#include <bits/stdc++.h> #define read read() #define up(i,l,r) for(register int i = (l);i <= (r);i++) #define down(i,l,r) for(register int i = (l);i >= (r);i--) #define traversal_vedge(i) for(register int i = head[u]; i ;i = e[i].nxt) #define ll long long using namespace std; int read { int x = 0, f = 1; char ch = getchar(); while(ch < 48 || ch > 57) {if(ch == '-')f = -1; ch = getchar();} while(ch >=48 && ch <=57) {x = 10 * x + ch - 48;ch = getchar();} return x * f; } int n,m,s; const int N = 500005; int dep[N],fa[N],size[N],top[N]; struct edge{ int v,nxt; }e[N<<1];int cnt,head[N]; void add(int u,int v){ e[++cnt] = (edge){v,head[u]}; head[u] = cnt; } void readdata() { n = read; m = read; s = read; up(i,1,n-1) { int u = read,v = read; add(u,v); add(v,u); } } //----------------------------------------------------------------------- void dfs(int u) { dep[u] = dep[fa[u]] + 1; size[u] = 1; top[u] = u; //debug 未写 top[u] = u; int heavyson_id = 0,heavyson_size = 0; traversal_vedge(i) { int v = e[i].v; if(v == fa[u]) continue; fa[v] = u; //top[v] = u; //debug 不写top[v] = u; dfs(v); size[u] += size[v]; //heavyson = max(heavyson,size[v]); if(size[v] > heavyson_size) heavyson_id = v,heavyson_size = size[v]; } if(heavyson_id) top[heavyson_id] = u;//debug heavyson_id -> u; //有重儿子才更新top[] //dfs后,top[]只相当于重链上的fa[] //调用find(u)过后,从u到链首的所有top[]才指向链首; } int find(int u) { if(u == top[u]) return u; top[u] = find(top[u]);//debug top[u] -> u return top[u]; //逆向搜索,并修改值; } int lca(int x,int y) { if(find(x) != find(y)) //如果不在一条链上 //**一条链:重链为一条链,轻链单独一条边为一条链; { if(dep[top[x]] > dep[top[y]]) return lca(fa[top[x]] , y);//debug fa[top[x]] -> fa[dep[top[x]]]; else return lca(x , fa[top[y]]); } return dep[x] > dep[y] ? y : x; } void work() { dfs(s); while(m--) { int a = read,b = read; printf("%d\n",lca(a,b)); } } int main() { freopen("input.txt","r",stdin); readdata(); work(); return 0; }
总结:
树链剖分版的LCA的dfs1稍有不同，不需要用数组记录每个点的重儿子；
树链剖分维护7个数组，树链剖分——LCA维护4个数组（fa[],dep[],size[],top[]）son[]简化成heavyson_id