 (Spanning Trees)
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- Prim's Algorithm
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- [cp-algo ](https://cp-algorithms.com/graph/mst_prim.html )
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- Similar to Dijkstra
- Kruskal's Algorithm
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- [cp-algo 1 ](https://cp-algorithms.com/graph/mst_kruskal.html )
- [cp-algo 2 ](https://cp-algorithms.com/graph/mst_kruskal_with_dsu.html )
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## USACO Gold Problems
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- [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 ...
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## Other Problems
- [Birthday Gifts ](https://www.hackerearth.com/practice/math/combinatorics/inclusion-exclusion/practice-problems/algorithm/mancunian-and-birthday-gifts-d44faa15/ ) [](73)
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- [Spanning Tree Fraction ](https://www.hackerrank.com/contests/w31/challenges/spanning-tree-fraction ) [](78)
