Basic Graph Algorithm Minimum Spanning Tree Prim algorithm (adjacent table + priority queue STL)

This article is a summary of the Prim algorithm for finding the minimal spanning tree of a undirected connected graph in the introduction to algorithms. I have a little bit about it.

The specific problem of the minimal spanning tree can be explained in the following languages:
　　　　Input: An undirected Weighted Graph G = (V, E). Each edge (u, v) belongs to E and has a weight of w.

　　　　Output: The minimum spanning tree of the graph, that is, a tree connected to all vertices, and the sum and minimum of edge values in the tree.

The following is an example of the Minimum Spanning Tree:

Tree T1 and T2,

1 # include <iostream> 2 # include <cstdio> 3 # include <vector> 4 # include <queue> 5 using namespace std; 6 7 # define maxn 110 // maximum number of vertices 8 int n, m; // Number of vertices, number of edges 9 10 struct arcnode // edge node 11 {12 int vertex; // vertex number 13 int weight adjacent to the header node; // weight of the edge connecting the two vertices 14 arcnode * next; // point to the next adjacent vertex 15 arcnode () {} 16 arcnode (int v, int w): vertex (v), weight (w), next (NULL) {}17}; 18 19 struct vernode // vertex node, 20 {2 1 int vex; // the current point number 22 arcnode * firarc; // edge formed by the first vertex connected to the vertex 23} Ver [maxn]; 24 25 void Init () // initialize the graph neighbor list and create the vertex node 26 {27 for (int I = 1; I <= n; I ++) 28 {29 Ver [I]. vex = I; 30 Ver [I]. firarc = NULL; 31} 32} 33 34 void Insert (int a, int B, int w) // end method, Insert With a as the start point, B as the end point, if the weight is w, the efficiency is not as good as that of the header insertion, but you can remove the duplicate edge 35 {36 arcnode * q = new arcnode (B, w); 37 if (Ver [a]. firarc = NULL) 38 Ver [a]. firarc = q; 39 else 40 {41 ar Cnode * p = Ver [a]. firarc; 42 if (p-> vertex = B) 43 {44 if (p-> weight> w) 45 p-> weight = w; 46 return; 47} 48 while (p-> next! = NULL) 49 {50 if (p-> next-> vertex = B) 51 {52 if (p-> next-> weight> w ); 53 p-> next-> weight = w; 54 return; 55} 56 p = p-> next; 57} 58 p-> next = q; 59} 60} 61 62 struct node // The node that stores the key value 63 {64 int v; 65 int key; 66 friend bool operator <(node a, node B) // custom priority. If the key is small, the priority is 67 {68 return. key> B. key; 69} 70}; 71 72 # define INF 0 xfffff // The maximum weight is 73 int parent [maxn]; // The parent node of each node 74 bool visited [ma Xn]; // whether 75 node vx [maxn] has been added; // you can specify 76 priority_queue for the edge connecting each node to its parent node. <node> q; // The priority queue stl implements 77 void Prim (int s) // s to indicate the root node 78 {79 for (int I = 1; I <= n; I ++) // initialize 80 {81 vx [I]. v = I; 82 vx [I]. key = INF; 83 parent [I] =-1; 84 visited [I] = false; 85} 86 vx [s]. key = 0; 87 q. push (vx [s]); 88 while (! Q. empty () 89 {90 node nd = q. top (); // get the first team. Remember to pop 91 visited [nd. v] = true; 92 q. pop (); 93 arcnode * p = Ver [nd. v]. firarc; 94 while (p! = NULL) // locate all adjacent nodes. if not accessed, enter the queue 95 {96 if (! Visited [p-> vertex] & p-> weight <vx [p-> vertex]. key) 97 {98 parent [p-> vertex] = nd. v; 99 vx [p-> vertex]. key = p-> weight; 100 vx [p-> vertex]. v = p-> vertex; 101 q. push (vx [p-> vertex]); 102} 103 p = p-> next; 104} 105} 106 107 int main () 108 {109 int, b, w; 111 cout <"input n and m:"; 112 cin> n> m; 113 Init (); 114 cout <"input all edges: "<endl; 115 while (m --) 116 {117 cin> a> B> w; 118 Insert (a, B, w); 119 Insert (B, a, w); 120} 121 Prim (1); 122 cout <"parent node of all output nodes:" <endl; 123 for (int I = 1; I <= n; I ++) 124 cout <parent [I] <"; 125 cout <endl; 126 cout <" The minimum generated tree weight is: "; 127 int cnt = 0; 128 for (int I = 1; I <= n; I ++) 129 cnt + = vx [I]. key; 130 cout <cnt <endl; 131 return 0; 132}View Code

 

The running result is as follows (based on the first example ):

 

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