题目传送门:http://www.lydsy.com/JudgeOnline/problem.php?id=2125
仙人掌上求最短路
先搞成树,然后树怎么搞,这题就怎么搞
#include<iostream> #include<cstdio> #include<vector> #include<cstdlib> using namespace std; const int MAXN = 10000+9; int n,m,Q,lowlink[MAXN],num[MAXN],dis[MAXN],nxt[MAXN*4],to[MAXN*4],head[MAXN],cost[MAXN*4]; int ring_cnt,fa[MAXN][16],dep[MAXN],length[MAXN],ring_num[MAXN],ori[MAXN],que[MAXN],fro; vector<int> rings[MAXN]; inline int read(){ char c=getchar(); int ret=0,f=1; while (c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();} while (c<='9'&&c>='0'){ret=ret*10+c-'0';c=getchar();} return ret*f; } inline void AddEdge(int a, int b, int c){ static int T = 0; to[++T] = b; nxt[T] = head[a]; head[a] = T; cost[T] = c; to[++T] = a; nxt[T] = head[b]; head[b] = T; cost[T] = c; } void DFS(int w, int f){ static int T = 0; fa[w][0] = f; lowlink[w] = num[w] = ++T; que[++fro] = w; for (int i=head[w];i;i=nxt[i]) if (to[i] != f) { if (!num[to[i]]) { DFS(to[i], w); if (lowlink[to[i]] > num[w]) fro--; else if (lowlink[to[i]] < num[w]) lowlink[w] = lowlink[to[i]]; else { ring_cnt++; int nw = que[fro--]; while (nw != w) { rings[ring_cnt].push_back(nw); nw = que[fro--]; } rings[ring_cnt].push_back(w); que[++fro] = w; } } else lowlink[w] = min(lowlink[w], num[to[i]]); } } inline void prework(){ for (int k=1;k<=ring_cnt;k++) { int size = rings[k].size(); int rt = rings[k][size-1],tmp=0; for (int i=1;i<=size;i++) que[i] = rings[k][i-1]; que[0] = rt; que[size+1] = que[1]; for (int i=1;i<size;i++) ring_num[que[i]] = k, fa[que[i]][0] = rt; for (int i=1;i<=size;i++) { for (int j=head[que[i]];j;j=nxt[j]) { if (to[j] == que[i-1]) to[j] = 0, tmp += cost[j]; else if (to[j] == que[i+1]) to[j] = 0; } ori[que[i]] = tmp; } ori[rt] = 0; length[k] = tmp; for (int i=1;i<size;i++) AddEdge(rt,que[i],min(ori[que[i]], tmp-ori[que[i]])); } } void GetDis(int w){ for (int i=head[w];i;i=nxt[i]) if (!dis[to[i]] && to[i]) dis[to[i]]=dis[w]+cost[i], dep[to[i]] = dep[w] + 1, GetDis(to[i]); } inline void LCA_init() { for (int k=1;k<=15;k++) for (int i=1;i<=n;i++) fa[i][k] = fa[fa[i][k-1]][k-1]; } inline int LCA(int a, int b, int &l1, int &l2){ if (dep[a] < dep[b]) swap(a,b); for (int k=15;~k;k--) if (dep[fa[a][k]] >= dep[b]) a = fa[a][k]; l1 = l2 = a; if (a == b) return a; else { for (int k=15;~k;k--) if (fa[a][k] != fa[b][k]) a = fa[a][k], b = fa[b][k]; l1 = a, l2 = b; return fa[a][0]; } } int main(){ n = read(); m = read(); Q = read(); for (int i=1,a,b,c;i<=m;i++) a = read(), b = read(), c = read(), AddEdge(a, b, c); DFS(1,0); prework(); dis[1] = dep[1] = 1; GetDis(1); LCA_init(); for (int i=1,a,b,r,lca1,lca2;i<=Q;i++){ a = read(); b = read(); r = LCA(a, b, lca1, lca2); if (ring_num[lca1] && ring_num[lca1] == ring_num[lca2]) { int len = abs(ori[lca1]-ori[lca2]); len = min(len, length[ring_num[lca1]]-len); printf("%d\n",dis[a]-dis[lca1]+dis[b]-dis[lca2]+len); } else printf("%d\n",dis[a]+dis[b]-2*dis[r]); } return 0; }
另外,这份代码在预处理环那里有问题
会被一个点连了几个环的情况卡成翔
正确的写法,参见BZOJ_1023
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