Dynamic-Programming/JobBounties(DP).cpp at master · robinrst/Dynamic-Programming · GitHub

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#include        "algorithm"
#include        "iostream"
#include        "numeric"
#include        "iomanip"
#include        "cstring"
#include        "math.h"
#include        "bitset"
#include        "string"
#include        "vector"
#include        "ctime"
#include        "queue"
#include        "stack"
#include        "map"
#include        "set"

#include        "ext/pb_ds/assoc_container.hpp" // Common file
#include        "ext/pb_ds/tree_policy.hpp" // Including tree_order_statistics_node_update
#include        "ext/pb_ds/detail/standard_policies.hpp"

using namespace std;
using namespace __gnu_pbds;


#define          f first
#define          lgn 25
#define          endl '\n'
#define          sc second
#define          pb push_back
#define          N (int)2e5+5
#define          PI acos(-1.0)
#define          int long long
#define          vi vector<int>
#define          mod 1000000007
#define          ld long double
#define          eb emplace_back
#define          mii map<int,int>
#define          vpii vector<pii>
#define          pii pair<int,int>
#define          pq priority_queue
#define          BLOCK (int)sqrt(N)
#define          test(x) while(x--)
#define          all(x) begin(x),end(x)
#define          allr(x) rbegin(x),rend(x)
#define          fo(i,a,n) for(int i=a;i<n;i++)
#define          rfo(i,n,a) for(int i=n;i>=a;i--)
#define          FAST ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define          time() cerr << "Time : " << (double)clock() / (double)CLOCKS_PER_SEC << "s\n"
#define 		 bug(...)       __f (#__VA_ARGS__, __VA_ARGS__)

typedef tree< int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update >
OS ;

template <typename Arg1>
void __f (const char* name, Arg1&& arg1) { cout << name << " : " << arg1 << endl; }
template <typename Arg1, typename... Args>
void __f (const char* names, Arg1&& arg1, Args&&... args)
{
     const char* comma = strchr (names + 1, ',');
     cout.write (names, comma - names) << " : " << arg1 << " | "; __f (comma + 1, args...);
}

const int inf = 0x3f3f3f3f;
const int INF = 0x3f3f3f3f3f3f3f3f;

int n,m,k,q;
string s;
int dp[N];
/*
dp[i] -> denotes maximum lenght valid string upto ith index

Case 1 - if we encounter this "()......." tthen dp[i] = 2 + dp[i-2];
Case 2 - if we encounter this "......))" then we have to check for a '(' previously encounter but not in maximum lenght till (i-1)
         so we check at ( i - dp[i-1] - 1) -> here dp[i-1] is maximum lenght valid string till (i-1)th index , so we have to check
         at just previous of its starting that's why ( dp[i-1] - 1) from ith index
		 , so if we encounter '(' then we can extend dp[i-1] answer by 2 and also add then maximum lenght valid string just previous of encountered '('
		 i.e dp[ i - dp[i-1] - 2].
*/

void go()
{
	cin >> s;
	n = s.size();

	s = " " + s;
	int ans = 0;

	fo(i,2,n+1)
	{
		if( s[i-1] == '(' and s[i] == ')' )
		{
			dp[i] = dp[i-2] + 2;
		}
		if( s[i] == ')' and s[i-1] == ')' )
		{
			if( s[ i - dp[i-1] - 1] == '(' ) dp[i] = dp[i-1] + 2 + dp[i - dp[i-1] - 2];
		}

		ans = max( ans , dp[i] );
	}

	cout << ans << endl;
}

int32_t main()
{
	FAST;
	int t=1;
	// cin>>t;
	test(t) go();
}