hdoj2544 最短路（Dijkstra || Floyd || SPFA）

题目链接

http://acm.hdu.edu.cn/showproblem.php?pid=2544

思路

最短路算法模板题，求解使用的Dijkstra算法、Floyd算法、SPFA算法可以当做求解最短路问题的模板使用。

代码

Dijkstra算法：

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdio>
 using namespace std;
 
 const int INF = 0x3f3f3f;
 const int N =  + ;
 int map[N][N];
 int dist[N];
 int visit[N];
 int n, m;
 
 void dijkstra()
 {
     memset(visit, , sizeof(visit));
     for (int i = ; i <= n; i++)
         dist[i] = map[][i];
     dist[] = ;
     int min_dist, now;
     for (int i = ; i <= n; i++)
     {
         min_dist = INF;
         for (int j = ; j <= n; j++)
         {
             if (!visit[j] && dist[j] < min_dist)
             {
                 min_dist = dist[j];
                 now = j;
             }
         }
         if (min_dist == INF) break;
         visit[now] = ;
         for (int j = ; j <= n; j++)    //“松弛”操作
         {
             if (dist[now] + map[now][j] < dist[j])
                 dist[j] = dist[now] + map[now][j];
         }
     }
     printf("%d\n", dist[n]);
 }
 
 int main()
 {
     //freopen("hdoj2544.txt", "r", stdin);
     while (scanf("%d%d", &n, &m) ==  && n)
     {
         memset(map, INF, sizeof(map));
         int a, b, c;
         for (int i = ; i < m; i++)
         {
             scanf("%d%d%d", &a, &b, &c);
             map[a][b] = map[b][a] = c;
         }
         dijkstra();
     }
     return ;
 }

Floyd算法：

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdio>
 using namespace std;
 
 const int INF = 0x3f3f3f;
 const int N =  + ;
 int map[N][N];
 int n, m;
 
 void floyd()
 {
     for (int k = ; k <= n; k++)
         for (int i = ; i <= n; i++)
             for (int j = ;j <= n; j++)
                 map[i][j] = min(map[i][j], map[i][k] + map[k][j]);
     printf("%d\n", map[][n]);
 }
 
 int main()
 {
     //freopen("hdoj2544.txt", "r", stdin);
     while (scanf("%d%d", &n, &m) ==  && n)
     {
         memset(map, INF, sizeof(map));
         int a, b, c;
         for (int i = ; i < m; i++)
         {
             scanf("%d%d%d", &a, &b, &c);
             map[a][b] = map[b][a] = c;
         }
         floyd();
     }
     return ;
 }

SPAF算法：

 #include <algorithm>
 #include <iostream>
 #include <cstring>
 #include <cstdio>
 #include <queue>
 #include <vector>
 using namespace std;
 
 struct Edge
 {
     int s, e, dist;    //边的起点、终点、长度
 
     Edge() {}
     Edge(int s, int e, int d) :s(s), e(e), dist(d) {}
 };
 
 const int INF = 0x3f3f3f;
 const int N =  + ;
 vector<Edge> v[N];    //使用邻接表存储图
 int dist[N];
 int visit[N];
 int n, m;
 
 void spfa(int s)
 {
     queue<int> q;
     memset(dist, INF, sizeof(dist));
     memset(visit, , sizeof(visit));
     q.push(s);
     visit[s] = ;
     dist[s] = ;
 
     while (!q.empty())
     {
         int s = q.front();
         q.pop();
         visit[s] = ;
         for (int i = ; i < v[s].size(); i++)
         {
             int e = v[s][i].e;
             if (dist[e] > dist[s] + v[s][i].dist)
             {
                 dist[e] = dist[s] + v[s][i].dist;
                 if (visit[e] == )
                 {
                     visit[e] = ;
                     q.push(e);
                 }
             }
         }
     }
     printf("%d\n", dist[n]);
 }
 
 int main()
 {
     //freopen("hdoj2544.txt", "r", stdin);
     while (scanf("%d%d", &n, &m) ==  && n)
     {
         for (int i = ;i <= n; i++)
             v[i].clear();
         int a, b, c;
         for (int i = ; i < m; i++)
         {
             scanf("%d%d%d", &a, &b, &c);
             v[a].push_back(Edge(a, b, c));
             v[b].push_back(Edge(b, a, c));
         }
         spfa();    //求结点1到其余各点的最短路径
     }
     return ;
 }