Which of the following are necessary parts of all recursive methods? A tail call. Tail-call optimization. Backtracking. One or more base cases. One or more recursive calls.

Recursive solutions can often be solved with non-recursive loop based implementations. Explain how a developer would decide which solution (recursive vs. non-recursive) he/she would implement in final production code.

For each of the following recursive methods, identify the base case, the general case, and the constraints on the argument values, and explain what the method does. (images below)

How is the repeated calling of a recursion function controlled? What kind of command and control structure is being utilized in this instance?

Do the trace in detail and submit  The source Code As Well From the following recursive method Trace (in details) the calling of the above method with any input from your choice such that thereturned value will be 19. public static int think(int x) {if(x<10)if(x%2!=0)return x;elsereturn 0;elseif(x%2!=0)return x%10 + think(x/10);elsereturn think(x/10);}

in kotlin Write two versions of a recursive palindrome check function.  One version should have a block body, and the other should have an expression body.  Review the lecture slide about the substring function first.  Use this algorithm: if the length of the string is less than 2, return true else if the first and last characters are not equal (!=) return false else return the result of a recursive call with the substring from the second character (the one at index 1) to the second to last character. Use a main that uses a loop to test the palindrome function using this list of strings:     val ss = listOf("", "A", "AA", "AB", "AAA", "ABA", "ABB", "AAAA", "AABA", "ABBA", "ABCBA", "ABCAB")

Write a recursive algorithm with the following prototype: int add (int x, int y); that returns x if y is 0; and adds x to y otherwise. THE FUNCTION MUST BE RECURSIVE. (hint: the base case should involve a test for y being 0; recursive case should reduce y towards 0)

Why would you use recursion instead of a loop? Is there anything that can be done using recursion that can't be done with a loop?

Attached is a programming question and its Java solution. My question regarding the recursion part:      1. "arr.add(j)" but then "arr.remove(arr.size() - 1)" follows soon after, and I think nothing should be printed. How does the program still print out permutations? Is it because the recursive method call only recurse all instructions from the start of the recursion method to that line? Otherwise, say the input is "5", how does "5=1+1+1+1+1" get printed?      2. Does the recursion stop when "j<=n" evaluates false because of "for(int j = i; j <= n; j++)"? Otherwise, which line of code tells the recursion to stop?