From ddf149b0d84d35f1aa54a21819c56389f4201ac5 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Sun, 6 May 2018 22:18:09 +0300 Subject: [PATCH] Update README. --- README.md | 3 +- src/algorithms/graph/prim/README.md | 46 +++++++++++++++++++++++++++++ 2 files changed, 48 insertions(+), 1 deletion(-) create mode 100644 src/algorithms/graph/prim/README.md diff --git a/README.md b/README.md index cdc396c9..3be218bf 100644 --- a/README.md +++ b/README.md @@ -69,7 +69,7 @@ * [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices * [Bellman-Ford Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/bellman-ford) - finding shortest path to all graph vertices * [Detect Cycle](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/detect-cycle) - for both directed and undirected graphs (DFS and Disjoint Set based versions) - * Prim’s Algorithm - finding Minimum Spanning Tree (MST) + * [Prim’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) * Kruskal’s Algorithm - finding Minimum Spanning Tree (MST) * Topological Sorting * Eulerian path, Eulerian circuit @@ -85,6 +85,7 @@ * **Greedy** * [Unbound Knapsack Problem](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/knapsack-problem) * [Dijkstra Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/dijkstra) - finding shortest path to all graph vertices + * [Prim’s Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/graph/prim) - finding Minimum Spanning Tree (MST) * **Divide and Conquer** * [Euclidean Algorithm](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD) * [Permutations](https://github.com/trekhleb/javascript-algorithms/tree/master/src/algorithms/sets/permutations) (with and without repetitions) diff --git a/src/algorithms/graph/prim/README.md b/src/algorithms/graph/prim/README.md new file mode 100644 index 00000000..908629c2 --- /dev/null +++ b/src/algorithms/graph/prim/README.md @@ -0,0 +1,46 @@ +# Prim's Algorithm + +In computer science, **Prim's algorithm** is a greedy algorithm that +finds a minimum spanning tree for a weighted undirected graph. + +The algorithm operates by building this tree one vertex at a +time, from an arbitrary starting vertex, at each step adding +the cheapest possible connection from the tree to another vertex. + +![Prim's Algorithm](https://upload.wikimedia.org/wikipedia/commons/f/f7/Prim%27s_algorithm.svg) + +Prim's algorithm starting at vertex `A`. In the third step, edges +`BD` and `AB` both have weight `2`, so `BD` is chosen arbitrarily. +After that step, `AB` is no longer a candidate for addition +to the tree because it links two nodes that are already +in the tree. + +## Minimum Spanning Tree + +A **minimum spanning tree** (MST) or minimum weight spanning tree +is a subset of the edges of a connected, edge-weighted +(un)directed graph that connects all the vertices together, +without any cycles and with the minimum possible total edge +weight. That is, it is a spanning tree whose sum of edge weights +is as small as possible. More generally, any edge-weighted +undirected graph (not necessarily connected) has a minimum +spanning forest, which is a union of the minimum spanning +trees for its connected components. + +![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/d/d2/Minimum_spanning_tree.svg) + +A planar graph and its minimum spanning tree. Each edge is +labeled with its weight, which here is roughly proportional +to its length. + +![Minimum Spanning Tree](https://upload.wikimedia.org/wikipedia/commons/c/c9/Multiple_minimum_spanning_trees.svg) + +This figure shows there may be more than one minimum spanning +tree in a graph. In the figure, the two trees below the graph +are two possibilities of minimum spanning tree of the given graph. + +## References + +- [Minimum Spanning Tree on Wikipedia](https://en.wikipedia.org/wiki/Minimum_spanning_tree) +- [Prim's Algorithm on Wikipedia](https://en.wikipedia.org/wiki/Prim%27s_algorithm) +- [Prim's Algorithm on YouTube by Tushar Roy](https://www.youtube.com/watch?v=oP2-8ysT3QQ)