Question

I am trying to check the time complexity of the below simple program.
The program replaces spaces in a string with '%20'.

1. The loop to count spaces (O(1) time)

       foreach (char k in s)
       {
           if (k == ' ')
           {
               spaces_cnt++;
           }
       }
   

2. The loop to replace the spaces (O(n) where n is size of string)

       char[] c = new char[s.Length + spaces_cnt * 3];
       int i = 0;
       int j = 0;
       while (i<s.Length)
       {
           if (s[i] != ' ')
           {
               c[j] = s[i];
               j++;
               i++;
           }
           else
           {
   
               c[j] = '%';
               c[j + 1] = '2';
               c[j + 2] = '0';
               j = j + 3;
               i++;
           }
       }
   

So I am guessing it is a “O(n) + O(1)” solution. Please correct me if I am wrong.

Answer 1

The loop to count spaces takes O(n), not O(1), since you’re iterating over – and performing a check on – each of the n characters in your string.

As you stated, the replacement loop takes O(n). Two O(n) operations performed sequentially have a combined complexity of O(n) (constant factors are discarded in Big-O notation).

P.S. You know that you can achieve the equivalent of all your code using a single line?

s = s.Replace(" ", "%20");