SPFA 算法

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cmath>
  4 #include <vector>
  5 #include <cstring>
  6 #include <string>
  7 #include <algorithm>
  8 #include <string>
  9 #include <set>
 10 #include <functional>
 11 #include <numeric>
 12 #include <sstream>
 13 #include <stack>
 14 #include <map>
 15 #include <queue>
 16 #include <deque>
 17 //#pragma comment(linker, "/STACK:102400000,102400000")
 18 #define CL(arr, val)    memset(arr, val, sizeof(arr))
 19 
 20 #define ll long long
 21 #define INF 0x7f7f7f7f
 22 #define lc l,m,rt<<1
 23 #define rc m + 1,r,rt<<1|1
 24 #define pi acos(-1.0)
 25 
 26 #define L(x)    (x) << 1
 27 #define R(x)    (x) << 1 | 1
 28 #define MID(l, r)   (l + r) >> 1
 29 #define Min(x, y)   (x) < (y) ? (x) : (y)
 30 #define Max(x, y)   (x) < (y) ? (y) : (x)
 31 #define E(x)        (1 << (x))
 32 #define iabs(x)     (x) < 0 ? -(x) : (x)
 33 #define OUT(x)  printf("%I64d\n", x)
 34 #define lowbit(x)   (x)&(-x)
 35 #define Read()  freopen("a.txt", "r", stdin)
 36 #define Write() freopen("b.txt", "w", stdout);
 37 #define maxn 1010
 38 #define maxv 1010
 39 #define mod 1000000000
 40 using namespace std;
 41 
 42 struct edge
 43 {
 44     int to,weight;
 45 };
 46 vector<edge>adjmap[maxn]; //动态邻接表
 47 bool in_queue[maxn]; //顶点是否在队列中
 48 int in_sum[maxn];//顶点入队次数
 49 int dist[maxn];//源点到各点的最短路径
 50 int path[maxn]; //存储到达i的前一个顶点
 51 int nodesum; //顶点数
 52 int edgesum; //边数
 53 
 54 bool SPFA(int source)
 55 {
 56     deque<int>dq;
 57     int i,j,x,to;
 58     for(int i=1;i<=nodesum;i++)
 59     {
 60         in_sum[i]=0;
 61         in_queue[i]=false;
 62         dist[i]=INF;
 63         path[i]=-1;
 64     }
 65     dq.push_back(source);
 66     in_sum[source]++;
 67     dist[source]=0;
 68     in_queue[source]=true;
 69     //初始化 完成
 70     while(!dq.empty())
 71     {
 72         x=dq.front();  //取出队首元素
 73         dq.pop_front();
 74         in_queue[x]=false; //访问标记置0 ,同一个顶点可以访问多次,只要dist值变小
 75         for(i=0;i<adjmap[x].size();i++)
 76         {
 77             to=adjmap[x][i].to;
 78             if((dist[x]<INF)&&(dist[to]>dist[x]+adjmap[x][i].weight))
 79             {
 80                 dist[to]=dist[x]+adjmap[x][i].weight;
 81                 path[to]=x;  //记录路径
 82                 if(!in_queue[to])
 83                 {
 84                     in_queue[to]=true;
 85                     in_sum[to]++;  //访问次数加1
 86                     if(in_sum[to]==nodesum) return false; //访问次数等于 顶点数 存在负权回路
 87                     if(!dq.empty())
 88                     {
 89                         if(dist[to]>dist[dq.front()]) dq.push_back(to); //大的加入 队尾
 90                         else dq.push_front(to); //小的加入队首
 91                     }
 92                     else dq.push_back(to); //队列为空加入队尾
 93                 }
 94             }
 95         }
 96     }
 97 }
 98 
 99 void Prit_Path(int x)
100 {
101     stack<int>s;
102     int w=x;
103     while(path[w]!=-1)  //用栈保存路径
104     {
105         s.push(w);
106         w=path[w];
107     }
108     cout<<"顶点1到顶点"<<x<<"最短路径长度为:"<<dist[x]<<endl;
109     cout<<"所经过的路径为:1 ";
110     while(!s.empty())
111     {
112         cout<<s.top()<<" ";
113         s.pop();
114     }
115     cout<<endl;
116 }
117 int main()
118 {
119     freopen("a.txt","r",stdin);
120     int i,s,e,w;
121     edge temp;
122    // cout<<"输入顶点数和边数：";
123     cin>>nodesum>>edgesum;
124     for(int i=1;i<=nodesum;i++) adjmap[i].clear();
125     for(int i=1;i<=edgesum;i++)
126     {
127        // cout<<"输入第"<<i<<"条边的起点,终点还有对应的权值:";
128         cin>>s>>e>>w;
129         temp.to=e;
130         temp.weight=w;
131         adjmap[s].push_back(temp);
132     }
133     if(SPFA(1))
134     {
135         for(int i=2;i<=nodesum;i++) Prit_Path(i);
136     }
137     else cout<<"图中存在负权回路"<<endl;
138     return 0;
139 }