Solution to LIS using DP

dp_sol.cpp

#include<bits/stdc++.h>
using namespace std;
 
const int maxn = 1e5+10;
int a[maxn], lis[maxn], lds[maxn];
int l[maxn], r[maxn], lcnt[maxn];
 
int main(){
	int n;
	cin >> n;
	memset(lis, 63, sizeof(lis));
	memset(lds, 63, sizeof(lds));
	for(int i = 0; i < n; i++){
		cin >> a[i];
		l[i] = lower_bound(lis, lis+n, a[i]) - lis;
		lis[l[i]] = a[i];
	}
	for(int i = n-1; i > -1; i--){
		r[i] = lower_bound(lds, lds+n, -a[i]) - lds;
		lds[r[i]] = -a[i];
	}
	int lissize = lower_bound(lis, lis+n, lis[maxn-1]) - lis;
	for(int i = 0; i < n; i++)
		if(l[i] + r[i] +1 >= lissize)
			lcnt[l[i]]++;
	for(int i = 0; i < n; i++){
		if(l[i] + r[i] +1 < lissize)
			cout << 1;
		else if(lcnt[l[i]] > 1)
			cout << 2;
		else
			cout << 3;
	}
	cout << '\n';
	return 0;
}