What approach we can make to tjis problem except recursion as I recursion give TLE. I want some idea how we can approach this problem

ray = input("Enter the string : ")

ben = ''
kevin = ''

ben = ray[0]                     # Do move 1
ray = ray[1:]

while ben or ray:
                         # First two if conditions are for empty strings
    if ben == '':
        ben = ray[0]             # If ben string is empty do move 1
        ray = ray[1:]
    if ray == '':                # If ray string is empty then
        kevin = kevin+ben[::-1]  # reverse ben string and add it to kevin
        break                    # break here to prevent string indexing
                                 # error in next condition

    # Below if and else conditions works only 
    # when both ray and ben are not empty
    
    if min(ray) < ben[-1] :
        ben = ben+ray[0]         # Do move 1
        ray = ray[1:]            # Remove first character from ray string
    else:
        kevin = kevin+ben[-1]    # Do move 2
        ben = ben[:-1]           # Remove last character from ben string
print(kevin)

/* Take string length and string as input 

   Example: 6 master
*/

#include <bits/stdc++.h>
using namespace std;

int main()
{
    int n;
    string ray, ben = "", kevin = "";
    cin >> n >> ray; 
    
    int count = 0, k = 0, m;
    stack<char> next;
    while(count < n)
    {
        char ch = 'z';
        for(int i = k; i < n; i++)
        {
            if(ray[i] < ch)
            {
                ch = ray[i];
                m = i;
            }
        }
        
        for(int i = k; i < m; i++)
        {
            next.push(ray[i]);
        }
        
        if(next.top() < ch)
        {
            kevin = kevin + next.top();
            next.pop();
        }
        else
            kevin = kevin + ray[m];
        k = m+1;
        count++;
    }
    
    cout << kevin << endl;
    
    return 0;
}

def move1(ray,ben):
    ben=    ben+ray[0]
    ray = ray[1:]
    return(ray,ben)
def move2(ben, kevin):
    kevin = kevin+ben[-1]
    ben = ben[:-1]
    return(ben,kevin)
ray = "vedant"
ben = ""
kevin =""

# find smallest letter in a string
def smallest(string):
    smallest = string[0]
    for letter in string:
        if letter < smallest:
            smallest = letter
    return smallest

ray,ben= move1(ray,ben)
while(ray or ben):
    if(ray and ben):
        if(smallest(ray) < smallest(ben)):
            ray,ben = move1(ray,ben)
        else:
            ben,kevin = move2(ben,kevin)
    elif(ray):
        ray,ben = move1(ray,ben)
    else:
        ben,kevin = move2(ben,kevin)

print( kevin)

#include<bits/stdc++.h>
using namespace std;

//TC:O(n^2), SC:O(n)
int main() {
	string s = "xyzbazybc"; //abbcyzzyx
	// cin >> s;
	string ans, mid;
	auto st = s.begin();
	while (st != s.end()) {
		auto itr = min_element(st, s.end());

		if (mid.length() and mid.back() <= *itr) {
			ans += mid.back();
			mid.pop_back();
		} else {
			mid += s.substr(st - s.begin(), (itr - st ) + 1);
			st = ++itr;
		}
	}
	if(mid.length()){
		reverse(mid.begin(),mid.end());
		ans+=mid;
	}
	cout<<ans;
}

input="cba"
n=[]
o=[]
im=[]
n=[ord(i)-96 for i in input]
while len(n)>0:
  min_val=min(n)
  min_index=n.index(min_val)
  o+=[min_val]
  im+=n[:min_index]
  n=n[min_index+1:]
  if len(n)>0:
    min_val=min(n)
    min_index=n.index(min_val)
    while len(im)>0 and min_val>=im[-1]:
      o+=[im[-1]]
      im=im[:-1]
if len(im)>0:
  o+=im[::-1]  
  
op="".join(chr(i+96) for i in o)
print(op)

import string
n=int(input("Enter the Number of Elements : "))
ray=input("Enter a String : ")
ben=""
kevin=""
ray1=list(ray)
n=1
ben1=list(ray)
ben1.sort()
ray=''
ben=''
for ele in ben1:
	kevin+= ele
print(kevin)