代码随想录算法训练营第六十天|图论part10

#include <iostream>
#include <vector>
#include <climits>
#include <queue>
#include <list>struct Edge{int s,t;int val;Edge(int _s,int _t,int _val):s(_s),t(_t),val(_val){}
};using namespace std;
int main(){int n,m;cin>>n>>m;vector<list<Edge>>grid(n+1);vector<bool>isInQueue(n+1,false);vector<int>minDist(n+1,INT_MAX);queue<int>myQueue;while(m--){int s,t,v;cin>>s>>t>>v;grid[s].push_back(Edge(s,t,v));}int start=1;int end=n;minDist[start]=0;myQueue.push(start);while(!myQueue.empty()){int cur=myQueue.front();myQueue.pop();isInQueue[cur]=false;//出队后需标记const auto& edges=grid[cur];for(auto& edge:edges){int s=edge.s;int t=edge.t;int val=edge.val;if(minDist[s]==INT_MAX)continue;minDist[t]=min(minDist[s]+val,minDist[t]);if(!isInQueue[t]){myQueue.push(t);isInQueue[t]=true;//入队后需标记}}}if(minDist[end]!=INT_MAX)cout<<minDist[end];else cout<<"unconnected";}

思路：

普通版的福特算法，考虑第n次松弛是否会出现更短的路径。出现就标记

#include <iostream>
#include <vector>
#include <climits>
using namespace std;int main(){//数据读取int n,m;cin>>n>>m;vector<vector<int>>grid;vector<int>minDist(n+1,INT_MAX);while(m--){int s,t,v;cin>>s>>t>>v;grid.push_back({s,t,v});}int start=1;int end=n;minDist[start]=0;bool flag=false;for(int i=1;i<=n;i++){for(int j=0;j<grid.size();j++){int s=grid[j][0];int t=grid[j][1];int val=grid[j][2];if(minDist[s]==INT_MAX)continue;if(i<n){minDist[t]=min(minDist[t],minDist[s]+val);}else{if(minDist[s]+val<minDist[t]) flag=true;}}}//输出if(flag){cout<<"circle";return 0;} if(minDist[end]!=INT_MAX)cout<<minDist[end];else cout<<"unconnected";
}

队列优化版的福特算法 ，统计节点入队次数。如果节点入队次数超过n，说明出现环。

#include <iostream>
#include <vector>
#include <climits>
#include <queue>
#include <list>struct Edge{int s,t;int val;Edge(int _s,int _t,int _val):s(_s),t(_t),val(_val){}
};using namespace std;
int main(){//数据读取int n,m;cin>>n>>m;vector<list<Edge>>grid(n+1);vector<bool>isInQueue(n+1,false);vector<int>minDist(n+1,INT_MAX);queue<int>myQueue;while(m--){int s,t,v;cin>>s>>t>>v;grid[s].push_back(Edge(s,t,v));}int start=1;int end=n;minDist[start]=0;myQueue.push(start);bool flag=false;vector<int>count(n+1,0);//统计每个节点的入队数量while(!myQueue.empty()){int cur=myQueue.front();myQueue.pop();isInQueue[cur]=false;//出队后需标记const auto& edges=grid[cur];for(auto& edge:edges){int s=edge.s;int t=edge.t;int val=edge.val;if(minDist[s]==INT_MAX)continue;minDist[t]=min(minDist[s]+val,minDist[t]);if(!isInQueue[t]){myQueue.push(t);isInQueue[t]=true;//入队后需标记count[t]++;if(count[t]==n){flag=true;while(!myQueue.empty()){myQueue.pop();}//这里是防止再次进入while循环 break;}}}}//输出if(flag){cout<<"circle";return 0;} if(minDist[end]!=INT_MAX)cout<<minDist[end];else cout<<"unconnected";}

#include <iostream>
#include <vector>
#include <climits>using namespace std;int main(){int n,m;cin>>n>>m;vector<vector<int>>grid;while(m--){int s,t,v;cin>>s>>t>>v;grid.push_back({s,t,v});}int start,end,k;cin>>start>>end>>k;vector<int>minDist(n+1,INT_MAX);minDist[start]=0;for(int i=1;i<=k+1;i++){auto copy_minDist=minDist;for(int j=0;j<grid.size();j++){int s=grid[j][0];int t=grid[j][1];int val=grid[j][2];if(copy_minDist[s]==INT_MAX)continue;minDist[t]=min(copy_minDist[s]+val,minDist[t]);}}if(minDist[end]==INT_MAX)cout<<"unreachable";else cout<<minDist[end];}