解題模型:

 （1）佇列式(FIFO):  分支限界法按照佇列先進先出（FIFO）原則選取下一個節點為擴充套件節點。

 （2）優先佇列式分支限界: 按照優先佇列中規定的優先順序選取優先順序最高的節點成為當前擴充套件節點。

分支限界法與回溯法的差別：

/**
   @回溯法-優先佇列解単源最短路徑
*/
#include<iostream>
#include<algorithm>
#include<queue>
#define MAX 100
#define LIMITLESS 65535
using namespace std;
int cost[MAX];                 //源點到頂點的距離
typedef struct{
    bool operator()(int &a,int &b){
         return cost[a]>cost[b];
    }
}cmp;
typedef struct Graph{
    int v,e;
    int vex[MAX];
    int wei[MAX][MAX];
}Graph,*graph;
void createGraph(graph g){
    cout<<"輸入頂點和邊數:"<<endl;
    cin>>g->v>>g->e;
    cout<<"輸入頂點值:"<<endl;
    for(int i = 1;i<=g->v;i++){
         cin>>g->vex[i];
    }
    for(int i = 1;i<=g->v;i++){          //圖的權值初始化
        for(int j = 1;j<=g->v;j++){
            g->wei[i][j] = LIMITLESS;
        }
    }
    cout<<"輸入兩連線點下標和權值:"<<endl;
    int k1,k2,weight;
    for(int i = 1;i<=g->e;i++){
        cin>>k1>>k2>>weight;
        g->wei[k1][k2] = weight;
    }
}
void  printGraph(graph g){
       for(int i = 1;i<=g->v;i++){
          for(int j = 1;j<=g->v;j++){
              if(g->wei[i][j]!=LIMITLESS){
                  cout<<g->wei[i][j]<<"  ";
              }
              else{
                  cout<<"oo"<<"  ";
              }
          }
          cout<<endl;
      }
}
void  dijkstra(graph g,int sour){
      cost[sour] = 0;
      for(int i = 2;i<=g->v;i++){                   //cost[i]初始化為源點到各頂點的權值
          cost[i] = g->wei[sour][i];
      }
      priority_queue<int,vector<int>,cmp> p;      //優先佇列
      p.push(sour);                              //源點入佇列
      int flag [MAX];                           //頂點的出隊順序
      int k = 0;
      while(!p.empty()){
          int item = p.top();
          flag[k++] = item;
          p.pop();
          /*頂點間距離優化*/
          for(int i = item;i<=g->v;i++){
             if((g->wei[item][i]!=LIMITLESS)&&(cost[item]+g->wei[item][i]<=cost[i])){
                  cost[i] = cost[item]+g->wei[item][i];
                  p.push(i);
             }
          }
      }
      for(int i = 2;i<=g->v;i++){
          cout<<"源點到"<<i<<"頂點的最短距離為:"<<cost[i]<<endl;
      }
      cout<<"頂點的出佇列順序(按源點到頂點距離短的優先):"<<endl;
      for(int i = 0;i<k;i++){
          cout<<flag[i]<<" ";
      }
}
int main(){
     Graph g;               //不能用指標定義(graph g)
     createGraph(&g);
     cout<<"構建的圖為:"<<endl;
     printGraph(&g);
     cout<<"(分治限界法-優先佇列)単源最短路徑為:"<<endl;
     dijkstra(&g,1);
}