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Copy path1553. Caves and Tunnels.cpp
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1553. Caves and Tunnels.cpp
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///HEADERS
#include <bits/stdc++.h>
///PREPROCESSORS
#define ll long long int
#define ull unsigned ll
#define vii vector<int>
#define vll vector<ll>
#define pb push_back
#define LIM 100000
#define MOD 1000000007
#define MAX 10000000
#define LOG 20
#define pi acos(-1)
#define segVar int lft = node << 1 , rgt = (node << 1) + 1 , md = (st+ed) >> 1;
#define pii pair<int,int>
#define mpr make_pair
#define EPS 1e-9
#define sqr(x) ((x)*(x))
#define gamma 0.5772156649
#define harm(x) log(x) + gamma + 1.0/(2*x) - 1.0/(12*sqr(x))
#define joshephus(n,k) j(int n, int k) {ll res = 1; for(ll i=2; i<=n; i++) res = (res+k-1) % i + 1; return res;}
#define FAST ios_base::sync_with_stdio(false);cin.tie(NULL);
///IMPORTANT EQUATIONS
///STARS AND BARS : (n+k-1)C(k-1)
///STIRLING TWO : F(n,k) = F(n-1,k-1) + k*(n-1,k); F(n,1) = 1 , F(n,n) = 1;
///STIRLING ONE : F(n,k) = F(n-1,k-1) + (n-1)*(n-1,k); F(n,1) = (n-1)! , F(n,n) = 1;
///CATALAN NUMBER : Cat(n) = Comb(2n,n) - Comb(2n,n-1) = Comb(2n,n)/(n+1);
using namespace std;
int n,q, ara[LIM+100];
vii graph[LIM+10], costs[LIM+10];
int lev[LIM+10], par[LIM+10][LOG+10], sub[LIM+10];
int dfs(int u) {
if(u == 1) lev[u] = 0;
else lev[u] = lev[ par[u][0] ] + 1;
int sz = graph[u].size();
int cnt = 1;
for(int i=0; i<sz; i++) {
int v = graph[u][i];
if(!lev[v] && v != 1) {
par[v][0] = u;
cnt += dfs(v);
}
}
return sub[u] = cnt;
}
void makeSparse() {
for(int p=1; p<=LOG; p++) {
for(int u=1; u<=n; u++) {
if(par[u][p-1] != -1) par[u][p] = par[ par[u][p-1] ][ p-1 ];
}
}
}
int getLCA(int u, int v) {
if(lev[u] < lev[v]) swap(u,v);
int up = log2(lev[u]) ;
while(up >= 0) {
int sp = par[u][up];
if( lev[u] - (1 << up) >= lev[v]) u = sp;
up--;
}
up = log2(lev[u]) ;
while(up >= 0) {
if(par[u][up] != par[v][up]) {
u = par[u][up];
v = par[v][up];
}
up--;
}
if (u == v) return u;
return par[u][0];
}
int chains = 0, ptr=0, chainHead[LIM+10], chainSize[LIM+10], whichChain[LIM+10], posInChain[LIM+10], posInBase[LIM+10], baseArray[LIM+10];
void makeHLD(int u) {
if(chainHead[chains] == -1) chainHead[chains] = u;
whichChain[u] = chains;
posInChain[u] = chainSize[chains]++;
ptr++;
posInBase[u] = ptr;
baseArray[ptr] = ara[u];
// ptr++;
int sz = graph[u].size();
int specialSize=0, specialId = -1;
for(int i=0; i<sz; i++) {
int v = graph[u][i];
if(v != par[u][0] && sub[v] > specialSize) {
specialId = v;
specialSize = sub[v];
}
}
if(specialId == -1) return;
makeHLD(specialId);
for(int i=0; i<sz; i++) {
int v = graph[u][i];
if(v != par[u][0] && v != specialId) {
chains++;
makeHLD(v);
}
}
}
int segTree[4*LIM];
void segTreeInit(int node, int st, int ed) {
if(st == ed) {
segTree[node] = baseArray[st];
return;
}
segVar;
segTreeInit(lft, st,md); segTreeInit(rgt, md+1,ed);
segTree[node] = max( segTree[lft] , segTree[rgt] );///ASSUMING PROBLEM WANTS SUM!!
}
void segTreeUpdate(int node, int st, int ed, int p, int v) { ///ASSUMING SINGLE UPDATE!!
if(ed < p || st > p) return;
if(st >= p && ed <= p) {
segTree[node] += v;
return;
}
segVar;
segTreeUpdate(lft, st,md, p, v); segTreeUpdate(rgt, md+1, ed, p, v);
segTree[node] = max( segTree[lft] , segTree[rgt] );
}
int segTreeQuery(int node, int st, int ed, int l, int r) { ///ASSUMING SINGLE UPDATE, RANGE QUERY!!
if(ed < l || st > r) return 0;
if(st >= l && ed <= r) return segTree[node];
segVar;
return max(segTreeQuery(lft, st,md, l,r) , segTreeQuery(rgt, md+1,ed, l,r));
}
void update(int p, int v) {
int base = posInBase[p];
segTreeUpdate(1, 1, ptr, base, v);
}
int queryUp(int u, int v) {
int uchain = whichChain[u], vchain = whichChain[v], ubase = posInBase[u] , vbase = posInBase[v], ans = 0;
if(u == v) return segTreeQuery(1, 1,ptr, vbase , ubase );
while(true) {
uchain = whichChain[u];
ubase = posInBase[u];
int uhead = chainHead[uchain];
int sz = chainSize[uchain];
int utail = uhead + sz - 1;
if(uchain == vchain) {
ans = max( ans, segTreeQuery(1, 1,ptr, vbase , ubase ) );
// cout << "RET " << vbase << ' ' << ubase << ' ' << segTreeQuery(1, 1,ptr, vbase , ubase ) << ' ' << ans << endl;
break;
}
ans = max( ans, segTreeQuery(1, 1,ptr, posInBase[uhead], ubase ) );
u = par[uhead][0];
}
return ans;
}
int query(int a, int b) {
int lca = getLCA(a,b);
// cout << "LCA " << a << ' ' << b << ' ' << lca << endl;
return max( queryUp(a, lca) , queryUp(b, lca) ) ;
}
int main() {
// freopen("i.txt", "r", stdin);
// freopen("o.txt", "w",stdout);
for(int t=1; t<=1; t++) {
scanf("%d", &n);
memset(graph, NULL, sizeof graph);
memset(ara, 0, sizeof ara);
memset(lev, 0, sizeof(lev));
memset(par, 0, sizeof(par));
memset(chainHead, -1, sizeof(chainHead));
memset(chainSize, 0, sizeof(chainSize));
chains = ptr = 0;
for(int i=1; i<n; i++) {
int u,v;
scanf("%d %d", &u,&v);
graph[u].pb(v);
graph[v].pb(u);
}
///ASSUMING 1 IS ROOT NODE!!
dfs(1);
makeSparse();
makeHLD(1);
// cout << "BUG" << endl;
segTreeInit(1, 1,ptr);
// cout << "BASE " << endl;
// for(int i=1; i<=n; i++) cout << i << ' ' << posInBase[i] << endl;
// cout << "TREE" << endl;
// for(int i=1; i<=4*n; i++) cout << i << ' ' << segTree[i] << endl;
scanf("%d", &q);
while(q--) {
char cmd[100]; int x,y,z;
scanf("%s %d %d", cmd, &x,&y);
if(cmd[0] == 'I') update(x, y);
else printf("%d\n", query(x,y));
}
}
return 0;
}