Question

consider an array that contains a permutation of the integers . assume we use the merge-sort algorithm to sort this array. consider the recursion tree of this algorithm; the initial call is at level . let be the integer such that, once level of the recursion tree is completed, the array contains the input elements in the following order: . what is the value of ?

Answer 1

The merge-sort algorithm involves recursively dividing an array into halves and sorting each half. Level k of the recursion tree divides the array into 2^k blocks. However, without the specific ordering provided, the value of k cannot be determined.

Step-by-step explanation:

The question pertains to the application of the merge-sort algorithm to an array containing a permutation of integers. Merge-sort is a divide-and-conquer algorithm that divides the input array into two halves, recursively sorts the two halves, and then merges the sorted halves to produce the sorted array. At each level of the recursion tree, the array is divided in half, so the progression of levels represents increasingly smaller subsets of the array being sorted and merged.

At level k of the recursion tree, the array is divided into 2^k blocks (or segments), each sub-array being sorted within itself. When level k is completed, each of these blocks is a sorted sequence of the integers. The question asks for the value of k that results in a specific ordering once level k is completed. Unfortunately, since the specific ordering is not specified in the given question due to a potential typo or missing information, an exact value of k cannot be provided without additional details.