2020-06-04 01:42:57 +00:00
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---
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slug: /gold/mst
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2020-06-04 05:39:49 +00:00
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title: "Minimum Spanning Tree"
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2020-06-04 02:09:42 +00:00
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author: Benjamin Qi
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2020-06-04 05:39:49 +00:00
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order: 3
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2020-06-04 01:42:57 +00:00
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---
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2020-06-04 05:39:49 +00:00
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<div class="syllabus-only">
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Description: Todo
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</div>
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<!-- END DESCRIPTION -->
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2020-06-03 20:56:04 +00:00
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2020-06-03 23:03:14 +00:00
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Standard Problems:
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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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- [CSES Road Reparation](https://cses.fi/problemset/task/1675)
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- equivalent to above
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2020-06-03 20:56:04 +00:00
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## Tutorial
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- CPH 15
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- Prim's Algorithm
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2020-06-03 21:42:26 +00:00
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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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- 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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2020-06-03 23:03:14 +00:00
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- same as [CSES Road Construction](https://cses.fi/problemset/task/1676)
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2020-06-03 20:56:04 +00:00
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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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