数据结构 Kruskal Prim Dijkstra Floyd算法（C++）

最新推荐文章于 2025-04-15 17:03:20 发布

TheLegendOfZelda

最新推荐文章于 2025-04-15 17:03:20 发布

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本文链接：https://blog.youkuaiyun.com/TheLegendOfZelda/article/details/80663265

本文介绍了四种图算法的具体实现：Prim算法和Kruskal算法用于求最小生成树，Dijkstra算法用于解决单源最短路径问题，而Floyd算法则用于解决任意两点间的最短路径问题。代码中详细展示了每种算法的数据结构定义、核心函数实现及调用过程。

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写给自己做个备份的。

Kruskal Prim算法基本上是看别人的写的，Dijkstra Floyd算法是靠自己的理解写的。

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
#define UINT unsigned int
#define vexCounts 6
#define INF 0xFFFFFFFF
///Kruskal算法
///储存边的信息
struct Arc
{
	int u;
	int v;
	UINT cost;
};
///Prim算法
///通过不断更新点到现有点的距离来取最短距离的点形成一个生成树
struct Node
{
	UINT data;
	UINT lowerestCost;
}Nodes[vexCounts];
///vextex 顶点
char vextex[] = { 'A', 'B', 'C', 'D', 'E', 'F' };

void AdjMatrix(unsigned int adjMat[][vexCounts])
{
	for(int i=0;i<vexCounts;i++)
		for(int j=0;j<vexCounts;j++)
		{
			if (i == j)
				adjMat[i][j] = 0;
			else 
				adjMat[i][j] = INF;
		}
	adjMat[0][1] = 6; adjMat[0][2] = 1; adjMat[0][3] = 5;
	adjMat[1][0] = 6; adjMat[1][2] = 5; adjMat[1][4] = 3;
	adjMat[2][0] = 1; adjMat[2][1] = 5; adjMat[2][3] = 5; adjMat[2][4] = 6; adjMat[2][5] = 4;
	adjMat[3][0] = 5; adjMat[3][2] = 5; adjMat[3][5] = 2;
	adjMat[4][1] = 3; adjMat[4][2] = 6; adjMat[4][5] = 6;
	adjMat[5][2] = 4; adjMat[5][3] = 2; adjMat[5][4] = 6;
}

int Minmum(Node* node)
{
	int index = -1;
	unsigned lower = INF;
	for(int i=0;i<vexCounts;i++)
	{
		if(node[i].lowerestCost<lower&&node[i].lowerestCost)
		{
			lower = node[i].lowerestCost;
			index = i;
		}
	}
	return index;
}

void Prim(unsigned int adjMat[][vexCounts],UINT idx)
{

	Nodes[idx].data = idx;
	Nodes[idx].lowerestCost = 0;
	for (unsigned i = 0; i < vexCounts; i++)  //初始化辅助数组
	{
		if (i != idx)
		{
			Nodes[i].data = idx;
			Nodes[i].lowerestCost = adjMat[idx][i];
		}
	}
	for(unsigned e=1;e<vexCounts;e++)
	{
		int min = Minmum(Nodes);
		cout << vextex[Nodes[min].data] << "----" << vextex[min] << endl;
		Nodes[min].lowerestCost = 0;
		for(UINT i=0;i<vexCounts;i++)
		{
			if (!Nodes[i].lowerestCost) continue;
			if(Nodes[i].lowerestCost>adjMat[min][i])
			{
				Nodes[i].lowerestCost = adjMat[min][i];
				Nodes[i].data = min;
			}
		}
	}
}

void ReadArc(UINT adjMat[][vexCounts],vector<Arc>& vertexArc)
{
	Arc* tmp = NULL;
	for(UINT i=0;i<vexCounts;i++)
	{
		for(UINT j=0;j<i;j++)				///因为是无向图只需要遍历一遍
		{
			if(adjMat[i][j]!=INF)
			{
				tmp = new Arc;
				tmp->cost = adjMat[i][j];
				tmp->u = i;
				tmp->v = j;
				vertexArc.push_back(*tmp);
				delete tmp;
			}
		}
	}
}

bool cmp(Arc a,Arc b)
{
	return a.cost < b.cost;
}

bool FindTree(UINT a,UINT b,vector<vector<UINT>> &Tree)
{
	UINT index_u = INF;
	UINT index_v = INF;
	for(int i=0;i<Tree.size();i++)
	{
		if (find(Tree[i].begin(), Tree[i].end(), a) != Tree[i].end())
			index_u = i;
		if (find(Tree[i].begin(), Tree[i].end(), b) != Tree[i].end())
			index_v = i;
		if (index_u != INF&&index_v != INF) break;
	}
	if(index_u!=index_v)
	{
		for(int i=0;i<Tree[index_v].size();i++)
		{
			Tree[index_u].push_back(Tree[index_v][i]);
		}
		Tree[index_v].clear();
		return true;
	}
	else return false;
}

void Kruskal(UINT adjMat[][vexCounts])
{
	vector<Arc> vertexArc;
	int ct = 0;
	ReadArc(adjMat, vertexArc);
	sort(vertexArc.begin(), vertexArc.end(), cmp);
	vector<vector<UINT>> Tree(vexCounts);
	for(UINT i=0;i<vexCounts;i++)
	{
		Tree[i].push_back(i);
	}
	for(UINT i=0;i<vertexArc.size();i++)
	{
		UINT u = vertexArc[i].u;
		UINT v = vertexArc[i].v;
		if(FindTree(u,v,Tree))
		{
			ct++;
			cout << vextex[u] << "----" << vextex[v] << endl;
		}
		if (ct == vexCounts - 1)break;
	}
}

unsigned FindMin(UINT Dis[])
{
	UINT min=INF,idx=0;
	for (int i=0;i<vexCounts;i++)
	{
		if(min>Dis[i]&&Dis[i])
		{
			idx = i;
			min = Dis[i];
		}
	}
	return idx;
}

void ChangeDis(UINT adjMat[][vexCounts],UINT Distance[],UINT Dis[],UINT idx)
{
	for(int i=0;i<vexCounts;i++)
	{
		if(Dis[i]&&adjMat[idx][i]!=INF&&(Distance[idx]+adjMat[idx][i])<Dis[i])
		{
			Dis[i]=Distance[idx] + adjMat[idx][i];
		}
	}
}

UINT Dis[vexCounts],Distance[vexCounts];

void Dijkstra(UINT adjMat[][vexCounts],int idx)
{
	for(int i=0;i<vexCounts;i++)
	{
		Dis[i] = adjMat[i][idx];
	}
	Dis[idx] = 0;
	Distance[idx] = 0;
	for(int i=1;i<vexCounts;i++)
	{
		UINT min = FindMin(Dis);
		Distance[min] = Dis[min];
		Dis[min] = 0;
		ChangeDis(adjMat, Distance, Dis, min);
	}
}

void Floyd(UINT adjMat[][vexCounts])
{
	UINT data[vexCounts][vexCounts];
	memcpy(data, adjMat, sizeof(UINT)*vexCounts*vexCounts);
	for(int i=0;i<vexCounts;i++)
	{
		for(int j=0;j<vexCounts;j++)
		{
			for(int k=0;k<vexCounts;k++)
			{
				if(data[j][i]!=INF&&data[i][k]!=INF)
					data[j][k] = min(data[j][k], data[j][i] + data[i][k]);
			}
		}
	}
	for(int i=0;i<vexCounts;i++)
	{
		for(int j=0;j<vexCounts;j++)
		{
			cout << data[i][j] << '\t';
		}
		cout << endl;
	}
}

int main()
{
	UINT adjMat[vexCounts][vexCounts];
	AdjMatrix(adjMat);
	cout << "Prim" << endl;
	Prim(adjMat, 0);
	cout << "Kruskal" << endl;
	Kruskal(adjMat);
	Dijkstra(adjMat, 0);
	for(int i=0;i<vexCounts;i++)
	{
		cout << Distance[i] << ' ';
	}
	cout << endl;
	cout << "Floyd" << endl;
	Floyd(adjMat);
	return 0;
}