spoj 10628

http://www.spoj.com/problems/COT/ 树上第k小元素

LCA + 可持久化线段树

每个新的版本都是由其父亲版本转化而来。

 #include <cstdio>
 #include <iostream>
 #include <algorithm>
 #include <cstring>

 using namespace std;

 const int maxn = 1e5 + ;
 const int maxd = ;
 struct Edge{
     int v, next;
 }p[maxn << ];
 int head[maxn], e, d[maxn], f[maxn][maxd];
 //LCA
 void init(){
     memset(d, , sizeof(d));
     memset(f, , sizeof(f));
     memset(head, -, sizeof(head));
     e = ;
 }
 void addEdge(int u, int v){
     p[e].v = v; p[e].next = head[u]; head[u] = e++;
     swap(u, v);
     p[e].v = v; p[e].next = head[u]; head[u] = e++;
 }
 int lca(int u, int v){
     if (d[u] < d[v]) swap(u, v);
     int k = d[u] - d[v];
     for (int i = ; i < maxd;  ++i)
         if (( << i) & k) u = f[u][i];
     if (u == v) return u;
     for (int i = maxd - ; i >= ; --i){
         if (f[u][i] != f[v][i]){
             u = f[u][i];
             v = f[v][i];
         }
     }
     return f[u][];
 }
 //CMT
 int ls[maxn * ], rs[maxn * ], sum[maxn * ], T[maxn], tot, rt;
 int num[maxn], san[maxn], n, m; // 离散化前点数,离散化后点数
 void init_hash(){
     for (int i = ; i <= n; ++i) san[i] = num[i];
     sort(san + , san + n + );
     m = unique(san + , san + n + ) - san - ;
 }
 int hash(int x){
     return lower_bound(san + , san + m + , x) - san;
 }
 void build(int l, int r, int& rt){
     rt = ++ tot; sum[rt] = ;
     if (l == r) return;
     int mid = (l + r) >> ;
     build(l, mid, ls[rt]);
     build(mid + , r, rs[rt]);
 }
 void update(int last, int pos, int l, int r, int& rt){
     rt = ++ tot;
     ls[rt] = ls[last], rs[rt] = rs[last], sum[rt] = sum[last] + ;
     if (l == r) return ;
     int mid = (l + r) >> ;
     if (pos <= mid) update(ls[last], pos, l, mid, ls[rt]);
     else update(rs[last], pos, mid + , r, rs[rt]);
 }
 int query(int pos, int left_rt, int right_rt, int lca_rt, int l, int r, int k){
     if (l == r) return l;
     int mid = (l + r) >> ;
     int cnt = sum[ls[left_rt]] + sum[ls[right_rt]] -  * sum[ls[lca_rt]] + (pos >= l && pos <= mid);//注意lca为跟的时候
     if (k <= cnt) return query(pos, ls[left_rt], ls[right_rt], ls[lca_rt], l, mid, k);
     else return query(pos, rs[left_rt], rs[right_rt], rs[lca_rt], mid + , r, k - cnt);
 }
 //LCA && CMT
 void dfs(int u, int fa){
     f[u][] = fa;//注意
     d[u] = d[f[u][]] + ;
     update(T[fa], hash(num[u]), , m, T[u]);
     for (int i = ; i < maxd; ++i) f[u][i] = f[ f[u][i - ] ][i - ];
     for (int i = head[u]; ~i; i = p[i].next){
         if (p[i].v == fa) continue;
         dfs(p[i].v, u);
     }
 }
 int main(){
     int q, u, v, k;
     while (scanf("%d%d", &n, &q) == ){
         for (int i = ; i <= n; ++i) scanf("%d", &num[i]);
         init();
         init_hash();
         tot = ;
         for (int i = ; i < n; ++i){
             scanf("%d%d", &u, &v);
             addEdge(u, v);
         }
         build(, m, T[]);
         dfs(, );
         while (q--){
             scanf("%d%d%d", &u, &v, &k);
             printf("%d\n",san[query(hash(num[lca(u, v)]), T[u], T[v], T[lca(u, v)],, m, k)]);
         }
     }
     return ;
 }