C++Prim算法求最小生成树

C++Prim算法求最小生成树

MGraph.h

#pragma once
#include
#include
#include
using namespace std;
constexpr auto Infinity = 63353;

class MGraph {
public:
	MGraph() = default;
	~MGraph() = default;
	void CreateMGraph() {
		cout << "Please set the number of vertexes:";
		cin >> this->NumVertexes;
		for (int i = 0;i < NumVertexes;++i) {
			cout << "Please set data for this vertex:";
			string str;
			cin >> str;
			Vertexes.push_back(str);
		}
		arc.resize(NumVertexes);//set the number of lines
		for (int i = 0;i < NumVertexes;++i) {
			arc[i].resize(NumVertexes);//set the number colomns
			for (int j = 0;j < NumVertexes;++j) {
				if (i == j) arc[i][j] = 0;
				else arc[i][j] = Infinity;
			}
		}//Init MGraph's elemts
		cout << "Please set the number of edges:";
		cin >> this->NumEdges;
		for (int i = 0;i < NumEdges;++i) {
			cout << "Please enter the start and end of an edge,and weight:";
			int start, end, weight;
			cin >> start >> end >> weight;
			arc[start][end] = weight;
			arc[end][start] = weight;
		}
	}
	void DFSTraverse() {
		for (int i = 0;i < NumVertexes;++i) visited.push_back(false);
		for (int i = 0;i < NumVertexes;++i) {
			if (!visited[i]) dfs(i);
		}
	}
private:
	void dfs(int index) {
		visited[index] = true;
		cout << Vertexes[index] << " ";
		for (int i = 0;i < NumVertexes;++i) {
			if (arc[index][i] != Infinity && index != i && !visited[i]) {
				dfs(i);
			}
		}
	}
	friend class Prim;
private:
	int NumVertexes = 0;
	int NumEdges = 0;
	vector<string>Vertexes;
	vector<vector<int>>arc;
	vector<bool>visited;
};

Prim.h

#pragma once
#include
#include
#include"MGraph.h"
using namespace std;

class Prim {
public:
	Prim(MGraph&graph):M(graph) {
		for (int i = 0;i < M.NumVertexes;++i) visited.push_back(false);
		for (int i = 0;i < M.NumVertexes - 1;++i) lowest.push_back(Infinity);
	}
	~Prim() = default;
	void PrimAlgorithm(int &begin) {
		visited.at(begin) = true;
		int numlowest = 0;
		while (true) {
			int flag = 0;
			for (int i = 0;i < M.NumVertexes;++i) {
				if (visited[i]) {
					for (int j = 0;j < M.NumVertexes;++j) {
						if (i != j && M.arc[i][j] < lowest[numlowest] && !visited[j]) {
							lowest[numlowest] = M.arc[i][j];
							flag = j;
						}
					}
				}
			}
			visited[flag] = true;
			numlowest++;
			if (numlowest == M.NumVertexes - 1) break;
		}
	}
	void ShowLowest() {
		int sum = 0;
		for (auto x : lowest) {
			cout << x << " ";
			sum += x;
		}
		cout << endl;
		cout << "Lowest:" << sum << endl;
	}
private:
	vector<bool>visited;
	vector<int>lowest;
	MGraph& M;
};

Prim算法原理：

1）以某一个点开始，寻找当前该点可以访问的所有的边；
2）在已经寻找的边中发现最小边，这个边必须有一个点还没有访问过，将还没有访问的点加入我们的集合，记录添加的边；
3）寻找当前集合可以访问的所有边，重复2的过程，直到没有新的点可以加入；
4）此时由所有边构成的树即为最小生成树。