With the Binary Search algorithm, the algorithm can be developed by the loop-based form as well as a recursive form. Which of the following is not true? O If the item is not found, the loop version returns when the range bounds reach, but the recursive version finishes when the recursive depth is more than half the initial search range. O The search range starts with the whole array, and only the recursive version can work on a subrange passed through arguments. O Both forms of the program divide the search range repeatedly in half. O If the item is found, the loop version returns from the entire method, whereas the recursive version returns from one level of recursion.

Quicksort SPLIT (the 2-pointer algorithm covered in class) is applied to the integer array [4,3,5,7,9,2,1], using the first entry as the pivot. Show the series of item swaps that are performed in the split process, and the array after each of these swaps, up to and including the step of placing the pivot at its correct location. You only need to show the split of the original array, you are not required to continue working on the subarrays after the split.

Write a recursive function to determine if an array of integers contains any even numbers: bool hasEvens(int nums[], int size)

Design and implement an algorithm using recursion and backtracking to sort an array of integers into ascending order. Consider the given array as input and produce a sorted array as output. Each time you take an integer from the input array, place it at the end of the output array. If the result is unsorted, backtrack.

The recursive algorithm below takes as input an array A of distinct integers, indexed between s andf, and an integer k. The algorithm returns the index of the integer k in the array A, or ?1 if the integerk is not contained within A. Complete the missing portion of the algorithm in such a way that you makethree recursive calls to subarrays of approximately one third the size of A.• Write and justify a recurrence for the runtime T(n) of the above algorithm.• Use the recursion tree to show that the algorithm runs in time O(n).FindK(A,s,f,k)if s < fif f = s + 1if k = A[s] return sif k = A[f] return felseq1 = b(2s + f)=3cq2 = b(q1 + 1 + f)=2c... to be continued.else... to be continued.

Can u answer this please

Using recursion and java, please make a sierpenski carpet Please also comment the code just like the image below. Do not make it fill of hastags

1. Given, nCr= n! (n-r)!r!" Write a function to compute nCr without recursion.

Try to do it asap