38 lines
1.5 KiB
Markdown
38 lines
1.5 KiB
Markdown
---
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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:
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- 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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- [PAPS 12.4](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
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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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## USACO Gold Problems
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- [Old Silver - SuperBull](http://www.usaco.org/index.php?page=viewproblem2&cpid=531)
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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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## 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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- [Spanning Tree Fraction](https://www.hackerrank.com/contests/w31/challenges/spanning-tree-fraction) [](78) |