Codeforces Round #Pi (Div. 2) 567E President and Roads ( dfs and similar, graphs, hashing, shortest paths )
图给得很良心,一个s到t的有向图,权值至少为1,求出最短路,如果是一定经过的边,输出"YES",如果可以通过修改权值,保证一定经过这条边,输出"CAN",并且输出最小修改值,否则输出"NO"。保证有s到t的路径,可能有重边。
建正反两个图,分别求出s和t的最短路径,用来判断一条边是不是在最短路径上,然后把最短路径取出来建一个图求割边。
不要用spfa,最坏O(VE),(出卡spfa数据的方法:Hard Test),会TLE 109(数据好啊),自以为是的加了个优化结果跑得更慢了,估计也是那组数据卡的吧,带重边的tarjan处理:前向星i^1!=fa,或者每条边再记录一个信息,不能用v!=fa来判断。。
#include<bits/stdc++.h> using namespace std; typedef long long ll; #define fi first #define se second #define bug(x) cout<<#x<<'='<<x<<endl; #define FOR(i,s,e) for(int i = s; i < e; i++) const int maxn = 1e5+5; const int maxe = maxn<<1; struct Graph { ll d[maxn]; int head[maxn],fro[maxe],to[maxe],nxt[maxe],ecnt; ll w[maxe]; void init() { memset(head,-1,sizeof(head)); ecnt = 0; } Graph(){ init(); } void addEdge(int u,int v,ll l) { fro[ecnt] = u; to[ecnt] = v; w[ecnt] = l; nxt[ecnt] = head[u]; head[u] = ecnt++; } }G1,G2,G3; int id[maxe]; const ll INF = 0x3f3f3f3f3f3f3f3fLL; int flag[maxe]; // 0 not shortest path 1 shortest path 2 unique shortest path int dfs_clock,dfn[maxn],low[maxn]; void Tarjan(int u,int fa) { dfn[u] = low[u] = ++dfs_clock; for(int i = G3.head[u]; ~i; i = G3.nxt[i]){ if((i^1) == fa) continue; // == 优先级比^高 int v = G3.to[i]; if(!dfn[v]){ Tarjan(v,i); low[u] = min(low[u],low[v]); if(low[v]>dfn[u]) { flag[id[i]] = 2; } }else { low[u] = min(low[u],low[v]); } } } struct Node { ll d; int u; bool operator < (const Node& x) const{ return d > x.d; } }; bool vis[maxn]; void Dijkstra(int s,Graph &g) { priority_queue<Node> q; memset(g.d,0x3f,sizeof(g.d)); g.d[s] = 0; q.push(Node{0,s}); while(q.size()){ Node x = q.top(); q.pop(); int u = x.u; if(vis[u]) continue; vis[u] = true; for(int i = g.head[u]; ~i; i = g.nxt[i] ){ int v = g.to[i]; if(g.d[v]> g.d[u]+g.w[i]){ g.d[v] = g.d[u]+g.w[i]; q.push(Node{g.d[v],v}); } } } memset(vis,0,sizeof(vis)); } #define local int main() { #ifdef local freopen("in.txt","r",stdin); // freopen("out.txt","w",stdout); #endif // local int n,m,s,t; scanf("%d%d%d%d",&n,&m,&s,&t); for(int i = 0; i < m; i++){ int u,v,l; scanf("%d%d%d",&u,&v,&l); G1.addEdge(u,v,l); G2.addEdge(v,u,l); } Dijkstra(s,G1); Dijkstra(t,G2); ll shortest = G1.d[t]; for(int i = 0; i < m; i++){ int u = G1.fro[i], v = G1.to[i]; if(shortest == G1.w[i] + G1.d[u] + G2.d[v] ){ id[G3.ecnt] = i; G3.addEdge(u,v,G1.w[i]); id[G3.ecnt] = i; G3.addEdge(v,u,G1.w[i]); flag[i] = 1; } } Tarjan(s,-1); for(int i = 0; i < m; i ++){ if(flag[i] == 2) puts("YES"); else if(flag[i] == 1){ if(G1.w[i]>1) printf("CAN 1\n"); else puts("NO"); }else { ll detal = G1.w[i] - shortest + G1.d[G1.fro[i]]+G2.d[G1.to[i]] + 1; if(G1.w[i] > detal) printf("CAN %d\n",detal); else puts("NO"); } } return 0; } /* 自以为是的优化: q.push(s); while(q.size()){ int u = q.front(); q.pop(); for(int i = G1.head[u]; ~i; i = G1.nxt[i]) if(!vis[i]) { vis[i] = true; int v = G1.to[i]; if(G1.d[u] + G1.w[i] == G1.d[v] && G2.d[v] + G1.w[i] == G2.d[u]){ id[G3.ecnt] = i; G3.addEdge(u,v,G1.w[i]); id[G3.ecnt] = i; G3.addEdge(v,u,G1.w[i]); flag[i] = 1; q.push(v); } } } */