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---
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2020-06-15 23:19:07 +00:00
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id: mst
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2020-06-05 00:21:03 +00:00
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title: "Minimum Spanning Trees"
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2020-06-04 02:09:42 +00:00
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author: Benjamin Qi
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2020-06-05 00:21:03 +00:00
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prerequisites:
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-
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- Gold - Shortest Paths
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2020-06-04 01:42:57 +00:00
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---
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2020-06-17 22:18:07 +00:00
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<module-excerpt>
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2020-06-16 17:09:59 +00:00
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**Disjoint Set Union** and **Minimum Spanning Trees**
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2020-06-04 05:39:49 +00:00
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2020-06-17 22:18:07 +00:00
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</module-excerpt>
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2020-06-03 20:56:04 +00:00
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2020-06-04 21:42:30 +00:00
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## Standard
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2020-06-03 21:08:42 +00:00
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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
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- Kruskal's Algorithm
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- [cp-algo 1](https://cp-algorithms.com/graph/mst_kruskal.html)
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- [cp-algo 2](https://cp-algorithms.com/graph/mst_kruskal_with_dsu.html)
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- Requires "Disjoint Set Union" (DSU) data structure
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- [CSAcademy Disjoint-Set](https://csacademy.com/lesson/disjoint_data_sets)
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- [Topcoder Union Find](https://www.topcoder.com/community/data-science/data-science-tutorials/disjoint-set-data-structures/)
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- [CPC.3](https://github.com/SuprDewd/T-414-AFLV/tree/master/03_data_structures)
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- DSU Complexity Proofs (optional of course)
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- [log\*n](https://en.wikipedia.org/wiki/Proof_of_O(log*n)\_time_complexity\_of_union%E2%80%93find)
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- [a(m,n)](https://dl.acm.org/doi/pdf/10.1145/321879.321884)
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## USACO Gold Problems
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2020-06-04 02:09:42 +00:00
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- MST
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- [Walk](http://usaco.org/index.php?page=viewproblem2&cpid=946)
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- Prim's is applicable, but the edge weights are special so you don't actually need to use an MST algo ...
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- [Fencedin](http://www.usaco.org/index.php?page=viewproblem2&cpid=623)
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- also special ...
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- DSU
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- [Mootube](http://www.usaco.org/index.php?page=viewproblem2&cpid=789)
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- same as [CSES Road Construction](https://cses.fi/problemset/task/1676)
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- [Closing the Farm](http://www.usaco.org/index.php?page=viewproblem2&cpid=646)
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- [Favorite Colors](http://www.usaco.org/index.php?page=viewproblem2&cpid=1042)
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- fairly tricky
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## Other Problems
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- [Birthday Gifts](https://www.hackerearth.com/practice/math/combinatorics/inclusion-exclusion/practice-problems/algorithm/mancunian-and-birthday-gifts-d44faa15/) [](73)
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2020-06-08 19:51:58 +00:00
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- [Spanning Tree Fraction](https://www.hackerrank.com/contests/w31/challenges/spanning-tree-fraction) [](78)
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