Longest increasing subseqeunce.cpp

///Status : AC
///Remark : recursion + memoization . O(n^2)

typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#include<bits/stdc++.h>

//MACROS{
#define rep(x,a,b) for(x=a;x<b;x++)
#define reptill(x,a,b) for(x=a;x<=b;x++)

#define scani(x) scanf("%d",&x)
#define scan2i(x,y) scanf("%d %d",&x,&y)
#define scan3i(x,y,z) scanf("%d %d %d",&x,&y,&z)

#define scanfl(x) scanf("%f",&x)
#define scanc(x) scanf("%c",&x)
#define scand(x) scanf("%lf",&x)

#define scanll(x) scanf("%lli",&x)
#define scan2ll(x,y) scanf("%lli %lli",&x,&y)
#define scan3ll(x,y,z) scanf("%lli %lli %lli",&x,&y,&z);

#define scanl(x) scanf("%ld",&x)
#define scans(x) scanf("%s",x)
#define printi(x) printf("%d\n",x)
#define printl(x) printf("%ld\n",x)
#define printll(x) printf("%lli\n",x)
#define printd(x) printf("%lf\n",x)
#define printfl(x) printf("%f\n",x)
#define printc(x) printf("%c\n",x)
#define prints(x) printf("%s\n",x);
#define sloop(x) loop(i,0,strlen(x)-1)
#define nl ("\n")
#define newl cout<<nl
#define FILL(A,value) memset(A,value,sizeof(A))
#define FILL_MAT(x,rrrr,cccc,value) for(int iiii=0;iiii<rrrr;iiii++){for(int jjjj=0;jjjj<cccc;jjjj++) x[iiii][jjjj]=value;}


#define whole(x) x.begin(),x.end()
#define pb push_back
#define in insert
#define mp make_pair
#define get(tp_name,x) (get<x>(tp_name))   ///to access tuple(i)
#define umap unordered_map


#define F first
#define S second
//}END MACROS

using namespace std;


///comparator class for ordering on the basis of 'Second'
/*
class CompareDist
{
public:				///pairType doesn't name a type ,its just to show type of pair object passed in operatorfunction

bool operator()( pairType p1, pairType p2) {
return p1.S>p2.S;
}
};
*/

typedef pair<int,int> II;
typedef pair<ll,ll> LL;
typedef vector<II> VII;
typedef vector<LL> VLL;
typedef vector<int> VI;
typedef vector<bool> VB;
typedef vector<ll> VL;
typedef vector< VI > VVI;
typedef vector< VL > VVL;
typedef vector<string> VS;

//maths
#define PI acos(-1)

#define INTmax numeric_limits<int>::max()
#define INTmin numeric_limits<int>::min()

#define LLmax numeric_limits<ll>::max()
#define LLmin numeric_limits<ll>::min()

#define ULLmax numeric_limits<ull>::max()

typedef priority_queue<II,vector<II>, greater<II> > P_Queue;             ///priority queue contianing II (having vector<II> as underlying container) with greater as functor
															///		heapify on the basis of comparisons of  II.first  values

template<typename type>
void get_arr(type a[],type n)
{
for(type i=0;i<n;i++) cin>>a[i];
}

template<typename type>
void show_arr(type a[],type n=1) {for(type i=0;i<n;i++) cout<<a[i]<<" ";}

template<typename type>
inline type max3(type a,type b,type c){	 return max(max(a,b),c);}

template<typename type>
inline type min3(type a,type b,type c){	 return min(a,min(b,c));}

template<typename type>
inline type min4(type a,type b,type c,type d){	 return min(a,min3(b,c,d));}

template<typename type>
inline type max4(type a,type b,type c,type d){	 return max(a,max3(b,c,d));}


template<typename type>
type modpowIter(type a, type b, type c) { type ans=1;  while(b != 0){ if(b%2 == 1) ans=(ans*a)%c;  a=(a*a)%c; b /= 2; } return ans; }

template<typename type>
type phi(type n){ type result = n;  for (type p=2; p*p<=n; ++p) { if (n % p == 0){ while (n % p == 0)   n /= p; result -= result / p; } } if (n > 1) result -= result / n; return result; }

template<typename type> type gcd(type A,type B){	if(B==0)	return A;	else return gcd(B, A % B);	}

template<class type>
type ncr(type n,type r){  	assert(n>=r); type ans=1,i; 	if(n==r) return 1; if(r==1) return n; if(r>(n-r)) r=n-r; reptill(i,0,r-1) ans=ans*(n-i)/(i+1);	return ans; }

template<typename type>  unsigned long long fact(type x){ ull ans=1; for(type i=1;i<=x;i++){ ans*=i;        /*ans%=MOD;   /Optional*/ } return ans; }

template<typename type>
int Digs(type n){ return (n >= 10) ? 1 + Digs(n/10): 1; }

template<typename type>
type tonum(string s){	type ans=0,i;	rep(i,0,s.size())	ans=ans*10+(s[i]-'0'); return ans; }

template<typename T_> inline bool is_perfsq(T_ n){T_ a=(T_)sqrt((double) n); return (a*a==n || (a+1)*(a+1)==n);/* in case of an off-by-one float error*/}

inline void FAST_IO(){ios_base::sync_with_stdio(false);}


#define printMat(x,r,c) for(int i=0;i<r;i++){ for(int j=0;j<c;j++) cout<<x[i][j]<<" "; newl; }

#define SIZE (int(2e3)+1)
#define MOD
#define debug
#define MAX1
#define MAX2

///frequently useable
class comp
{
	public :
		bool operator()(pair< II,int > A, pair< II,int > B)		///for sorting through comparator ,can be modified
		{
			return (A.F.F < B.F.F);
		}

		bool operator()(pair<II,int> A, int val)
		{
			return A.F.F< val;
		}

		bool operator()(pair<int,int> A,int val)
		{
			return A.F<val;
		}
};

class Graph
{
  public:
    int n;
    vector<VII> adj ;
    VB visited;
	Graph(int n){		this->n = n, visited= VB(n+1,false), adj= vector<VII> (n+1); }
	void uedge(int x, int y,int wt=1) {adj[x].push_back({y,wt}),adj[y].push_back({x,wt});  }
	void dedge(int x,int y,int wt=1) { adj[x].pb({y,wt});}
};


	class DSU 	///nodes from 0...n-1
	{
		public:
		int n;
		VI par,Size;
		int disjointSets;
		DSU(int n){this->n=n ,par = VI(n),Size= VI(n,1); for(int i=0;i<par.size();i++) par[i]=i; disjointSets=n; }
		int findroot(int x){ while(par[x]!=x){ par[x] = par[par[x]]; x=par[x]; } return x; }
		bool sameset(int x,int y){	 return (findroot(x)==findroot(y)); }
		void Union(int x,int y)
		{
			int rx= findroot(x),ry=findroot(y);		if(rx==ry) return; disjointSets--;
			if(Size[rx]>=Size[ry]) par[ry]=rx,Size[rx]+= Size[ry];
			else par[rx]= ry,Size[ry]+=Size[rx];
		}
	};

VI v;

//VVI DP;

int LIS(int i,int bound)
{

	if(i==v.size()-1) return (v[i]>bound) ;//DP[i][bound]=(v[i]>bound);

   // if(DP[i][bound]!=-1) return DP[i][bound];

	int ans=LIS(i+1,bound);

	if(v[i]>bound) ans= max(ans, 1+ LIS(i+1,v[i]));

	return ans;

	//return DP[i][bound]=ans;
}

int main()
{

	FAST_IO();

	#ifndef ONLINE_JUDGE
		ifstream cin("/home/aditya/Documents/ip");
	#endif
	//ofstream cout("/home/aditya/Documents/op");

		//int t;	cin>>t;while(t--){


            int n;

            cin>>n;
            //DP= VVI(n+1,VI(302,-1));


			v=VI(n);

			for(int i=0;i<n;i++)
			{
				cin>>v[i];
				v[i]++;
			}

			cout<<LIS(0,0)<<nl;
//        }

}