基本思想
对于图G而言，V是所有顶点的集合；现在，设置两个新的集合U和T，其中U用于存放G的最小生成树中的顶点，T存放G的最小生成树中的边。 从所有uЄU，vЄ(V-U) (V-U表示出去U的所有顶点)的边中选取权值最小的边(u, v)，将顶点v加入集合U中，将边(u, v)加入集合T中，如此不断重复，直到U=V为止，最小生成树构造完毕，这时集合T中包含了最小生成树中的所有边。
public class Edge
{
public int start;
public int end;
public int weight;
public Edge(int start, int end, int weight)
{
this.start = start;
this.end = end;
this.weight = weight;
}
}
public class Vertex
{
public object Data;
public Vertex(object data)
{
this.Data = data;
}
}
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
namespace Prim
{
public class Graph
{
//INFINITY=无穷大的数字 = 无穷远的点
public const int INFINITY = 65535;
public int VertexCount;
public int[,] matrix;
/// <summary>
/// 生成领接矩阵
/// </summary>
/// <returns></returns>
public static Graph CreateGraph(Vertex[] vertexs,Edge[] edges)
{
Graph graphPrim = new Graph();
graphPrim.VertexCount = vertexs.Length;
graphPrim.matrix = new int[vertexs.Length, vertexs.Length];
//初始化 默认都是无穷大
for (int i = 0; i < vertexs.Length; i++)
{
for (int j = 0; j < vertexs.Length; j++)
{
if (i != j)
{
graphPrim.matrix[i, j] = INFINITY;
}
}
}
//初始化边真正存在的权值
for (int i = 0; i < edges.Length; i++)
{
int start = edges[i].start;
int end = edges[i].end;
graphPrim.matrix[start, end] = edges[i].weight;
graphPrim.matrix[end, start] = edges[i].weight;
}
return graphPrim;
}
public static void Prim(Graph graph)
{
//顶点的下表索引
int[] adjvex = new int[graph.VertexCount];
//顶点的边的权值
int[] lowCost = new int[graph.VertexCount];
//初始化数据:lowCast装入v0的对应的领接矩阵的第一行数据
// :adjvex全部初始化为0
for (int i = 0; i < graph.VertexCount; i++)
{
lowCost[i] = graph.matrix[0, i];
adjvex[i] = 0;
}
//计算权值最小的边
for (int i = 0; i < graph.VertexCount-1; i++)
{
int min = INFINITY;
int j = 0;
int k = 0;
//计算当前顶点U集合到顶点V-U集合的最短距离
while (j < graph.VertexCount)
{
if (lowCost[j] != 0 && lowCost[j] < min)
{
min = lowCost[j];
k = j;
}
j++;
}
Debug.LogError("(" + adjvex[k] + "," + k + ") ");
lowCost[k] = 0;//表示此顶点已经完成任务
//动态重新规划
//若下表为k顶点到各个边的权值 < lowCost数组中的各个值需要更新lowCast数组中的权值
for (int n = 0; n < graph.VertexCount; n++)
{
if (lowCost[n] != 0 && graph.matrix[k, n] < lowCost[n])
{
lowCost[n] = graph.matrix[k, n];
adjvex[n] = k;
}
}
}
}
}
}
测试
using Prim;
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class TestPrim : MonoBehaviour
{
// {0,10,65535,65535,65535,11,65535,65535,65535 },
// {10,0,18,65535,65535,65535,16,65535,12},
// {65535,65535,0,22,65535,65535,65535,65535,8 },
// {65535,65535,22,0,20,65535,65535,16,21},
// {65535,65535,65535,20,0,26,65535,7,65535 },
// {11,65535,65535,65535,26,0,17,65535,65535},
// {65535,16,65535,65535,65535,17,0,19,65535 },
// {65535,65535,65535,16,7,65535,19,0,65535 },
// {65535,12,8,21,65535,65535,65535,65535,0},
Graph graph;
void Start()
{
Vertex[] vertexs = GenerateVertex(9);
Edge[] edges = GenerateEdges();
graph = Graph.CreateGraph(vertexs,edges);
Graph.Prim(graph);
}
private Vertex[] GenerateVertex(int len)
{
Vertex[] vertexs = new Vertex[len];
for (int i = 0; i < len; i++)
{
vertexs[i] = new Vertex(i);
}
return vertexs;
}
private Edge[] GenerateEdges()
{
Edge edge0 = new Edge(0, 1, 10);
Edge edge1 = new Edge(0, 5, 11);
Edge edge2 = new Edge(1, 2, 18);
Edge edge3 = new Edge(1, 6, 16);
Edge edge4 = new Edge(1, 8, 12);
Edge edge5 = new Edge(2, 3, 22);
Edge edge6 = new Edge(2, 8, 8);
Edge edge7 = new Edge(3, 4, 20);
Edge edge8 = new Edge(3, 7, 16);
Edge edge9 = new Edge(3, 8, 21);
Edge edge10 = new Edge(4, 5, 26);
Edge edge11 = new Edge(4, 7, 7);
Edge edge12 = new Edge(5, 6, 17);
Edge edge13 = new Edge(6, 7, 19);
Edge edge14 = new Edge(6, 7, 19);
Edge[] edges = {
edge0, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, edge9, edge10, edge11, edge12, edge13, edge14 };
return edges;
}
}