Minimum number of strictlly increasing subsequences.cpp

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
typedef long long ll;
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds;
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#define ios ios_base::sync_with_stdio(0) ; cin.tie(0) ; cout.tie(0)
#define so sizeof
#define pb push_back
#define cl clear() ;
#define vl vector<ll>
#define sz size()
#define len length()
#define emp empty()
#define el endl;cout.flush()
#define be begin()
#define fi first
#define se second
#define br break
#define en end()
#define ro return 0
#define eb emplace_back
#define con continue
#define ms(x) memset(x , 0, so x)
#define all(x) (x).be , (x).en
#define acc(x) accumulate((x).be , (x).en , 0ll)
#define forn(i,a,b) for(ll i=a;i<=b;++i)
#define rng_58 mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define vll vector<pair<ll,ll> >
#define pll pair<ll,ll>
#define plll pair<ll,pair<ll,ll>>
#define plvl pair<pair<ll,ll> ,ll>
#define mp make_pair
#define trace3(a,b,c) cerr <<"a is " << a << " b is " << b << " c is " << c << el;
#define trace4(a,b,c,d) cerr <<"a is " << a << " b is " << b << " c is " << c <<" d is " << d << el ;
#define trace5(a,b,c,d,e) cerr <<"a is " << a << " b is " << b << " c is " << c <<" d is " << d << " e is " << e << el;
#define trace6(a,b,c,d,e,f) cerr <<"a is " << a << " b is " << b << " c is " << c <<" d is " << d << " e is " << e << " f is " << f << el ;
int main()
{
   // ios;
   /// find the largest element less than the current element x , replace it with x else append x.
   /// for proof refer dilworth's theorem.
    ll n ;
    vl v;
    cin >> n ;
    forn(i , 1 , n ){
       ll x;
       cin >> x;
       v.pb(x) ;
    }
    multiset<ll> s;
    forn(i , 0 , n-1){
       if(i == 0 or ll(s.sz) == 0){
        s.insert(v[i] ) ;
        con ;
       }
       ll curr = v[i] ;
       auto it = s.lower_bound(curr) ;
       if(it == s.begin()){
         s.insert(curr) ;
         con ;
       }
       else {
         --it ;
        s.erase(it);
        s.insert(curr);
       }
    }
    cout << ll(s.sz ) << el ;
    ro ;

}