最短路

复习下图论算法

1. 邻接表的Dijkstra

//邻接表存储图的最短路 
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
using namespace std;

#define MAXN 100100
struct Edge
{
  int u, next, val;
  Edge() {}
  Edge( int v , int Next ,int Val): u(v),next(Next), val(Val) { }      
}edge[MAXN];

const int inf = 0x7f7f7f7f;
int head[MAXN],dis[MAXN], visit[MAXN], size, S, T, N, M;

void init( )
{
  for( int i = 0; i < MAXN; i++)
       head[i] = -1;
  size = 0;     
}

void AddEdge( int u, int v, int val)
{
   edge[size] = Edge( v, head[u], val);
   head[u] = size++;
   
   edge[size] = Edge( u, head[v], val);
   head[v] = size++;
     
}


int dij( )
{
   for( int i = 1; i <= N; i++)
   {
        dis[i] = inf;
        visit[i] = 0;
   }
   for( int e = head[S]; e != -1; e = edge[e].next )
   {
      
        int v = edge[e].u;
        int w = edge[e].val;
        dis[v] = w;          
        
   }
   visit[S] = 1;
   dis[S] = 0;
   for( int i = 1; i <= N; i++)
   {   
       int oo = inf, k;
       for( int j = 1; j <= N; j++)      
       {
          if( !visit[j] && dis[j] < oo )
          {
             oo = dis[j];
             k = j;
              
          }     
       }
       visit[k] = 1;
       for( int e = head[k]; e != -1; e = edge[e].next)
       {  
          int v = edge[e].u;
          int w = edge[e].val;
          if( !visit[v] && dis[v] > dis[k] + w && dis[k] != inf)
          {
                dis[v] = dis[k] + w;    
              
          }  
            
       }
   }
   return dis[T];
} 
        

    
    

int main( )
{
  int a, b, c;
  while( scanf("%d%d", &N, &M), N + M)
  {
     init( );
     for( int i = 1; i <= M; i++)
     {
         scanf("%d%d%d",&a, &b, &c);
         AddEdge(a, b, c);   
     } 
     S = 1;
     T = N;      
     printf("%d\n", dij());
  }      
  return 0;  
}

2. 邻接表 + 优先队列 + Dijkstra

//邻接表存储图的最短路 
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
#include <queue>
using namespace std;

#define MAXN 100100
struct Edge
{
  int u, next, val;
  Edge() {}
  Edge( int v , int Next ,int Val): u(v),next(Next), val(Val) { }      
}edge[MAXN];

const int inf = 0x7f7f7f7f;
int head[MAXN],dis[MAXN], visit[MAXN], size, S, T, N, M;


struct node
{
  int ID,dis;
  bool operator < ( const node &A) const 
  {
      return dis < A.dis;     
       
  }
};

void init( )
{
  for( int i = 0; i <= N; i++)
  {
       head[i] = -1;
       visit[i] = 0;
       dis[i] = inf;
  }
  size = 0;
       
}

void AddEdge( int u, int v, int val)
{
   edge[size] = Edge( v, head[u], val);
   head[u] = size++;
   
   edge[size] = Edge( u, head[v], val);
   head[v] = size++;
     
}

//优先队列优化 
int dij( )
{
   priority_queue<node>q;
   node p;
   p.ID = S;
   p.dis = 0;
   q.push(p);
   dis[S] = 0;
   while( !q.empty( ))
   {  
       p = q.top( );
       q.pop();
       int v = p.ID;
       int wx = p.dis;
       if( wx != dis[v] ) continue;  
       for( int e = head[v]; e != -1; e = edge[e].next)
       {  
          int u = edge[e].u;
          int w = edge[e].val;
          if( dis[u] > wx + w )
          {
                dis[u] = wx + w;    
                p.ID = u;
                p.dis = dis[u];
                q.push( p );
          }  
            
       }
   }
   return dis[T];
} 
        

    
    

int main( )
{
  int a, b, c;
  while( scanf("%d%d", &N, &M), N + M)
  {
     init( );
     for( int i = 1; i <= M; i++)
     {
         scanf("%d%d%d",&a, &b, &c);
         AddEdge(a, b, c);   
     } 
     S = 1;
     T = N;      
     printf("%d\n", dij());
  }      
  return 0;  
}