From e55aa83c94e9eec6bb351e0604ed5d5297042105 Mon Sep 17 00:00:00 2001 From: TornjV Date: Mon, 23 May 2016 22:48:49 +0200 Subject: [PATCH] MST and Prim's Algorithm --- algorithm/category.json | 6 ++++++ algorithm/mst/prim/desc.json | 14 ++++++++++++++ algorithm/mst/prim/normal/code.js | 32 +++++++++++++++++++++++++++++++ algorithm/mst/prim/normal/data.js | 10 ++++++++++ 4 files changed, 62 insertions(+) create mode 100644 algorithm/mst/prim/desc.json create mode 100644 algorithm/mst/prim/normal/code.js create mode 100644 algorithm/mst/prim/normal/data.js diff --git a/algorithm/category.json b/algorithm/category.json index 528e8276..b2c010a5 100644 --- a/algorithm/category.json +++ b/algorithm/category.json @@ -10,6 +10,12 @@ "topological_sort": "Topological-Sort" } }, + "mst": { + "name": "Minimum Spanning Tree", + "list": { + "prim": "Prim's Algorithm" + } + }, "search": { "name": "Search", "list": { diff --git a/algorithm/mst/prim/desc.json b/algorithm/mst/prim/desc.json new file mode 100644 index 00000000..0f91ca42 --- /dev/null +++ b/algorithm/mst/prim/desc.json @@ -0,0 +1,14 @@ +{ + "Prim's Algorithm": "Greedy algorithm that finds a minimum spanning tree for a weighted undirected graph.", + "Applications": [ + ], + "Complexity": { + "time": "worst O(|V|²)" + }, + "References": [ + "Wikipedia" + ], + "files": { + "normal": "Finds minimum spanning tree of a given graph." + } +} \ No newline at end of file diff --git a/algorithm/mst/prim/normal/code.js b/algorithm/mst/prim/normal/code.js new file mode 100644 index 00000000..62044bbe --- /dev/null +++ b/algorithm/mst/prim/normal/code.js @@ -0,0 +1,32 @@ +function prim(){ + // Finds a tree so that there exists a path between + // every two nodes while keeping the cost minimal + var minD, minI, minJ, sum=0, D=[]; + for(var i = 0; i < G.length; i++) D.push(0); + D[0] = 1; // First node is visited + for(var k = 0; k < G.length-1; k++){ // Searching for k edges + minD = Infinity; + for(i = 0; i< G.length; i++) + if(D[i]) // First node in an edge must be visited + for(var j = 0; j < G.length; j++) + if(!D[j] && G[i][j]){ + tracer._visit(i, j); + // Second node must not be visited and must be connected to first node + if(G[i][j] < minD){ + // Searching for cheapest edge which satisfies requirements + minD = G[i][j]; + minI = i; + minJ = j; + } + tracer._leave(i, j); + } + tracer._visit(minI, minJ); + D[minJ] = 1; // Visit second node and insert it into or tree + sum += G[minI][minJ]; + } + tracer._print("The sum of all edges is: " + sum); +} + +tracer._pace(500); +tracer._print("nodes that belong to minimum spanning tree are: "); +prim(); \ No newline at end of file diff --git a/algorithm/mst/prim/normal/data.js b/algorithm/mst/prim/normal/data.js new file mode 100644 index 00000000..fcd3f951 --- /dev/null +++ b/algorithm/mst/prim/normal/data.js @@ -0,0 +1,10 @@ +var tracer = new WeightedUndirectedGraphTracer(); +/*var G = [ // G[i][j] indicates the weight of the path from the i-th node to the j-th node + [0, 3, 0, 1, 0], + [5, 0, 1, 2, 4], + [1, 0, 0, 2, 0], + [0, 2, 0, 0, 1], + [0, 1, 3, 0, 0] + ];*/ +var G = WeightedUndirectedGraph.random(10, .4, 1, 9); +tracer._setData(G); \ No newline at end of file pFad - Phonifier reborn

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