Question

I have written a function and I need to know the big O notation for it.
I have tried to slove this myself and I get O(N^2), however I have been told that this is not the correct answer.

Can someone please tell me what the correct notation is and also a step by step explanation of how they came to that answer?

The function is below.

Thanks in advance

    public static string Palindrome(string input) 
    {
        string current = string.Empty;
        string longest = string.Empty;

        int left;
        int center;
        int right;


        if (input == null || input == string.Empty || input.Length == 1)  {   return input;   }


        for (center = 1; center < input.Length -1; center++) 
        {
            left = center - 1;  
            right = center + 1;

            if (input[left] == input[center])
            {
                left--;
            }

            while (0 <= left && right < input.Length) 
            {
                if (input[left] != input[right])
                {
                    break;
                }

                current = input.Substring(left, (right - left + 1));

                longest = current.Length > longest.Length ? current : longest;

                left--;  
                right++;
            }
        }
        return longest;
    }

Answer 1

This is O(n^3) algorithm:

This part takes O(n^2):

// O(n) times for while loop

        while (0 <= left && right < input.Length)   
        {
            if (input[left] != input[right])
            {
                break;
            }

// taking substring is O(n)

            current = input.Substring(left, (right - left + 1)); 

            longest = current.Length > longest.Length ? current : longest;

            left--;  
            right++;
        }

Also there is an outer O(n), for loop, which causes to O(n*n^2).

You can improve your algorithm by changing this lines:

   current = input.Substring(left, (right - left + 1)); 
   longest = current.Length > longest.Length ? current : longest;

to:

   currentLength = right - left + 1;
   if(currentLength > longest)
   { 
     longest = current.Length > longest.Length ? current : longest;
     longestLeft = left;
     longestRight = right;
   }

and finally return a substring from longestLeft to longestRight. Actually avoid to use substring method too many times.