Each question is about designing a backtracking algorithm. First, give a brief explanation of your solution to the problem $($perhaps with the help of a mathematical recurrence$).$ Then, write down pseudocode for the backtracking algorithm. Each algorithm must be a pure function, and should not contain any other function calls inside of it$.$

$1.$ In class, we looked at the text splitting problem: given a string $\backslash ($ S $\backslash ),$ determine whether $\backslash ($ S $\backslash )$ can be split into individual words. One of the algorithms we wrote down looks like the following:

By only modifying the highlighted parts and introducing a temporary variable in the above algorithm $($and changing the name of the function$),$ design a backtracking algorithm for counting the number of ways to split the string $\backslash ($ S $\backslash )$ into words. Your algorithm should be a pure, integer$-$valued function of the form:

COUntSplit $\backslash (($S$[1,\backslash$ldots$,$ n$],$ i$)\backslash )$ :

$//$ your code here