Assignment 7: Shortest Path Algorithms
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1125 Stockbroker Grapevine (1)
1847 Tram (1)
3259 Wormholes (3)
3169 Layout (4)
2253 Frogger (4)
3255 Roadblocks (5)
1556 The Doors (5)
2502 Subway (6)
1344 Tree Size Problem (6)
3463 Sightseeing (6)
2135 Farm Tour (7)
2404 Jogging Trails (9, challenge problem)
poj3169
spfa做差分约束
#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>#include<queue>#include<vector>using namespace std;#define maxn 10010#define inf 0x3f3f3f3fint d[maxn],cnt[maxn];bool vis[maxn];queue<int> q;typedef pair<int,int> pii;vector <pii> adj[maxn];int main(){ // freopen("layout.6.in","r",stdin); int n,a,b,i,j,k,u,v,ok,c; vector<pii>::iterator it; scanf("%d%d%d",&n,&a,&b); d[1]=0; for(i=2;i<=n;++i){ d[i]=inf; adj[i].push_back(make_pair(i-1,0)); } while(a--){ scanf("%d%d%d",&u,&v,&c); adj[u].push_back(make_pair(v,c)); } while(b--){ scanf("%d%d%d",&u,&v,&c); adj[v].push_back(make_pair(u,-c)); } ok=0; for(i=1;i<n;++i){ q.push(i); vis[i]=cnt[i]=1; } while(!q.empty()){ u=q.front(); vis[u]=0; q.pop(); // printf("u=%d\n",u); for(it=adj[u].begin();it!=adj[u].end();++it){ v=(*it).first; c=(*it).second; // printf("v=%d\n",v); if(d[v]>d[u]+c){ d[v]=d[u]+c; if(!vis[v]){ if(++cnt[v]>=n) { ok=1; goto L; } vis[v]=1; // printf("%d ",v); q.push(v); } } } }L: if(d[n]==inf){ printf("-2\n"); return 0; } for(u=1;u<=n;++u){ for(it=adj[u].begin();it!=adj[u].end();++it){ v=(*it).first; c=(*it).second; if(d[v]>d[u]+c){ // printf("u=%d v=%d c=%d du=%d dv=%d\n",u,v,c,d[u],d[v]); ok=1; goto G; } } }G: if(ok){ printf("-1\n"); }else{ printf("%d\n",d[n]); } return 0;}
poj3255A*+dijkstra求次短路（k=2短路）
#include<cstdio>#include<cstring>#include<algorithm>#include<queue>#include<iostream>using namespace std;#define inf 0x3f3f3f3f#define maxn 5010typedef pair<int,int> pii;int d[maxn];vector <pii> adjz[maxn];vector <pii> adjf[maxn];priority_queue<pii,vector<pii>,greater<pii> > pq;bool vis[maxn];int cnt[maxn];int n,m,s,t,k;typedef struct S{ int v,c; S(){} S(int cc,int vv):c(cc),v(vv){} bool operator < (const struct S& tt) const{ return c+d[v]>tt.c+d[tt.v]; }}NODE;priority_queue<NODE> q;void init(){ int i; for(i=1;i<=n;++i) { d[i]=inf; adjz[i].clear(); adjf[i].clear(); } memset(vis,0,sizeof(vis)); memset(cnt,0,sizeof(cnt)); while(!pq.empty()) pq.pop(); while(!q.empty()) q.pop();}void dijkstra(){ int u,v,c; d[t]=0; pq.push(make_pair(0,t)); vector<pii>::iterator it; while(!pq.empty()){ u=pq.top().second; pq.pop(); if(vis[u]) continue; vis[u]=1; for(it=adjf[u].begin();it!=adjf[u].end();++it){ v=(*it).second; if(vis[v]) continue; c=(*it).first; if(d[v]>d[u]+c){ d[v]=d[u]+c; pq.push(make_pair(d[v],v)); } } }}int Astar(){ int u,v,c,dc; if(d[s]==inf) return -1; q.push(NODE(0,s)); while(!q.empty()){ u=q.top().v; c=q.top().c; q.pop(); ++cnt[u]; if(u==t && cnt[u]==k) return c; if(cnt[u]>k) continue; vector<pii>::iterator it; for(it=adjz[u].begin();it!=adjz[u].end();++it){ v=(*it).second; dc=(*it).first; q.push(NODE(dc+c,v)); } } return -1;}int main(){ int i,j,u,v,c; while(scanf("%d%d",&n,&m)!=EOF){ init(); while(m--){ scanf("%d%d%d",&u,&v,&c); adjz[u].push_back(make_pair(c,v)); adjf[v].push_back(make_pair(c,u)); adjz[v].push_back(make_pair(c,u)); adjf[u].push_back(make_pair(c,v)); } s=1,t=n,k=2; if(s==t) ++k; dijkstra(); // for(i=1;i<=n;++i) printf("di=%d\n",d[i]); printf("%d\n",Astar()); } return 0;}
poj2502dijkstra和spfa的模板
#include<cstdio>#include<cstring>#include<algorithm>#include<queue>#include<iostream>#include<cmath>using namespace std;#define inf 1e10#define eps 1e-8#define maxn 210typedef pair<double,int> pii;double d[maxn];vector <pii> adj[maxn];priority_queue<pii,vector<pii>,greater<pii> > pq;bool vis[maxn];typedef struct S{ double x,y;}NODE;NODE node[maxn];double dis(int a,int b){ return sqrt((node[a].x-node[b].x)*(node[a].x-node[b].x)+(node[a].y-node[b].y)*(node[a].y-node[b].y));}int n;void dijkstra(){ int u,v; double c; d[0]=0; for(u=1;u<n;++u) d[u]=inf; pq.push(make_pair(0.0,0)); vector<pii>::iterator it; while(!pq.empty()){ u=pq.top().second; pq.pop(); // if(u==1) return; if(vis[u]) continue; vis[u]=1; for(it=adj[u].begin();it!=adj[u].end();++it){ v=(*it).second; if(vis[v]) continue; c=(*it).first; if(d[v]>d[u]+c){ d[v]=d[u]+c; pq.push(make_pair(d[v],v)); } } }}void spfa(){ int u,v; double c; queue<int> q; q.push(0); vis[0]=1; d[0]=0; for(u=1;u<n;++u) d[u]=inf; vector<pii>::iterator it; while(!q.empty()){ u=q.front(); q.pop(); vis[u]=0; for(it=adj[u].begin();it!=adj[u].end();++it){ v=(*it).second; c=(*it).first; if(d[v]>d[u]+c){ d[v]=d[u]+c; if(!vis[v]) { q.push(v); vis[v]=1; } } } }}bool equal(double x,double y){ if(x-y<eps && y-x<eps) return 1; return 0;}int main(){ // freopen("d.in","r",stdin); int i,j,s,l; double x,y,dc; scanf("%lf%lf%lf%lf",&node[0].x,&node[0].y,&node[1].x,&node[1].y); n=2; s=2; while(scanf("%lf%lf",&x,&y)!=EOF){ if(equal(x,-1)) continue; node[n].x=x; node[n].y=y; ++n; while(scanf("%lf%lf",&x,&y)!=EOF){ if(equal(x,-1)){ for(i=s;i<n-1;++i){ dc=dis(i,i+1)*0.0015; adj[i].push_back(make_pair(dc,i+1)); adj[i+1].push_back(make_pair(dc,i)); } s=n; break; } node[n].x=x; node[n].y=y; ++n; } } for(i=0;i<n;++i){ for(j=i+1;j<n;++j){ dc=dis(i,j)*0.006; adj[i].push_back(make_pair(dc,j)); adj[j].push_back(make_pair(dc,i)); } } // spfa(); dijkstra(); printf("%.0f\n",d[1]); return 0;}
poj1344根据公式： w(x, c) = (M[a, c] +M[b, c] -M[a, b])/2
#include<cstdio>int a[35][35],n;int main(){ int i,j; int ans; while(scanf("%d",&n)!=EOF && n){ for(i=0;i<n-1;++i){ for(j=i+1;j<n;++j){ scanf("%d",&a[i][j]); } } ans=0; ans+=a[0][1]; for(i=2;i<n;++i){ ans+=(a[i-2][i]+a[i-1][i]-a[i-2][i-1])>>1; } printf("%d\n",ans); } return 0;}
poj2135spfa松弛的最大流最小费模板
#include<cstdio>#include<cstring>#include<iostream>#include<algorithm>#include<queue>#include<vector>using namespace std;#define maxn 1005#define inf 0x3f3f3f3fstruct NODE{ NODE(){} NODE(int uu,int vv,int cc,int ww,int pp):u(uu),v(vv),c(cc),w(ww),p(pp){} int u,v,c,w,p;};vector<NODE> adj[maxn],nu;vector<NODE>::iterator pre[maxn];queue<int> q;int cnt[maxn];int d[maxn];bool vis[maxn];int n;void add(int u,int v,int c,int w){ adj[u].push_back(NODE(u,v,c,w,adj[v].size())); adj[v].push_back(NODE(v,u,0,-w,adj[u].size()-1));}int spfa(){ while(!q.empty()) q.pop(); fill(d,d+n+2,inf); memset(cnt,0,sizeof(cnt)); memset(vis,0,sizeof(vis)); d[0]=0; cnt[0]=1; vis[0]=1; pre[0]=nu.begin(); q.push(0); int u,v,c; vector<NODE>::iterator it; while(!q.empty()){ u=q.front(); q.pop(); vis[u]=0; for(it=adj[u].begin();it!=adj[u].end();++it){ v=it->v; if(it->c && d[v]>d[u]+it->w){ d[v]=d[u]+it->w; pre[v]=it; if(!vis[v]){ if(++cnt[v]>n+1) return 0; vis[v]=1; q.push(v); } } } } if(d[n+1]==inf) return 0; return 1;}int mfmc(){ int ans=0,m; vector<NODE>::iterator it; while(spfa()){ m=inf; for(it=pre[n+1];it!=nu.begin();it=pre[it->u]){ m=min(m,it->c); } for(it=pre[n+1];it!=nu.begin();it=pre[it->u]){ it->c-=m; adj[it->v][it->p].c+=m; } ans+=m*d[n+1]; } return ans;}int main(){ // freopen("d.in","r",stdin); int u,v,w,m; scanf("%d%d",&n,&m); while(m--){ scanf("%d%d%d",&u,&v,&w); add(u,v,1,w); add(v,u,1,w); } add(0,1,2,0); add(n,n+1,2,0); printf("%d\n",mfmc()); return 0;}
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