## Editorial for VM 08 Bài 15 - Truy vấn trên cây

Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.

Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

#### Code mẫu của flashmt

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <vector>
using namespace std;
const int N = 100100;

struct segmentTree
{
int low, high, mid, black;
segmentTree *L, *R;

segmentTree() {}
segmentTree(int _low, int _high)
{
low = _low; high = _high; mid = (low + high) / 2;
black = -1;
if (low < high)
{
L = new segmentTree(low, mid);
R = new segmentTree(mid + 1, high);
}
}

void update(int x, int v)
{
if (low == high)
{
if (black < 0) black = v;
else black = -1;
}
else
{
if (x <= mid) L -> update(x, v);
else R -> update(x, v);
if (L -> black < 0) black = R -> black;
else black = L -> black;
}
}

int get(int x, int y)
{
if (low == x && high == y) return black;
int u = -1;
if (x <= mid) u = L -> get(x, min(y, mid));
if (u > 0) return u;
if (mid < y) return R -> get(max(x, mid + 1), y);
return -1;
}
};

int n, par[N], s[N], heavyDown[N], heavyUp[N];
int sizeChain[N], idChain[N], posChain[N], numChain, firstOnChain[N];
vector <int> a[N];
vector <segmentTree> tree;

void visit(int x)
{
s[x] = 1;
for (int i = 0; i < int(a[x].size()); i++)
{
int y = a[x][i];
if (y != par[x])
{
par[y] = x;
visit(y);
s[x] += s[y];
}
}

for (int i = 0; i < int(a[x].size()); i++)
{
int y = a[x][i];
if (y != par[x] && s[y] * 2 >= s[x]) heavyDown[x] = y, heavyUp[y] = 1;
}
}

void initHeavyLight()
{
visit(1);
for (int i = 1; i <= n; i++)
{
int x = i;
if (heavyUp[x]) continue;
firstOnChain[numChain] = x;
while (x)
{
idChain[x] = numChain;
posChain[x] = sizeChain[numChain]++;
x = heavyDown[x];
}
tree.push_back(segmentTree(0, sizeChain[numChain++] - 1));
}
}

int main()
{
int Q, x, y, type;
cin >> n >> Q;
for (int i = 1; i < n; i++)
{
scanf("%d%d", &x, &y);
a[x].push_back(y);
a[y].push_back(x);
}

initHeavyLight();
while (Q--)
{
scanf("%d%d", &type, &x);
if (type)
{
int ans = -1;
while (x)
{
int u = tree[idChain[x]].get(0, posChain[x]);
if (u > 0) ans = u;
x = par[firstOnChain[idChain[x]]];
}
printf("%d\n", ans);
}
else tree[idChain[x]].update(posChain[x], x);
}
}


//by ladpro98
//Heavy - Light Decomposition
#include <bits/stdc++.h>
#define SetLength(a, n, t) free(a), a=(t*) calloc(n, sizeof(t))

const int N = 100005;
const int oo = 2000000000;
const int C = N;
using namespace std;
int n, q;
vector<int> a[N];
int Size[N], par[N], chainHead[N], chainNo, chainPos[N], chainID[N], chainSize[N];

struct segment_tree {
int n; int *tree; int *node;
void init(int _n);
void Upd(int k, int l, int r, int x);
void Upd(int x) {Upd(1, 1, n, x);}
int Get(int k, int l, int r, int i, int j);
int Get(int i, int j) {return Get(1, 1, n, i, j);}
};

segment_tree t[C];

void segment_tree :: init(int _n) {
n = _n;
SetLength(tree, 4 * n, int);
SetLength(node, n + 2, int);
for(int i=1; i<=4 * n; i++) tree[i] = oo;
}

void segment_tree :: Upd(int k, int l, int r, int x) {
if (l > r || r < x || x < l) return;
if (l == r) {
if (tree[k] == oo) tree[k] = l; else tree[k] = oo;
return;
}
int mid = (l + r) >> 1;
Upd(k + k, l, mid, x);
Upd(k + k + 1, mid + 1, r, x);
tree[k] = min(tree[k + k], tree[k + k + 1]);
}

int segment_tree :: Get(int k, int l, int r, int i, int j) {
if (l > r || r < i || j < l) return oo;
if (i <= l && r <= j) return tree[k];
int mid = (l + r) >> 1;
return min(Get(k+k, l, mid, i, j), Get(k+k+1, mid + 1, r, i, j));
}

void Enter() {
scanf("%d %d", &n, &q);
int i, u, v;
for(i=1; i<n; i++) {
scanf("%d %d", &u, &v);
a[u].push_back(v); a[v].push_back(u);
}
}

void DFS(int u) {
int i, v; Size[u] = 1;
for(i=0; i<a[u].size(); i++) {
v = a[u][i];
if (v != par[u]) {
par[v] = u;
DFS(v);
Size[u] += Size[v];
}
}
}

void HLD(int u) {
chainID[u] = chainNo;
chainPos[u] = ++chainSize[chainNo];
int ind = -1, ma = -1;
for(int i=0; i<a[u].size(); i++)
if (a[u][i] != par[u])
if (ma < Size[a[u][i]]) {
ma = Size[a[u][i]];
ind = i;
}
if (ind >=0 ) HLD(a[u][ind]);
for(int i=0; i<a[u].size(); i++)
if (a[u][i] != par[u]) {
if (i != ind) {
chainNo++;
HLD(a[u][i]);
}
}
}

void init_Helper() {
for(int i=1; i<C; i++) chainHead[i] = -1;
chainNo = 1;
DFS(1);
HLD(1);
for(int i=1; i<=chainNo; i++) t[i].init(chainSize[i]);
for(int i=1; i<=n; i++) t[chainID[i]].node[chainPos[i]] = i;
}

int query(int u, int v) {
int res = oo, pos = oo;
while (1) {
if (chainID[u] == chainID[v]) {
pos = t[chainID[u]].Get(1, chainPos[u]);
if (pos < oo)
res = t[chainID[u]].node[pos];
break;
}
pos = t[chainID[u]].Get(1, chainPos[u]);
if (pos < oo)
res = t[chainID[u]].node[pos];
}
return res;
}

int main()
{
Enter();
init_Helper();
int kind, u, r;
while (q--) {
scanf("%d %d", &kind, &u);
if (kind == 0)
t[chainID[u]].Upd(chainPos[u]);
else {
r = query(u, 1);
if (r < oo) printf("%d\n", r);
else printf("-1\n");
}
}
return 0;
}


#### Code mẫu của RR

//Written by Nguyen Thanh Trung
{$R+,Q+} uses math; const FINP=''; FOUT=''; MAXN=100001; type list=^node; node=record u:longint; next:list; end; var f1,f2:text; n,q,count:longint; ke:array[1..MAXN] of list; num,sc,color:array[1..MAXN] of longint; trace,d,head,size:array[1..MAXN] of longint; first:array[1..MAXN] of array of longint; procedure openF; inline; begin assign(f1,FINP); reset(f1); assign(f2,FOUT); rewrite(f2); end; procedure closeF; inline; begin close(f1); close(f2); end; procedure add(u:longint; var a:list); inline; var p:list; begin new(p); p^.u:=u; p^.next:=a; a:=p; end; function cal(n:longint):longint; inline; var temp:longint; begin temp:=trunc(ln(n)/ln(2)+2); cal:=1<<temp+2; end; procedure inp; inline; var i,u,v:longint; begin read(f1,n,q); for i:=1 to n-1 do begin read(f1,u,v); add(u,ke[v]); add(v,ke[u]); end; end; procedure dfs1(u:longint); inline; var v:longint; p:list; begin sc[u]:=1; p:=ke[u]; while p<>nil do begin v:=p^.u; p:=p^.next; if sc[v]>0 then continue; dfs1(v); inc(sc[u],sc[v]); end; end; procedure dfs2(u:longint); inline; var v,next,ln:longint; p:list; begin inc(count); num[u]:=count; ln:=-1; next:=0; p:=ke[u]; while p<>nil do begin v:=p^.u; p:=p^.next; if head[v]>0 then continue; if sc[v]>ln then begin ln:=sc[v]; next:=v; end; end; if next=0 then exit; head[next]:=head[u]; d[next]:=d[u]+1; inc(size[head[u]]); dfs2(next); p:=ke[u]; while p<>nil do begin v:=p^.u; p:=p^.next; if head[v]>0 then continue; trace[v]:=u; head[v]:=v; size[v]:=1; d[v]:=1; dfs2(v); end; end; procedure solve; inline; var i:longint; begin count:=0; head[1]:=1; d[1]:=1; size[1]:=1; dfs1(1); dfs2(1); for i:=1 to n do if head[i]=i then setlength(first[i],cal(size[i])); end; procedure update(tree,u,k:longint); procedure visit(i,l,r:longint); inline; var mid:longint; begin if l>r then exit; if (d[u]<l) or (r<d[u]) then exit; if (l=r) then begin if k=0 then first[tree,i]:=0 else first[tree,i]:=u; exit; end; mid:=(l+r)>>1; visit(i<<1,l,mid); visit(i<<1+1,mid+1,r); if first[tree,i<<1]>0 then first[tree,i]:=first[tree,i<<1] else first[tree,i]:=first[tree,i<<1+1]; end; begin visit(1,1,size[tree]); end; function get(tree,u:longint):longint; inline; var kq:longint; procedure visit(i,l,r:longint); inline; var mid:longint; begin if l>r then exit; if u<l then exit; if u>=r then begin if first[tree,i]>0 then kq:=first[tree,i]; exit; end; mid:=(l+r)>>1; visit(i<<1,l,mid); if kq=0 then visit(i<<1+1,mid+1,r); end; begin kq:=0; visit(1,1,size[tree]); get:=kq; end; function query(u:longint):longint; inline; var h,x,kq:longint; begin h:=head[u]; if h>1 then begin kq:=query(trace[h]); if kq=0 then kq:=get(h,d[u]); end else kq:=get(h,d[u]); query:=kq; end; procedure ans; var i,yc,u,kq:longint; begin for i:=1 to q do begin read(f1,yc,u); if yc=0 then begin color[u]:=1-color[u]; update(head[u],u,color[u]); end else begin kq:=query(u); if kq=0 then kq:=-1; writeln(f2,kq); end; end; end; begin openF; inp; solve; ans; closeF; end.  #### Code mẫu của ll931110 //This program using heavy-light decomposition method, which is known with the name Dynamic Tree {$MODE DELPHI,R+,Q+}
program QTREE3;
const
input  = '';
output = '';
maxn = 100000;
type
pnode = ^tnode;
tnode = record
val: integer;
end;
var
fi,fo: text;
n,q,dyna: integer; //dyna: number of node in dynamic tree
tree: array[1..4 * maxn] of integer;
stat: array[1..maxn] of boolean;
a: array[1..maxn] of pnode;
lab,pos,size,maxnode: array[1..maxn] of integer;
pr,st,fin: array[1..maxn] of integer;
u1,u2,k: integer;  //Use for queries in Interval Tree
ch: boolean;
tk,res: integer;

procedure openfile;
begin
assign(fi, input);
reset(fi);

assign(fo, output);
rewrite(fo);
end;

var
p: pnode;
begin
new(p);
p^.val := v;
a[u] := p;
end;

procedure init;
var
i,u,v: integer;
begin
for i := 1 to n do a[i] := nil;
for i := 1 to n - 1 do
begin
end;
end;

procedure prepare;
begin
fillchar(pr, sizeof(pr), 0);
fillchar(pos, sizeof(pos), 0);
end;

//Dynamic tree construction

procedure DFS(u: integer);
var
p: pnode;
max,v: integer;
begin
p := a[u];
size[u] := 1;
max := 0;

while p <> nil do
begin
v := p^.val;
if v <> pr[u] then
begin
pr[v] := u;
DFS(v);

size[u] := size[u] + size[v];
if size[v] > max then
begin
max := size[v];
maxnode[u] := v;
end;
end;
end;
end;

procedure struct(u: integer);
var
p: pnode;
v,endnode: integer;
begin
p := a[u];
if (pos[u] = 0) and (p <> nil) then
begin
inc(dyna);
pos[u] := dyna;
lab[dyna] := u;
st[u] := u;
endnode := u;

v := maxnode[u];
while v <> 0 do
begin
inc(dyna);
pos[v] := dyna;
lab[dyna] := v;
st[v] := u;
if maxnode[v] = 0 then endnode := v;
v := maxnode[v];
end;

v := u;
while v <> 0 do
begin
fin[v] := endnode;
v := maxnode[v];
end;
end;

while p <> nil do
begin
v := p^.val;
if v <> pr[u] then struct(v);
end;
end;

//End of Dynamic tree construction

procedure upIT(i,low,high: integer);
var
mid: integer;
begin
if low = high then
begin
if ch then tree[i] := low else tree[i] := -1;
exit;
end;

mid := (low + high) div 2;
if k <= mid then upIT(2 * i,low,mid) else
upIT(2 * i + 1,mid + 1,high);

if tree[2 * i] = -1 then tree[i] := tree[2 * i + 1] else tree[i] := tree[2 * i];
end;

procedure calc(i,low,high: integer);
var
mid: integer;
begin
if (u2 < low) or (high < u1) then exit;
if (u1 <= low) and (high <= u2) then
begin
if (tree[i] <> -1) and ((tk = -1) or (tk > tree[i])) then tk := tree[i];
exit;
end;

mid := (low + high) div 2;
calc(2 * i,low,mid);
calc(2 * i + 1,mid + 1,high);
end;

procedure update(y: integer);
begin
k := pos[y];
stat[y] := not stat[y];
ch := stat[y];
if pos[y] <> 0 then upIT(1,1,dyna);
end;

var
tmp: integer;
begin
if y = 0 then exit;
if stat[y] then tmp := y else tmp := -1;
if tmp <> -1 then res := tmp;

if (y = st[y]) or (pos[y] = 0) then ask(pr[y])
else
begin
u1 := pos[st[y]];
u2 := pos[y];
tk := -1;
calc(1,1,dyna);
if tk <> -1 then res := lab[tk];
end;
end;

procedure query;
var
i,x,y: integer;
begin
DFS(1);
dyna := 0;
struct(1);

for i := 1 to 4 * dyna do tree[i] := -1;
fillchar(stat, sizeof(stat), false);

for i := 1 to q do
begin
if x = 0 then update(y) else
begin
res := -1;
writeln(fo, res);
end;
end;
end;

procedure closefile;
begin
close(fo);
close(fi);
end;

begin
openfile;
init;
prepare;
query;
closefile;
end.