# HackerEarth Flipping Brackets problem solution

In this HackerEarth Flipping Brackets problem solution A regular bracket sequence is a sequence of '(' and ')' characters defined as follows:

The empty string (without any characters) is a regular bracket sequence.
If A is a regular bracket sequence, then (A) is also considered a regular sequence.
If A and B are regular bracket sequences, then AB is also considered as a regular bracket sequence.
For a string S that consists of only '(' and ')' characters, consider a sequence of M operations that are of one of the following types:

C i: If the character Si is an opening bracket '(', then it is replaced by a closing bracket ')'. Similarly, the ')' character is replaced by the '(' character.
Q i: Determine the maximum length K of the regular bracket sequence starting at index i of the string. Formally, the string Si Si+1 ... Si+k-1 should be a regular bracket sequence, where K is maximized. If there is no regular bracket sequence starting at index i, then print 0.

## HackerEarth Flipping Brackets problem solution.

#include <bits/stdc++.h>
using namespace std;

#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"

const int N=2e5+5;

int n, m;
string s;
int pref[N], st[4*N], lazy[4*N];

void build(int node, int L, int R)
{
if(L==R)
{
st[node]=pref[L];
return;
}
int M=(L+R)/2;
build(node*2, L, M);
build(node*2+1, M+1, R);
st[node]=min(st[node*2], st[node*2+1]);
}

void propagate(int node, int L, int R)
{
if(L!=R)
{
lazy[node*2]+=lazy[node];
lazy[node*2+1]+=lazy[node];
}
st[node]+=lazy[node];
lazy[node]=0;
}

int query(int node, int L, int R, int i, int j)
{
if(lazy[node])
propagate(node, L, R);
if(j<L || i>R)
return 1e9;
if(i<=L && R<=j)
return st[node];
int M=(L+R)/2;
int left=query(node*2, L, M, i, j);
int right=query(node*2 + 1, M+1, R, i, j);
return min(left, right);
}

void update(int node, int L, int R, int i, int j, int val)
{
if(lazy[node])
propagate(node, L, R);
if(j<L || i>R)
return;
if(i<=L && R<=j)
{
lazy[node]+=val;
propagate(node, L, R);
return;
}
int M=(L+R)/2;
update(node*2, L, M, i, j, val);
update(node*2 + 1, M+1, R, i, j, val);
st[node]=min(st[node*2], st[node*2 + 1]);
}

int check(int p, int idx, int mid)
{
int mn=query(1, 0, n, idx, mid);
return mn>=p;
}

int binsearch(int p, int lo, int hi)
{
int idx=lo;
while(lo<hi)
{
int mid=(lo+hi+1)/2;
if(check(p, idx, mid))
lo=mid;
else
hi=mid-1;
}
return lo;
}

int check2(int p, int idx, int mid)
{
int mn=query(1, 0, n, mid, n);
return mn==p;
}

int binsearch2(int p, int lo, int hi)
{
int idx=lo;
while(lo<hi)
{
int mid=(lo+hi+1)/2;
if(check2(p, idx, mid))
lo=mid;
else
hi=mid-1;
}
return lo;
}

int work(int idx)
{
int p=query(1, 0, n, idx-1, idx-1);
int mn=query(1, 0, n, idx, n);
if(mn<p)
{
int ans=binsearch(p, idx, n);
ans=ans-idx+1;
if(ans%2)
ans--;
return ans;
}
else if(mn>p)
return 0;
else
{
int ans=binsearch2(p, idx, n);
ans=ans-idx+1;
if(ans%2)
ans--;
return ans;
}
}

int32_t main()
{
IOS;
cin>>s;
n=s.size();
for(int i=1;i<=n;i++)
{
pref[i]=pref[i-1];
if(s[i-1]=='(')
pref[i]++;
else
pref[i]--;
}
build(1, 0, n);
cin>>m;
for(int i=1;i<=m;i++)
{
char ch;
cin>>ch;
int idx;
cin>>idx;
if(ch=='C')
{
if(s[idx-1]=='(')
update(1, 0, n, idx, n, -2), s[idx-1]=')';
else
update(1, 0, n, idx, n, +2), s[idx-1]='(';
}
else
cout<<work(idx)<<endl;
}
return 0;
}

### Second solution

#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#endif

#define ll long long
#define pb push_back
#define mp make_pair
#define pii pair<int,int>
#define vi vector<int>
#define all(a) (a).begin(),(a).end()
#define F first
#define S second
#define sz(x) (int)x.size()
#define hell 1000000007
#define endl '\n'
#define rep(i,a,b) for(int i=a;i<b;i++)
using namespace std;

string to_string(string s) {
return '"' + s + '"';
}

string to_string(const char* s) {
}

string to_string(bool b) {
return (b ? "true" : "false");
}

string to_string(char ch) {
return string("'")+ch+string("'");
}

template <typename A, typename B>
string to_string(pair<A, B> p) {
return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <class InputIterator>
string to_string (InputIterator first, InputIterator last) {
bool start = true;
string res = "{";
while (first!=last) {
if (!start) {
res += ", ";
}
start = false;
res += to_string(*first);
++first;
}
res += "}";
return res;
}

template <typename A>
string to_string(A v) {
bool first = true;
string res = "{";
for (const auto &x : v) {
if (!first) {
res += ", ";
}
first = false;
res += to_string(x);
}
res += "}";
return res;
}

void debug_out() { cerr << endl; }

void debug_out(Head H, Tail... T) {
cerr << " " << to_string(H);
debug_out(T...);
}

template <typename A, typename B>
istream& operator>>(istream& input,pair<A,B>& x){
input>>x.F>>x.S;
return input;
}

template <typename A>
istream& operator>>(istream& input,vector<A>& x){
for(auto& i:x)
input>>i;
return input;
}

#ifdef PRINTERS
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

long long readInt(long long l,long long r,char endd){
long long x=0;
int cnt=0;
int fi=-1;
bool is_neg=false;
while(true){
char g=getchar();
if(g=='-'){
assert(fi==-1);
is_neg=true;
continue;
}
if('0'<=g && g<='9'){
x*=10;
x+=g-'0';
if(cnt==0){
fi=g-'0';
}
cnt++;
assert(fi!=0 || cnt==1);
assert(fi!=0 || is_neg==false);

assert(!(cnt>19 || ( cnt==19 && fi>1) ));
} else if(g==endd){
assert(cnt>0);
if(is_neg){
x= -x;
}
assert(l<=x && x<=r);
return x;
} else {
debug(int(g));
assert(false);
}
}
}
string ret="";
int cnt=0;
while(true){
char g=getchar();
if(g==endd){
break;
}
else if(g==')' or g=='('){
cnt++;
ret+=g;
}
else{
assert(false);
}
}
assert(l<=cnt && cnt<=r);
return ret;
}
long long readIntSp(long long l,long long r){
}
long long readIntLn(long long l,long long r){
}
}
}

int segtree[1<<22];
int lazy[1<<22];
void build(vi& arr,int pos,int l,int r){
if(l==r){
segtree[pos]=arr[l];
return;
}
else{
int mid = (l+r)/2;
build(arr,pos*2+1,l,mid);
build(arr,pos*2+2,mid+1,r);
segtree[pos]=min(segtree[pos*2+1],segtree[pos*2+2]);
}
}

void update(int pos,int l,int r,int a,int b,int val){
if(lazy[pos]){
segtree[pos]+=lazy[pos];
if(l!=r){
lazy[pos*2+1]+=lazy[pos];
lazy[pos*2+2]+=lazy[pos];
}
lazy[pos]=0;
}
if(a>r or b<l) return;
if(a<=l and r<=b){
segtree[pos]+=val;
if(l!=r){
lazy[pos*2+1]+=val;
lazy[pos*2+2]+=val;
}
return;
}
int mid = (l+r)/2;
update(pos*2+1,l,mid,a,b,val);
update(pos*2+2,mid+1,r,a,b,val);
segtree[pos]=min(segtree[pos*2+1],segtree[pos*2+2]);
}

int query(int pos,int l,int r,int a,int b){
if(lazy[pos]){
segtree[pos]+=lazy[pos];
if(l!=r){
lazy[pos*2+1]+=lazy[pos];
lazy[pos*2+2]+=lazy[pos];
}
lazy[pos]=0;
}
if(a>r or b<l) return INT_MAX;
if(a<=l and r<=b){
return segtree[pos];
}
int mid = (l+r)/2;
return min(query(pos*2+1,l,mid,a,b),query(pos*2+2,mid+1,r,a,b));
}

void solve(){
int N = int(s.size());
assert(all_of(all(s),[](char ch){return ch==')' or ch=='(';}));
vi prefix_sum(N);
int cursum = 0;
for(int i = 0; i < N; i++){
cursum += (s[i] == '(' ? 1 : -1);
prefix_sum[i] = cursum;
}
debug(prefix_sum);
build(prefix_sum,0,0,N-1);
for(int i = 0; i < M; i++){
char ch;
ch = getchar();
assert(ch=='C' or ch=='Q');
if(ch == 'C'){
ch = getchar();
assert(ch == ' ');
int idx;
if(i+1 == M) idx = readInt(1,N,EOF);
idx--;
if(s[idx] == ')'){
s[idx] = '(';
update(0,0,N-1,idx,N-1,2);
}
else{
s[idx] = ')';
update(0,0,N-1,idx,N-1,-2);
}
}
else{
ch = getchar();
assert(ch == ' ');
int idx;
if(i+1 == M) idx = readInt(1,N,EOF);
idx--;
int zero = idx ? query(0,0,N-1,idx-1,idx-1) : 0;
debug(zero);
int mina = idx-1;
int maxa = N;
while(maxa - mina > 1){
int mid = mina + (maxa - mina)/2;
if(query(0,0,N-1,idx,mid) < zero) maxa = mid;
else mina = mid;
}
if(maxa != N){
cout << (maxa - idx) << endl;
}
else{
mina = idx-1;
maxa = N;
while(maxa - mina > 1){
int mid = mina + (maxa - mina)/2;
if(query(0,0,N-1,mid,N-1) == zero) mina = mid;
else maxa = mid;
}
cout << mina - idx + 1 << endl;

}
}
}
}

int main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int t=1;
// cin>>t;
while(t--){
solve();
}
return 0;
}