洛谷2149 Elaxia的路線(dp+最短路)
阿新 • • 發佈:2018-12-22
QwQ好久沒更新部落格了,頹廢了好久啊,來補一點東西
題目大意
給定兩個點對,求兩對點間最短路的最長公共路徑。
其中\(n,m\le 10^5\)
比較簡單吧
就是跑四遍最短路,然後把最短路上的邊拿出來,跑一遍拓撲排序加\(dp\)就OK
對於一條邊\(u->v\),滿足\(dis[u]+w+disn[v]=dis[t]\)那麼這條邊就是最短路上的邊,其中\(disn[x]\)表示\(t\)到\(x\)的最短路,\(dis[x]\)表示\(s\)到\(x\)的最短路
直接上程式碼
#include<iostream> #include<cstdio> #include<algorithm> #include<cstring> #include<cmath> #include<queue> #define pa pair<int,int> using namespace std; inline int read() { int x=0,f=1;char ch=getchar(); while (!isdigit(ch)) {if (ch=='-') f=-1;ch=getchar();} while (isdigit(ch)) {x=(x<<1)+(x<<3)+ch-'0';ch=getchar();} return x*f; } const int maxn = 7010; const int maxm = 2e6+1e2; int point[maxn],nxt[maxm],to[maxm],val[maxm]; int dis[maxn]; int disn[maxn]; int dis1[maxn]; int disn1[maxn]; int vis[maxn]; int n,m,cnt; int x[maxm],y[maxm],w[maxm]; int dp[maxn]; int s1,t1,s2,t2; priority_queue<pa,vector<pa>,greater<pa> > q; void addedge(int x,int y,int w) { nxt[++cnt]=point[x]; to[cnt]=y; val[cnt]=w; point[x]=cnt; } void dijkstra(int s) { memset(vis,0,sizeof(vis)); memset(dis,127/3,sizeof(dis)); dis[s]=0; q.push(make_pair(0,s)); while (!q.empty()) { int x = q.top().second; q.pop(); if (vis[x]) continue; vis[x]=1; for (int i=point[x];i;i=nxt[i]) { int p = to[i]; if (dis[p]>dis[x]+val[i]) { dis[p]=dis[x]+val[i]; q.push(make_pair(dis[p],p)); } } } } void dijkstra1(int s) { memset(vis,0,sizeof(vis)); memset(disn,127/3,sizeof(disn)); disn[s]=0; q.push(make_pair(0,s)); while (!q.empty()) { int x = q.top().second; q.pop(); if (vis[x]) continue; vis[x]=1; for (int i=point[x];i;i=nxt[i]) { int p = to[i]; if (disn[p]>disn[x]+val[i]) { disn[p]=disn[x]+val[i]; q.push(make_pair(disn[p],p)); } } } } void dijkstra2(int s) { memset(vis,0,sizeof(vis)); memset(dis1,127/3,sizeof(dis1)); dis1[s]=0; q.push(make_pair(0,s)); while (!q.empty()) { int x = q.top().second; q.pop(); if (vis[x]) continue; vis[x]=1; for (int i=point[x];i;i=nxt[i]) { int p = to[i]; if (dis1[p]>dis1[x]+val[i]) { dis1[p]=dis1[x]+val[i]; q.push(make_pair(dis1[p],p)); } } } } void dijkstra3(int s) { memset(vis,0,sizeof(vis)); memset(disn1,127/3,sizeof(disn1)); disn1[s]=0; q.push(make_pair(0,s)); while (!q.empty()) { int x = q.top().second; q.pop(); if (vis[x]) continue; vis[x]=1; for (int i=point[x];i;i=nxt[i]) { int p = to[i]; if (disn1[p]>disn1[x]+val[i]) { disn1[p]=disn1[x]+val[i]; q.push(make_pair(disn1[p],p)); } } } } int tmp = 0; int num[maxm]; int ymh[maxm]; int in[maxn]; queue<int> que; int a[2100][2100]; int main() { memset(a,-1,sizeof(a)); n=read(),m=read(); s1=read(),t1=read(); s2=read(),t2=read(); for (int i=1;i<=m;i++){ int u,v,ww; u=read(),v=read(),ww=read(); addedge(u,v,ww); addedge(v,u,ww); x[++tmp]=u; y[tmp]=v; w[tmp]=ww; x[++tmp]=v; y[tmp]=u; w[tmp]=ww; } dijkstra(s1); dijkstra1(t1); dijkstra2(s2); dijkstra3(t2); memset(point,0,sizeof(point)); cnt=0; for (int i=1;i<=tmp;i++) { if (dis[x[i]]+w[i]+disn[y[i]]==dis[t1]) addedge(x[i],y[i],w[i]),num[i]=1,in[y[i]]++,a[x[i]][y[i]]++,a[y[i]][x[i]]++; } for (int i=1;i<=tmp;i++) { if (dis1[x[i]]+w[i]+disn1[y[i]]==dis1[t2]) {a[x[i]][y[i]]++,a[y[i]][x[i]]++;} } for (int i=1;i<=n;i++) if (!in[i]) que.push(i); while (!que.empty()) { int x = que.front(); que.pop(); for (int i=point[x];i;i=nxt[i]) { int p = to[i]; //cout<<x<<" "<<p<<" "<<a[x][p]<<endl; dp[p]=max(dp[p],dp[x]+a[x][p]*val[i]); in[p]--; if (!in[p]) que.push(p); } } int ans=-1e9; for (int i=1;i<=n;i++) ans=max(ans,dp[i]); cout<<ans; return 0; }