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- #include<bits/stdc++.h>
- using namespace std;
- #define ll long long
- #define ld long double
- #define ull unsigned long long
- #define pb push_back
- #define ppb pop_back
- #define mp make_pair
- #define F first
- #define S second
- #define PI 3.1415926535897932384626
- #define sz(x) ((int)(x).size())
- typedef pair<int, int> pii;
- typedef pair<ll, ll> pll;
- typedef vector<int> vi;
- typedef vector<ll> vll;
- typedef vector<ull> vull;
- typedef vector<bool> vb;
- typedef vector<char> vc;
- typedef vector<pii> vpii;
- typedef vector<pll> vpll;
- typedef vector<vi> vvi;
- typedef vector<vll> vvll;
- typedef vector<vull> vvull;
- typedef vector<vb> vvb;
- typedef vector<vc> vvc;
- /************************************************** DEBUGGER *******************************************************************************************************/
- #ifndef ONLINE_JUDGE
- #define debug(x) cerr << #x <<" "; _print(x); cerr << endl;
- #else
- #define debug(x)
- #endif
- void _print(ll t) { cerr << t; }
- void _print(int t) { cerr << t; }
- void _print(string t) { cerr << t; }
- void _print(char t) { cerr << t; }
- void _print(ld t) { cerr << t; }
- void _print(double t) { cerr << t; }
- void _print(ull t) { cerr << t; }
- template <class T, class V> void _print(pair <T, V> p);
- template <class T> void _print(vector <T> v);
- template <class T> void _print(vector <vector<T>> v);
- template <class T> void _print(set <T> v);
- template <class T, class V> void _print(map <T, V> v);
- template <class T> void _print(multiset <T> v);
- template <class T, class V> void _print(pair <T, V> p) { cerr << "{"; _print(p.F); cerr << ","; _print(p.S); cerr << "}"; }
- template <class T> void _print(vector <T> v) { cerr << "[ "; for (T i : v) {_print(i); cerr << " "; } cerr << "]"; }
- template <class T> void _print(vector <vector<T>> v) { cerr << "==>" << endl; for (vector<T> vec : v) { for(T i : vec) {_print(i); cerr << " "; } cerr << endl; } }
- template <class T> void _print(set <T> v) { cerr << "[ "; for (T i : v) {_print(i); cerr << " "; } cerr << "]"; }
- template <class T> void _print(multiset <T> v) { cerr << "[ "; for (T i : v) {_print(i); cerr << " "; } cerr << "]"; }
- template <class T, class V> void _print(map <T, V> v) { cerr << "[ "; for (auto i : v) {_print(i); cerr << " "; } cerr << "]"; }
- /*******************************************************************************************************************************************************************/
- mt19937_64 rang(chrono::high_resolution_clock::now().time_since_epoch().count());
- int rng(int lim) {
- uniform_int_distribution<int> uid(0,lim-1);
- return uid(rang);
- }
- const int INF = 0x3f3f3f3f;
- const int mod = 1e9+7;
- ll mod_exp(ll a, ll b) { a %= mod; if(a == 0) return 0LL; ll res = 1LL;
- while(b > 0) { if(b & 1) res = (res * a) % mod; a = (a * a) % mod; b >>= 1; } return res; }
- ll mod_inv(ll a) { return mod_exp(a, mod - 2); } // works only for prime value of "mod"
- ll GCD(ll a, ll b) { return (b == 0) ? a : GCD(b, a % b); }
- /******************************************************************************************************************************/
- int len_LIS(vi &v, int n, int prev) {
- // base case
- if(n == 0) return 0;
- // choice diagram code
- // for each element of v[], we have 2 choices ==>
- // Choice 1: exclude the current element and process the remaining elements
- // Choice 2: include the current element if it is smaller than prev element in LIS
- int exclude = len_LIS(v, n - 1, prev);
- int include = 0;
- if(v[n-1] < prev) include = 1 + len_LIS(v, n - 1, v[n-1]);
- // return maximum of above two choices
- return max(exclude, include);
- }
- void solve()
- {
- int n; cin >> n;
- vi v(n);
- for(int i = 0; i < n; i++) cin >> v[i];
- cout << len_LIS(v, n, INT_MAX) << "\n";
- }
- int main()
- {
- ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
- srand(chrono::high_resolution_clock::now().time_since_epoch().count());
- // #ifndef ONLINE_JUDGE
- // freopen("input.txt", "r", stdin);
- // freopen("output.txt", "w", stdout);
- // #endif
- // #ifndef ONLINE_JUDGE
- // freopen("error.txt", "w", stderr);
- // #endif
- int t = 1;
- // int test = 1;
- // cin >> t;
- while(t--) {
- // cout << "Case #" << test++ << ": ";
- solve();
- }
- return 0;
- }
- /* # prev is initialised with INT_MAX in the main() fâż
- # Time Complexity: The time complexity of this recursive approach is exponential (O(2âż)) as there
- is a case of overlapping subproblems.
- # Auxiliary Space: O(1). No external space used for storing values apart from the internal
- stack space (which use O(n) space).
- */
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