Minimum spanning Tree ~prim algorithm

Source: Internet
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The ~ Primm algorithm of the minimum spanning tree

The minimum spanning tree is the selection of n-1 bars from a well-connected graph (with n points, more than (n-1) edges) to connect n points to each other and to minimize the total weight of the tree. There are two famous ways to complete this construction, one is the Kruskal algorithm, which is to sort the weights of each edge, then select small edges to add to the tree, and ensure that it is a tree (that is, it cannot produce loops). The other one is the prim algorithm, which is considered from the point of view. First use map[][] two-dimensional arrays to hold weights between two points, and a one-dimensional array lowcost[] to hold the weights associated with the selected points, and also use a mark[] array to mark the points that have been used. The basic idea is very similar to the Dijkstra algorithm in the shortest path.

Basic idea of PRIM algorithm:

Select a point S from the connected network n={v,e}, choose the side (S,V) associated with it and the least weighted value, and add its vertices to the vertex collection U of the spanning tree. Each subsequent step selects a point that is not in the vertex collection U, minimizing its weight to u, and then adding it to the vertex collection U. This continues until all vertices in the network are joined to the vertex collection of the spanning tree.

The process of constructing a minimal spanning tree using the prim algorithm:

Suppose that in the construction process, the tree's vertex set U and the edge set are red, the points outside the U set are blue, the red and blue edges are purple, and the shortest purple edge is the one currently looking for. Each vertex is selected to be adjusted to the remaining vertices, updating its distance to the tree's vertex set U. Please refer to the code for details:

#include <stdio.h> #include <string.h> #define INF 0x3f3f3f3fint map[1010][1010];int lowcost[1010];int Mark [1010];int N,m;int Prim () {int vir,min,sum=0;for (int i=1;i<=n;i++)//Initialize the tag array to a 0,lowcost array to hold the weight of the point associated with the start 1 {mark[i]=0; Lowcost[i]=map[1][i];} mark[1]=1;//will start mark for (int i=1;i<n;i++)//have n points, so you need to find n-1 times {min=inf;for (int j=1;j<=n;j++)//Find the point {if (!mark) of the tree collection Weights least [j]&&lowcost[j]<min) {min=lowcost[j];vir=j;}} if (min==inf) break;sum+=min;//The minimum weight accumulation mark[vir]=1;//mark the points that have been found//update the distance for each point from the tree collection for (int j=1;j<=n;j++) {if (!mark[j]& &lowcost[j]>map[vir][j]) {lowcost[j]=map[vir][j];}}} Return sum;//returns the weight value of the minimum spanning tree}int main () {while (scanf ("%d%d", &n,&m)!=eof) {for (int i=1;i<=n;i++) for (int j=1;j <=n;j++)//Initialize the map array to a larger value map[i][j]=inf;for (int i=0;i<m;i++) {int x,y,cost;scanf ("%d%d%d",&x,&y,& Cost); if (map[x][y]>cost)///record points and weights, if there is a duplicate take the weight of the small {Map[x][y]=cost;map[y][x]=cost;}} printf ("%d\n", Prim ());//Output the weight of this minimum spanning tree}return 0;}

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Minimum spanning Tree ~prim algorithm

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