Code giving tle in some cases

#1 
/*

*-----------------------------------------------------------*
|                                                           |
|                                                           |
|               AUTHOR: Himanshu Aswal                      |
|                       (himanshu010)                       |
|                                                           |
|                                                           |
*-----------------------------------------------------------*


*/

#include<bits/stdc++.h>
#define moduli 998244353
#define int long long int
#define ld long double
#define F first
#define S second
#define P pair<int,int>
#define pb push_back
#define vi vector<int>
#define vvi vector<vector<int>>
#define vb vector<bool>
#define um unordered_map
#define R return

using namespace std;

int sum = 0;
void _printnum(int pos, int n, int one) {
    static char str[100];
    if (pos == n) {
        // cout << str << '\n';
        sum++;
        return;
    }
    if (one == 1) {
        str[pos] = '0';
        _printnum(pos + 1, n, one - 1);
    }
    else {
        str[pos] = '0';
        _printnum(pos + 1, n, one);
        str[pos] = '1';
        _printnum(pos + 1, n, one + 1);
    }


}




int32_t main()
{
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif

    ios_base:: sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    int t; cin >> t; while (t--)
    {
        int i, j, k, n, m, ans = 0, cnt = 0;
        cin >> n;
        _printnum(0, n, 0);
        cout << sum << endl;
        sum = 0;

    }
}
#2

hello @himanshu_aswal`,
you are getting tle because this recursive approach has exponential time complexity.

the recurrence relation for this problem will be->
t(n)=t(n-1) + t(n-2)

try using dynamic programming to optimise it furthur `

#3

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#4

I am not able to understand this by this condition can you give me the code so i can understand

#5

check this ->