单源最短路模板

Dijkstra(迪杰斯特拉)算法是典型的最短路径路由算法，用于计算一个节点到其他所有节点的最短路径。

一：SPFA

#define INF 1000000000
#define MAXN 50010  //点个数
#define MAXM 6000000 //边条数
int dis[MAXN];//结果
struct Node{
	int v, next;
	int  c;
}E[MAXM];
int head[MAXN];
int NE;
void init(int n)
{
	for (int i = 0; i <= n; i ++)
	{
		head[i] = -1;
		dis[i] = INF;
	}
	NE = 0;	
}

void insert(int x, int y, int c)
{
	E[NE].v = y;
	E[NE].c = c;
	E[NE].next = head[x];
	head[x] = NE ++;
}

bool spfa(int s, int n)//s为起点
{
	int p,i;
	queue<int>q;
	while(!q.empty())
		q.pop();

	bool hash[MAXN];
	int count[MAXN];
	memset (count, 0, sizeof(int) * (n + 2));
	memset(hash,0,sizeof(bool) * ( n + 2)) ;

	hash[s] = 1;
	
	dis[s] = 0;
	q.push(s);
	count [s] = 1;
	while(!q.empty())
	{
		p = q.front();
		q.pop();
		if(count[p] > n)
			return false; //负环
		hash[p] = 0;
		for(i = head[p]; i != -1; i = E[i].next)
		{
			int v = E[i].v;
			int cc = E[i].c;
			if(dis[p] + cc < dis[v] || dis[v] == INF)  
//v - u <= k时候是这样的,如果v - u >= k 改符号
			{
				dis[v] = dis[p] + cc;
				if(hash[v] == 0)
				{
					count[v] ++;
					hash[v] = 1;
					q.push(v);
				}
			}
		}
	}
	return 1;
}

二：dijkstra

const int N = 1001; //点
using namespace std;
struct node
{
	int l,dir;
}w;//边
struct In
{
	int idx;
	int l;
	bool friend operator<(const In &a, const In &b)
	{
		return a.l > b.l;
	}
}ww,zz;//bfs
vector<node>mmap[N];
priority_queue<In>q;
int dis[N];
int start, end; //start 起点, end 终点
int nodenum;//点数 = end
int n, m;
int base;
void init()
{
	while (!q.empty())
		q.pop();
	int i;
	for (i = 0; i <= nodenum; i++)
	{
		dis[i] = -1;
		mmap[i].clear();
	}
	return;
}

inline void creat(int s, int e, int value) 
{
	w.l = value;
	w.dir = e;
	mmap[s].push_back(w);
	return;
}
void dij()
{
	int i, j;
	ww.idx = start;
	ww.l = 0;
	int size = 0;
	node now;
	q.push(ww);
	while (!q.empty())
	{
		ww = q.top();
		q.pop();
		
		if (dis[ww.idx] != -1)
			continue;
		dis[ww.idx] = ww.l;
		if(ww.idx == end)
			return;
		size = mmap[ww.idx].size();
		for (i = 0;i < size; i++)
		{
			now = mmap[ww.idx][i];
			zz.idx = now.dir;
			zz.l = ww.l + now.l;
			if(dis[zz.idx] == -1)
			{
				q.push(zz);
			}
		}
	}
	return;
}