2013寒假ACM集训_最短路

一、单源最短路

1、正权

dijkstra

2、任意权

2、1 bellman-ford

2、2 spfa

二、任意点之间最短路

floyd

三、最短路的应用：差分约束系统

参考模板

http://www.toposort.com/blog/shortest-path.html

贴一个新的最新的 spfa模板:

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <queue>
#include <algorithm>
#include <vector>
#define LL __int64
const int maxm = 2e6 + 10;
const int maxn = 5e5 + 10;
const int INF = 1<<28;
using namespace std;
int cnt, head[maxn], d[maxn], vis[maxn], n, m;

struct node
{
    int v, w, next;
}edge[2*maxm];

void add(int u, int v, int w)
{
    edge[cnt].v = v;
    edge[cnt].w = w;
    edge[cnt].next = head[u];
    head[u] = cnt++;
};

void spfa(int s)
{
    queue<int>q;
    int i, u, v;
    for(i = 0; i <= n; i++)
        d[i] = INF;
    d[s] = 0;

    q.push(s);

    vis[s] = 1;
    while(!q.empty())
    {
        u = q.front();
        q.pop();
        vis[u] = 0;
        for(i = head[u]; i != -1; i = edge[i].next)
        {
            v=edge[i].v;
            if(d[u] + edge[i].w < d[v])
            {
                d[v] = d[u] + edge[i].w;
                if(!vis[v])
                {
                    vis[v] = 1;
                    q.push(v);
                }
            }
        }
    }
};
int main()
{
    int  i;
    int a, b, w;
    int s, t;
    while(~scanf("%d%d", &n, &m))
    {
        cnt = 0;
        memset(head, -1, sizeof(head));
        memset(vis, 0, sizeof(vis));
        for(i = 0; i < m; i++)
        {
            scanf("%d%d%d", &a, &b, &w);
            add(a, b, w);
            add(b, a, w);
        }
        scanf("%d%d", &s, &t);
        spfa(s);
        printf("%d\n", d[t]);
    }
}