Solved this after 3 days of analysis. Algorithm must be O(logN), otherwise it will time out. I process number digit by digit and update the count value. I created auxilarry arrays with values like: - number of reversible numbers for given number of digits and its cumulative sum - number of odd digit sums without carry over (exluding digit 0) and its cumulative sums - number of odd digit sum without carry over (including digit 0) and its cumulative sums - number of odd digits sums with carry over and its cumultaive sums - number of even digit sums without carryover and its cumulative sums

Time Out Error

def is_reversible(n):
    if n % 10 == 0:  # Avoid leading zeroes in the reverse
        return False
    
    sum_n_reverse = n + int(str(n)[::-1])  # Sum of n and its reverse
    for digit in str(sum_n_reverse):
        if int(digit) % 2 == 0:  # Check for even digits in the sum
            return False
    return True

def count_reversible_numbers(limit):
    count = 0
    for i in range(1, limit):
        if is_reversible(i):
            count += 1
    return count

def main():
    test_cases = int(input())
    for _ in range(test_cases):
        limit = int(input())
        reversible_count = count_reversible_numbers(limit)
        print(reversible_count)

if __name__ == "__main__":
    main()

For those who are struggling solving this. At one time it took me about a week of work to solve this problem, may be longer. This is no way an easy thing, and I doubt the solution can be written as one function. Particularly, my solution contains near 600 lines and 17 helper functions.

Time out can anyone fix it

n = [int(input()) for i in range(0,int(input()))]
def reverse(x):
    return int(str(x)[::-1])
def isInputOdd(x):
    lis = str(x)
    for i in lis:
        if int(i)%2==0:
            flag = False
            return flag
        else:
            flag = True
    return flag
def main(iter):    
    sum1=0
    for i in range(iter):
        k = i + reverse(i)
        if i%10!=0 and isInputOdd(k):
            sum1+=1
    print (sum1)
for i in n:
    main(i)

Facing timeout problem... !! def procedure(n): s=str(n) #print("s = ",s) s1 = s[::-1] if int(s1)>10: #print("s1 = ",s1) #print(int(s1)) s2=n+int(s1) #print("s2 = ",s2) if '2' not in str(s2) and '4' not in str(s2) and'6' not in str(s2) and'8' not in str(s2) and'0' not in str(s2): return True else: return False

t=int(input())#no of test cases while t>0: n=int(input()) c=0 for i in range(10,n): if procedure(i)==True: c=c+1

print(c)
t=t-1

Time Complexity :--- O(no.of test cases* n).. Suggest me ...some alternatives.. !!