最短路 dijkstra 优先队列

1.裸题 hdu2544

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

Way1:

好像不对

 #include <cstdio>
 #include <cstdlib>
 #include <cmath>
 #include <cstring>
 #include <stdbool.h>
 #include <set>
 #include <vector>
 #include <map>
 #include <queue>
 #include <algorithm>
 #include <iostream>
 using namespace std;
 #define maxn 100+5
 #define inf 1e9

 long dist[maxn],road[maxn][maxn];
 bool vis[maxn];
 struct cmp
 {
     bool operator() (long a,long b)
     {
         return dist[a]>dist[b];
     }
 };
 priority_queue<long,vector<long>,cmp> f;

 int main()
 {
     long n,m,i,j,x,y,z,d;
     while ()
     {
         scanf("%ld%ld",&n,&m);
         if (n== && m==)
             break;
         for (i=;i<=n;i++)
             for (j=;j<=n;j++)
                 road[i][j]=inf;
         for (i=;i<=m;i++)
         {
             scanf("%ld%ld%ld",&x,&y,&z);
             road[x][y]=min(road[x][y],z);
             road[y][x]=road[x][y];
         }
         for (i=;i<=n;i++)
         {
             vis[i]=false;
             dist[i]=inf;
         }
         dist[]=;
         //pay attention!
         while (!f.empty())
             f.pop();
         f.push();
         for (j=;j<n;j++) //use 'i' wrong!
         {
             while (vis[f.top()])
                 f.pop();
             d=f.top();
             if (d==n)
                 break;
             vis[d]=true;
             f.pop();

             for (i=;i<=n;i++)
                 if (!vis[i] && dist[i]>dist[d]+road[i][d])
                 {
                     dist[i]=dist[d]+road[i][d];;
                     f.push(i);
                 }
         }
         printf("%ld\n",dist[n]);
     }
     return ;
 }
 /*
 6 7
 1 2 10
 1 2 3
 1 3 1
 2 4 3
 4 5 1
 5 6 10
 2 5 1
 */

Way2:

自行写堆，让堆中的值减小(路径长度减小)，在堆中上升。

只要掌握了合理的写法，其实也不是特别不好理解和难写

 #include <cstdio>
 #include <cstdlib>
 #include <cmath>
 #include <cstring>
 #include <stdbool.h>
 #include <set>
 #include <vector>
 #include <map>
 #include <queue>
 #include <algorithm>
 #include <iostream>
 using namespace std;
 #define maxn 10000+5
 #define inf 1e9

 //pos[i]:编号为i的城市到起点的距离 在 树中的位置
 long dist[maxn],road[maxn][maxn],tree[maxn],pos[maxn],g=;
 bool vis[maxn];

 //minimum-heap
 void up(long i)
 {
     long j,temp;
     while (i>)
     {
         j=i>>;
         //i>j
         if (dist[tree[i]]<dist[tree[j]])
         {
             temp=tree[i];
             tree[i]=tree[j];
             tree[j]=temp;
             pos[tree[i]]=i;
             pos[tree[j]]=j;
         }
         else
             break;
         i=j;
     }
 }

 void down(long i)
 {
     long j,temp;
     while ((i<<)<=g)
     {
         j=i<<;
         if (dist[tree[j+]]<dist[tree[j]])
             j++;
         //i<j
         if (dist[tree[i]]>dist[tree[j]])
         {
             temp=tree[i];
             tree[i]=tree[j];
             tree[j]=temp;
             pos[tree[i]]=i;
             pos[tree[j]]=j;
         }
         else
             break;
         i=j;
     }
 }

 int main()
 {
     long n,m,i,j,x,y,z,d;
     while ()
     {
         scanf("%ld%ld",&n,&m);
         if (n== && m==)
             break;
         for (i=;i<=n;i++)
             for (j=;j<=n;j++)
                 road[i][j]=inf;
         for (i=;i<=m;i++)
         {
             scanf("%ld%ld%ld",&x,&y,&z);
             road[x][y]=min(road[x][y],z);
             road[y][x]=road[x][y];
         }
         for (i=;i<=n;i++)
         {
             vis[i]=false;
             dist[i]=-;
         }
         dist[]=;
         g=;
         tree[]=;
         pos[]=;
         for (j=;j<n;j++) //use 'i' wrong!
         {
             d=tree[];
             if (d==n)
                 break;
             tree[]=tree[g];
             pos[tree[]]=;
             g--;
             down();

             vis[d]=true;
             for (i=;i<=n;i++)
                 if (!vis[i])
                 {
                     if (dist[i]==-)
                     {
                         dist[i]=dist[d]+road[i][d];
                         g++;
                         tree[g]=i;
                         pos[i]=g;
                         up(g);
                     }
                     else if (dist[i]>dist[d]+road[i][d])
                     {
                         dist[i]=dist[d]+road[i][d];
                         up(pos[i]);
                     }
                 }
         }
         printf("%ld\n",dist[n]);
     }
     return ;
 }
 /*
 6 7
 1 2 10
 1 2 3
 1 3 1
 2 4 3
 4 5 1
 5 6 10
 2 5 1
 */

2.多关键字

L3-011. 直捣黄龙

https://www.patest.cn/contests/gplt/L3-011

 #include <cstdio>
 #include <cstdlib>
 #include <cstring>
 #include <cmath>
 #include <stdbool.h>
 #include <set>
 #include <vector>
 #include <map>
 #include <queue>
 #include <stack>
 #include <algorithm>
 #include <iostream>
 using namespace std;
 #define maxn 200+5
 #define inf 1e9

 struct node
 {
     long kill,dist,free,count;
 }point[maxn];

 struct cmp
 {
     bool operator() (long a,long b)
     {
         return point[a].dist>point[b].dist;
     }
 };
 priority_queue<long,vector<long>,cmp> f;

 long road[maxn][maxn],kill[maxn],pre[maxn],n;
 char s[maxn][];
 bool vis[maxn];

 long find(char ss[])
 {
     long i;
     for (i=;i<=n;i++)
         if (strcmp(s[i],ss)==)
             return i;
 }

 void print(long d)
 {
     if (pre[d]!=-)
     {
         print(pre[d]);
         printf("->%s",s[d]);
     }
     else
         printf("%s",s[d]);
 }

 int main()
 {
     char s1[],s2[];
     long m,i,j,d,x,y,e;
     scanf("%ld%ld%s%s",&n,&m,s1,s2);
     for (i=;i<=n;i++)
     {
         point[i].dist=inf;
         vis[i]=false;
     }
     for (i=;i<=n;i++)
         for (j=;j<=n;j++)
             road[i][j]=inf+;
     point[n].kill=;
     strcpy(s[n],s1);
     pre[n]=-;
     point[n].dist=;
     point[n].free=;
     point[n].count=;
     f.push(n);
     for (i=;i<n;i++)
     {
         scanf("%s%ld",s[i],&kill[i]);
         if (strcmp(s2,s[i])==)
             e=i;
     }
     for (i=;i<=m;i++)
     {
         scanf("%s%s%ld",s1,s2,&d);
         x=find(s1);
         y=find(s2);
         road[x][y]=min(road[x][y],d);
         road[y][x]=road[x][y];
     }
     for (j=;j<n;j++)
     {
         while (vis[f.top()])
             f.pop();
         d=f.top();
         if (d==e)
             break;
         vis[d]=true;
         for (i=;i<=n;i++)
             if (!vis[i])
             {
                 if (point[i].dist>point[d].dist+road[i][d])
                 {
                     pre[i]=d;
                     point[i].count=point[d].count;
                     point[i].dist=point[d].dist+road[i][d];
                     point[i].free=point[d].free+;
                     point[i].kill=point[d].kill+kill[i];
                     f.push(i);
                 }
                 else if (point[i].dist==point[d].dist+road[i][d])
                 {
                     point[i].count+=point[d].count;
                     if ((point[i].free<point[d].free+) ||
                         (point[i].free==point[d].free+ && point[i].kill<point[d].kill+kill[i]))
                     {
                         pre[i]=d;
                         point[i].free=point[d].free+;
                         point[i].kill=point[d].kill+kill[i];
                         f.push(i);
                     }
                 }
             }
     }
     print(e);
     printf("\n%ld %ld %ld\n",point[e].count,point[e].dist,point[e].kill);
     return ;
 }