A singly linked list contains n $1$ strings that are binary representations of numbers from the set $\{0,1,...$ n $1\}$ where n is an exact power of $2.$ However, the string corresponding to one of the numbers is missing. For example, if n $=4,$ the list will contain any three strings from $00,01,10$ and $11.$ Note that the strings in the list may not appear in any specific order. Also note that the length of each string is lgn$,$ hence the time to compare two strings in O$($lgn$).$ Write an algorithm that generates the missing string in O$($n$).[5$ points$]$

Hint: Zeno$$s Paradox