LCA模板题
题意：给一个无根树，有q个询问，每个询问两个点，问两点的距离。求出 lca = LCA(X,Y) , 然后 dir[x] + dir[y] - 2 * dir[lca]
dir[u]表示点u到树根的距离
下面两份代码都可以通过HDU的C++和G++，都不存在爆栈问题，网上很多人说会爆栈，加了申请系统栈语句，其实不用，而且好想比赛中不允许使用的
Tarjan算法跑得更快些，C++ 15ms， G++ 50ms 左右， RMQ大概60ms
在线算法：LCA转化为RMQ
#include <iostream> #include <cstdio> #include <cstring> #include <cmath> using namespace std; //#pragma comment(linker, "/STACK:102400000,102400000") //不需要申请系统栈 const int N = 40010; const int M = 25; int _pow[M]; int tot,head[N],ver[2*N],R[2*N],first[N],dir[N]; int dp[2*N][M]; //这个数组记得开到2*N，因为遍历后序列长度为2*n-1 bool vis[N]; struct edge { int u,v,w,next; }e[2*N]; inline void add(int u ,int v ,int w ,int &k) { e[k].u = u; e[k].v = v; e[k].w = w; e[k].next = head[u]; head[u] = k++; u = u^v; v = u^v; u = u^v; e[k].u = u; e[k].v = v; e[k].w = w; e[k].next = head[u]; head[u] = k++; } void dfs(int u ,int dep) { vis[u] = true; ver[++tot] = u; first[u] = tot; R[tot] = dep; for(int k=head[u]; k!=-1; k=e[k].next) if( !vis[e[k].v] ) { int v = e[k].v , w = e[k].w; dir[v] = dir[u] + w; dfs(v,dep+1); ver[++tot] = u; R[tot] = dep; } } void ST(int len) { int K = (int)(log((double)len) / log(2.0)); for(int i=1; i<=len; i++) dp[i][0] = i; for(int j=1; j<=K; j++) for(int i=1; i+_pow[j]-1<=len; i++) { int a = dp[i][j-1] , b = dp[i+_pow[j-1]][j-1]; if(R[a] < R[b]) dp[i][j] = a; else dp[i][j] = b; } } int RMQ(int x ,int y) { int K = (int)(log((double)(y-x+1)) / log(2.0)); int a = dp[x][K] , b = dp[y-_pow[K]+1][K]; if(R[a] < R[b]) return a; else return b; } int LCA(int u ,int v) { int x = first[u] , y = first[v]; if(x > y) swap(x,y); int res = RMQ(x,y); return ver[res]; } int main() { for(int i=0; i<M; i++) _pow[i] = (1<<i); int cas; scanf("%d",&cas); while(cas--) { int n,q,num = 0; scanf("%d%d",&n,&q); memset(head,-1,sizeof(head)); memset(vis,false,sizeof(vis)); for(int i=1; i<n; i++) { int u,v,w; scanf("%d%d%d",&u,&v,&w); add(u,v,w,num); } tot = 0; dir[1] = 0; dfs(1,1); /* printf("节点 "); for(int i=1; i<=2*n-1; i++) printf("%d ",ver[i]); cout << endl; printf("深度 "); for(int i=1; i<=2*n-1; i++) printf("%d ",R[i]); cout << endl; printf("首位 "); for(int i=0; i<n; i++) printf("%d ",first[i]); cout << endl; printf("距离 "); for(int i=0; i<n; i++) printf("%d ",dir[i]); cout << endl; */ ST(2*n-1); while(q--) { int u,v; scanf("%d%d",&u,&v); int lca = LCA(u,v); // printf("lca = %d\n",lca); printf("%d\n",dir[u] + dir[v] - 2*dir[lca]); } } return 0; }
离线算法：Tarjan算法解决
#include <iostream> #include <cstdio> #include <cstring> using namespace std; const int N = 40010; const int M = 410; int head[N],__head[N]; struct edge{ int u,v,w,next; }e[2*N]; struct ask{ int u,v,lca,next; }ea[M]; int dir[N],fa[N],ance[N]; bool vis[N]; inline void add_edge(int u,int v,int w,int &k) { e[k].u = u; e[k].v = v; e[k].w = w; e[k].next = head[u]; head[u] = k++; u = u^v; v = u^v; u = u^v; e[k].u = u; e[k].v = v; e[k].w = w; e[k].next = head[u]; head[u] = k++; } inline void add_ask(int u ,int v ,int &k) { ea[k].u = u; ea[k].v = v; ea[k].lca = -1; ea[k].next = __head[u]; __head[u] = k++; u = u^v; v = u^v; u = u^v; ea[k].u = u; ea[k].v = v; ea[k].lca = -1; ea[k].next = __head[u]; __head[u] = k++; } int Find(int x) { return x == fa[x] ? x : fa[x] = Find(fa[x]); } void Union(int u ,int v) { fa[v] = fa[u]; //可写为 fa[Find(v)] = fa[u]; } void Tarjan(int u) { vis[u] = true; ance[u] = fa[u] = u; //课写为 ance[Find(u)] = fa[u] = u; for(int k=head[u]; k!=-1; k=e[k].next) if( !vis[e[k].v] ) { int v = e[k].v , w = e[k].w; dir[v] = dir[u] + w; Tarjan(v); Union(u,v); //ance[Find(u)] = u; //可写为ance[u] = u; //甚至不要这个语句都行 } for(int k=__head[u]; k!=-1; k=ea[k].next) if( vis[ea[k].v] ) { int v = ea[k].v; ea[k].lca = ea[k^1].lca = ance[Find(v)]; } } int main() { int cas,n,q,tot; scanf("%d",&cas); while(cas--) { scanf("%d%d",&n,&q); memset(head,-1,sizeof(head)); memset(__head,-1,sizeof(__head)); tot = 0; for(int i=1; i<n; i++) { int u,v,w; scanf("%d%d%d",&u,&v,&w); add_edge(u,v,w,tot); } tot = 0; for(int i=0; i<q; i++) { int u,v; scanf("%d%d",&u,&v); add_ask(u,v,tot); } memset(vis,0,sizeof(vis)); dir[1] = 0; Tarjan(1); for(int i=0; i<q; i++) { int s = i * 2 , u = ea[s].u , v = ea[s].v , lca = ea[s].lca; printf("%d\n",dir[u] + dir[v] - 2*dir[lca]); } } return 0; }