#include <stdio.h>
#include <stdlib.h>

//图节点
typedef struct VertexNode
{
	char name;
	int key;
	VertexNode *p;
}Vertex,*pVertex;

//图
typedef struct 
{
	int vn;
	int **E;
	pVertex *V;
}Graph,*pGraph;
//根据算法导论 图24-4 初始化图
pGraph initGraph()
{
	pGraph g=(pGraph)malloc(sizeof(Graph));
	g->vn=5;
	pVertex vs=(pVertex)malloc(sizeof(Vertex));
	vs->name='s';
	vs->key=0;
	vs->p=NULL;
	pVertex vt=(pVertex)malloc(sizeof(Vertex));
	vt->name='t';
	vt->key=INT_MAX;
	vt->p=NULL;
	pVertex vy=(pVertex)malloc(sizeof(Vertex));
	vy->name='y';
	vy->key=INT_MAX;
	vy->p=NULL;
	pVertex vx=(pVertex)malloc(sizeof(Vertex));
	vx->name='x';
	vx->key=INT_MAX;
	vx->p=NULL;
	pVertex vz=(pVertex)malloc(sizeof(Vertex));
	vz->name='z';
	vz->key=INT_MAX;
	vz->p=NULL;

	g->V=(pVertex*)malloc(g->vn*sizeof(pVertex));
	g->V[0]=vs;
	g->V[1]=vt;
	g->V[2]=vy;
	g->V[3]=vx;
	g->V[4]=vz;

	g->E = (int**)malloc(g->vn*sizeof(int*));
	for(int i=0;i<g->vn;i++)
	{
		g->E[i]=(int*)malloc(g->vn*sizeof(int));
	}
	for(int i=0;i<g->vn;i++)
	{
		for(int j=0;j<g->vn;j++)
		{
			g->E[i][j]=INT_MAX;
		}
	}
	g->E[0][1]=6;
	g->E[0][2]=7;
	g->E[1][2]=8;
	g->E[1][3]=5;
	g->E[1][4]=-4;
	g->E[2][3]=-3;
	g->E[2][4]=9;
	g->E[3][1]=-2;
	g->E[4][3]=7;
	return g;
}

void relax(pGraph g,int u,int v)
{
	//无边，不进行松弛
	if(g->E[u][v]==INT_MAX)
		return;
	int sum,uk=g->V[u]->key,vk=g->V[v]->key,ew=g->E[u][v];
	//根据规则，加上无穷等于无穷
	if(uk==INT_MAX || ew==INT_MAX)
		sum=INT_MAX;
	else
		sum=uk+ew;
	if(vk>sum)
	{
		g->V[v]->key=sum;
		g->V[v]->p=g->V[u];
	}
}

bool BellmanFord(pGraph g)
{
	for(int i=1;i<=g->vn-1;i++)
	{
		for(int j=0;j<g->vn;j++)
		{
			for(int k=0;k<g->vn;k++)
			{
				if(g->E[j][k]<INT_MAX)
					relax(g,j,k);
			}
		}
	}
	for(int u=0;u<g->vn;u++)
	{
		for(int v=0;v<g->vn;v++)
		{
			if(g->E[u][v]>0)
			{
				int sum,uk=g->V[u]->key,vk=g->V[v]->key,ew=g->E[u][v];
				//根据规则，加上无穷等于无穷
				if(uk==INT_MAX || ew==INT_MAX)
					sum=INT_MAX;
				else
					sum=uk+ew;
				if(vk>sum)
					return false;
			}
		}
	}
	return true;
}

void printKey(pGraph g)
{
	for(int i=0;i<g->vn;i++)
	{
		pVertex v=g->V[i];
		printf("%c %d\n",v->name,v->key);
	}
}

void main()
{
	pGraph g=initGraph();
	bool b=BellmanFord(g);
	if(b)
		printKey(g);
	else
		printf("No Path!");
	getchar();
}