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Longest Increasing Subsequence(recursion).cpp
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Longest Increasing Subsequence(recursion).cpp
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#include<bits/stdc++.h>
using namespace std;
#define int long long
#define fr(i,n) for(int i=0;i<n;i++)
#define fre(i,a,b) for(int i=a;i<=b;i++)
#define endl '\n'
#define no cout << "NO" << endl
#define yes cout << "YES" << endl
#define mem(name, value) memset(name, value, sizeof(name))
#define pb push_back
#define ff first
#define ss second
#define mp make_pair
#define all(v) (v).begin(), (v).end()
#define case cout << "Case " << t++ << ": ";
// recursion solution LIS O(exponential)
int LIS(int *arr, int n, int *ans)
{
if (n == 1) {
return 1;
}
int res, answ = 1;
for (int i = 1; i < n; i++) {
res = LIS(arr, n, ans);
if (arr[i - 1] <= arr[n - 1] && res + 1 > answ) {
answ = 1 + res;
}
}
if (*ans < answ) {
*ans = answ;
}
return answ;
}
int LIS_util(int *arr, int n) {
int *lis = 1;
LIS(arr, n, &lis);
return lis;
}
// DP (Bottom UP) solution
int LIS_DP(int *arr, int n) {
int dp[n + 1];
dp[0] = INT_MIN;
for (int i = 1; i <= n; i++) {
dp[i] = INT_MAX;
}
// O(N2) Complexity
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (dp[j] < arr[i] && arr[i] < dp[j + 1]) {
dp[j + 1] = arr[i];
}
}
// binary Search optimisation O(N2)-->nlogn complexity
for (int i = 0; i < n; i++) {
int idx = upper_bound(dp, dp + n + 1, arr[i])-dp;
if(dp[idx-1]<arr[i] && dp[idx]>arr[i]){
dp[idx]=arr[i];
}
}
}
int ans = 0;
for (int i = 1; i <= n; i++) {
if (dp[i] != INT_MAX) {
ans = i;
}
}
// Length of LIS
return ans;
// For printing LIS
for (int i = 1; i <= n; i++) {
if (dp[i] != INT_MAX) {
cout<<dp[i];
}
}
}
int32_t main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin) ;
freopen("output.txt", "w", stdout);
#endif
int t;
cin >> t;
while (t--)
{
int n;
cin >> n;
int arr[n];
fr(i, n) {
cin >> arr[i];
}
cout << /*LIS_DP*/LIS_util(arr, n) << endl;
}
return 0;
}