Gold_Graphs

content/3_Gold/Gold_Graph_ShortestPath

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- - **Dijkstra**
-   - ex. [Milk Pumping](http://www.usaco.org/index.php?page=viewproblem2&cpid=969)
- - Floyd-Warshall
- - Bellman-Ford??
- - SPFA??

content/3_Gold/Gold_Graphs.md

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-
- - **Dijkstra**
-   - ex. [Milk Pumping](http://www.usaco.org/index.php?page=viewproblem2&cpid=969)
- - Floyd-Warshall
- - Bellman-Ford??
- - SPFA??
- - CPH 13
-
-
-     - CPH 15
-     - ex. [Fencedin](http://www.usaco.org/index.php?page=viewproblem2&cpid=623)
-     - Prim
-     - Kruskal
-
-
-     - CPH 16
-     - ex. [Timeline](http://www.usaco.org/index.php?page=viewproblem2&cpid=1017)
-
-     - DSU Complexity Proofs
-       - [log\*n](https://en.wikipedia.org/wiki/Proof_of_O(log*n)\_time_complexity\_of_union%E2%80%93find)
-       - [a(m,n)](https://dl.acm.org/doi/pdf/10.1145/321879.321884)

content/3_Gold/Gold_MST.md

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+# Gold - Minimum Spanning Tree
+
+ * [Kattis Minimum Spanning Tree](https://open.kattis.com/problems/minspantree)
+
+## Tutorial
+
+ - CPH 15
+ - Prim's Algorithm
+   - Similar to Dijkstra
+ - Kruskal's Algorithm
+   - Requires "Disjoint Set Union" (DSU) data structure
+     - [CSAcademy Disjoint-Set](https://csacademy.com/lessons)
+     - DSU Complexity Proofs (optional of course)
+       - [log\*n](https://en.wikipedia.org/wiki/Proof_of_O(log*n)\_time_complexity\_of_union%E2%80%93find)
+       - [a(m,n)](https://dl.acm.org/doi/pdf/10.1145/321879.321884)
+
+## USACO Gold Problems
+
+ - MST Problems
+   - [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 ...
+ - DSU Problems
+   - [Mootube](http://www.usaco.org/index.php?page=viewproblem2&cpid=789)
+   - [Closing the Farm](http://www.usaco.org/index.php?page=viewproblem2&cpid=646)
+   - [Favorite Colors](http://www.usaco.org/index.php?page=viewproblem2&cpid=1042)
+     - fairly tricky

content/3_Gold/Gold_ShortestPath.md

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+# Gold - Shortest Path
+
+Author: Benjamin Qi
+
+[CPC.7](https://github.com/SuprDewd/T-414-AFLV/tree/master/07_graphs_1)
+
+## Breadth First Search
+
+### Tutorial
+
+ - [CSAcademy BFS](https://csacademy.com/lesson/breadth_first_search)
+ - [cp-algo BFS](https://cp-algorithms.com/graph/breadth-first-search.html)
+ - [cp-algo 0/1 BFS](https://cp-algorithms.com/graph/01_bfs.html)
+
+### Problems
+
+ - [Cow Navigation](http://www.usaco.org/index.php?page=viewproblem2&cpid=695)
+ - [Dream](http://www.usaco.org/index.php?page=viewproblem2&cpid=575)
+ - [Lasers](http://www.usaco.org/index.php?page=viewproblem2&cpid=671)
+
+## Shortest Path
+
+### Non-Negative Edge Weights
+
+ * [Kattis SSSP Non-Negative](https://open.kattis.com/problems/shortestpath1)
+
+For non-negative weights, use *Dijkstra's Algorithm:*
+
+#### Tutorial
+
+ * CSES 13.2
+ * [cp-algo Dijkstra (Dense Graphs)](https://cp-algorithms.com/graph/dijkstra_sparse.html)
+ * [cp-algo Dijkstra (Sparse Graphs)](https://cp-algorithms.com/graph/dijkstra_sparse.html)
+   * Usually, it's this one that's applicable.
+
+#### USACO Gold Problems 
+
+ * [Milk Pumping](http://www.usaco.org/index.php?page=viewproblem2&cpid=969)
+   * fairly standard application
+ * [Shortcut](http://usaco.org/index.php?page=viewproblem2&cpid=899)
+ * [Fine Dining](http://usaco.org/index.php?page=viewproblem2&cpid=861)
+
+### All Pairs
+
+ * [Kattis All Pairs Shortest Path](https://open.kattis.com/problems/allpairspath)
+
+Use the *Floyd-Warshall* algorithm.
+
+#### Tutorial
+
+ * CSES 13.3
+ * [cp-algo Floyd-Warshall](https://cp-algorithms.com/graph/all-pair-shortest-path-floyd-warshall.html)
+
+#### USACO Gold Problems 
+
+ * [Moortal Cowmbat](http://usaco.org/index.php?page=viewproblem2&cpid=971)
+   * Use APSP before running DP.
+
+### Negative Edge Weights
+
+Hasn't appeared in recent USACO Gold as far as I know.
+
+ * [Kattis SSSP Negative](https://open.kattis.com/problems/shortestpath3)
+
+Can also modify Dijkstra's so it works with negative edge weights but not negative cycles. Running time bound no longer applies.

content/3_Gold/Gold_TopoSort.md

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+## Gold - Topological Sort
+
+### Tutorial
+
+ - CPH 16.1, 16.2
+ - [cp-algorithms](https://cp-algorithms.com/graph/topological-sort.html)
+
+### USACO Gold Problems
+
+ - [Timeline](http://www.usaco.org/index.php?page=viewproblem2&cpid=1017)
+ - [Milking Order](http://www.usaco.org/index.php?page=viewproblem2&cpid=838)