kuangbin最短路?模板

//floyd //復雜度O(N^2) #include<iostream> #include<cstdio>using namespace std;const int INF=0x3f3f3f3f; const int MAXN=1e3+50;int mapp[MAXN][MAXN]; int N,M;int main() {scanf("%d%d",&N,&M);for(int i=1;i<=N;i++){for(int j=1;j<=M;j++){if(i==j){mapp[i][j]=0;}else{mapp[i][j]=INF;}}}int u,v,w;for(int i=1;i<=M;i++){scanf("%d%d%d",&u,&v,&w);mapp[u][v]=w;}for(int k=1;k<=N;k++){for(int i=1;i<=N;i++){for(int j=1;j<=N;j++){if(mapp[i][j]>mapp[i][k]+mapp[k][j]){mapp[i][j]=mapp[i][k]+mapp[k][j];}}}}for(int i=1;i<=N;i++){for(int j=1;j<=N;j++){printf("%10d",mapp[i][j]);}printf("\n");}return 0; }

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//Dijkstra單源最短路+路徑輸出 //鄰接矩陣復雜度O(N^2) #include<iostream> #include<cstdio> #include<algorithm>using namespace std;const int maxn=1010;const int inf=0x3f3f3f3f;int cost[maxn][maxn]; int lowcost[maxn]; bool vis[maxn]; int pre[maxn]; int n,m,beg;void dijkstra() {for(int i=0;i<n;i++){lowcost[i]=inf;vis[i]=false;pre[i]=-1;}lowcost[beg]=0;for(int j=0;j<n;j++){int k=-1;int Min=inf;for(int i=0;i<n;i++){if(!vis[i]&&lowcost[i]<Min){Min=lowcost[i];k=i;}}if(k==-1){break;}vis[k]=true;for(int i=0;i<n;i++){if(!vis[i]&&lowcost[k]+cost[k][i]<lowcost[i]){lowcost[i]=lowcost[k]+cost[k][i];pre[i]=k;}}} }int main() {scanf("%d%d",&n,&m);int a,b,c;for(int i=0;i<n;i++){for(int j=0;j<n;j++){if(i!=j){cost[i][j]=inf;}}}for(int i=0;i<m;i++){scanf("%d%d%d",&a,&b,&c);cost[a][b]=c;cost[b][a]=c;}beg=0;dijkstra();for(int i=0;i<n;i++){cout<<lowcost[i]<<" ";}cout<<endl;int node=n-1;cout<<node<<" ";while(pre[node]!=-1){cout<<pre[node]<<" ";node=pre[node];}cout<<endl;return 0; }

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//Dijkstra+堆優化 //鄰接表復雜度(eloge) #include<iostream> #include<cstdio> #include<vector> #include<cstring> #include<queue>using namespace std;const int INF=0x3f3f3f3f; const int MAXN=1000010;struct qnode{int v,c;qnode(int _v=0,int _c=0):v(_v),c(_c){}friend bool operator < (qnode a,qnode b){return a.c>b.c;} };struct edge{int v,cost;edge(int _v=0,int _cost=0):v(_v),cost(_cost){} }; vector<edge>E[MAXN];void add_edge(int u,int v,int w) {E[u].push_back(edge(v,w)); }int N,M; bool vis[MAXN]; int dist[MAXN];void Dijkstra(int n,int start) {memset(vis,false,sizeof(vis));for(int i=1;i<=n;i++){dist[i]=INF;}priority_queue<qnode>que;while(!que.empty()){que.pop();}dist[start]=0;que.push(qnode(start,0));qnode tmp;while(!que.empty()){tmp=que.top();que.pop();int u=tmp.v;if(vis[u]){continue;}vis[u]=true;for(int i=0;i<E[u].size();i++){int v=E[tmp.v][i].v;int cost=E[u][i].cost;if(!vis[v]&&dist[v]>dist[u]+cost){dist[v]=dist[u]+cost;que.push(qnode(v,dist[v]));}}} }int main() {scanf("%d%d",&N,&M);int u,v,w;for(int i=0;i<M;i++){scanf("%d%d%d",&u,&v,&w);add_edge(u,v,w);}Dijkstra(N,1);for(int i=1;i<=N;i++){cout<<dist[i]<<" ";}cout<<endl;return 0; }

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//Dijkstra+堆優化 //鄰接表復雜度(eloge) #include<iostream> #include<cstdio> #include<vector> #include<cstring> #include<queue>using namespace std;const int INF=0x3f3f3f3f; const int MAXN=1000010;struct qnode{int v,c;qnode(int _v=0,int _c=0):v(_v),c(_c){}friend bool operator < (qnode a,qnode b){return a.c>b.c;} };struct edge{int v,cost;edge(int _v=0,int _cost=0):v(_v),cost(_cost){} }; vector<edge>E[MAXN];void add_edge(int u,int v,int w) {E[u].push_back(edge(v,w)); }int N,M; bool vis[MAXN]; int dist[MAXN];void Dijkstra(int n,int start) {memset(vis,false,sizeof(vis));for(int i=1;i<=n;i++){dist[i]=INF;}priority_queue<qnode>que;while(!que.empty()){que.pop();}dist[start]=0;que.push(qnode(start,0));qnode tmp;while(!que.empty()){tmp=que.top();que.pop();int u=tmp.v;if(vis[u]){continue;}vis[u]=true;for(int i=0;i<E[u].size();i++){int v=E[tmp.v][i].v;int cost=E[u][i].cost;if(!vis[v]&&dist[v]>dist[u]+cost){dist[v]=dist[u]+cost;que.push(qnode(v,dist[v]));}}} }int main() {scanf("%d%d",&N,&M);int u,v,w;for(int i=0;i<M;i++){scanf("%d%d%d",&u,&v,&w);add_edge(u,v,w);}Dijkstra(N,1);for(int i=1;i<=N;i++){cout<<dist[i]<<" ";}cout<<endl;return 0; }

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//spafa //復雜度O(KE) #include<iostream> #include<cstdio> #include<queue> #include<queue> #include<cstring>using namespace std;const int MAXN=1010; const int INF=0x3f3f3f3f;struct edge{int v,cost;edge(int _v,int _cost):v(_v),cost(_cost){} }; vector<edge>E[MAXN];void add_edge(int u,int v,int w) {E[u].push_back(edge(v,w)); }bool vis[MAXN]; int cnt[MAXN]; int dist[MAXN];bool spfa(int start,int n) {memset(vis,false,sizeof(vis));for(int i=1;i<=n;i++){dist[i]=INF;}vis[start]=true;dist[start]=0;queue<int>que;while(!que.empty()){que.pop();}que.push(start);memset(cnt,0,sizeof(cnt));cnt[start]=1;while(!que.empty()){int u=que.front();que.pop();vis[u]=false;for(int i=0;i<E[u].size();i++){int v=E[u][i].v;if(dist[v]>dist[u]+E[u][i].cost){dist[v]=dist[u]+E[u][i].cost;if(!vis[v]){vis[v]=true;que.push(v);if(++cnt[v]>n){return false;}}}}}return true; }int main() {return 0; }

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