题面
Luogu4175：[CTSC2008]网络管理Network
Sol
路径第\(k\)大
无解直接判断就好了
然后整体二分，加上树链剖分+树状数组统计
# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(2e5 + 5);
IL ll Input(){
RG ll x = 0, z = 1; RG char c = getchar();
for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
return x * z;
}
int size[_], fa[_], deep[_], top[_], son[_], dfn[_], Index;
int fst[_], nxt[_], to[_], cnt, n, c[_];
IL void Modify(RG int x, RG int v){
for(; x <= n; x += x & -x) c[x] += v;
}
IL int Query(RG int x){
RG int ret = 0;
for(; x; x -= x & -x) ret += c[x];
return ret;
}
IL void Add(RG int u, RG int v){
nxt[cnt] = fst[u]; to[cnt] = v; fst[u] = cnt++;
}
IL void Dfs1(RG int u){
size[u] = 1;
for(RG int e = fst[u]; e != -1; e = nxt[e]){
if(size[to[e]]) continue;
fa[to[e]] = u; deep[to[e]] = deep[u] + 1;
Dfs1(to[e]);
size[u] += size[to[e]];
if(size[to[e]] > size[son[u]]) son[u] = to[e];
}
}
IL void Dfs2(RG int u, RG int Top){
dfn[u] = ++Index; top[u] = Top;
if(son[u]) Dfs2(son[u], Top);
for(RG int e = fst[u]; e != -1; e = nxt[e])
if(!dfn[to[e]]) Dfs2(to[e], to[e]);
}
IL int LCA(RG int u, RG int v){
while(top[u] ^ top[v]){
if(deep[top[u]] > deep[top[v]]) swap(u, v);
v = fa[top[v]];
}
return deep[u] > deep[v] ? v : u;
}
IL int Calc(RG int u, RG int v){
RG int ret = 0;
while(top[u] ^ top[v]){
if(deep[top[u]] > deep[top[v]]) swap(u, v);
ret += Query(dfn[v]) - Query(dfn[top[v]] - 1);
v = fa[top[v]];
}
if(deep[u] > deep[v]) swap(u, v);
ret += Query(dfn[v]) - Query(dfn[u] - 1);
return ret;
}
int m, tot, ans[_], Q, val[_];
struct Data{
int id, x, y, k, op;
} q[_], q1[_], q2[_];
IL void Solve(RG int l, RG int r, RG int L, RG int R){
if(L > R) return;
if(l == r){
for(RG int i = L; i <= R; ++i)
if(q[i].id && ans[q[i].id] != -1) ans[q[i].id] = l;
return;
}
RG int mid = (l + r) >> 1, t1 = 0, t2 = 0;
for(RG int i = L; i <= R; ++i)
if(q[i].id){
RG int s = Calc(q[i].x, q[i].y);
if(s >= q[i].k) q2[++t2] = q[i];
else q[i].k -= s, q1[++t1] = q[i];
}
else{
if(q[i].y > mid) q2[++t2] = q[i], Modify(dfn[q[i].x], q[i].op);
else q1[++t1] = q[i];
}
for(RG int i = L; i <= R; ++i)
if(!q[i].id && q[i].y > mid) Modify(dfn[q[i].x], -q[i].op);
for(RG int i = L, j = 1; j <= t1; ++i, ++j) q[i] = q1[j];
for(RG int i = L + t1, j = 1; j <= t2; ++i, ++j) q[i] = q2[j];
Solve(l, mid, L, L + t1 - 1); Solve(mid + 1, r, L + t1, R);
}
int main(RG int argc, RG char* argv[]){
tot = n = Input(); m = Input(); RG int mx = 0;
for(RG int i = 1; i <= n; ++i){
q[i].x = i, q[i].y = val[i] = Input(), q[i].op = 1;
fst[i] = -1; mx = max(mx, val[i]);
}
for(RG int i = 1, x, y; i < n; ++i)
x = Input(), y = Input(), Add(x, y), Add(y, x);
Dfs1(1); Dfs2(1, 1);
for(RG int i = 1; i <= m; ++i){
RG int tk = Input(), tx = Input(), ty = Input();
if(tk){
RG int lca = LCA(tx, ty); ++Q;
RG int len = deep[tx] + deep[ty] - 2 * deep[lca] + 1;
if(tk > len) ans[Q] = -1;
q[++tot] = (Data){Q, tx, ty, tk, 0};
}
else{
q[++tot] = (Data){0, tx, val[tx], 0, -1};
q[++tot] = (Data){0, tx, val[tx] = ty, 0, 1};
mx = max(mx, ty);
}
}
Solve(0, mx, 1, tot);
for(RG int i = 1; i <= Q; ++i)
if(ans[i] == -1) puts("invalid request!");
else printf("%d\n", ans[i]);
return 0;
}