Question

Consider an array that contains a permutation of the integers 1, 2,.....,8. assume we use the merge-sort algorithm to sort this array. consider the recursion tree of this algorithm; the initial call is at level 0. let ℓ be the integer such that, once level ℓ of the recursion tree is completed, the array contains the input elements in the following order: 2,4,5,7,1,8,3,6. what is the value of ℓ?

a. 0
b. 1
c. 2
d. 3
e. 4
f. No valid answer

Answer 1

The value of ℓ is 2.

Step-by-step explanation:

The question is asking for the value of ℓ, which represents the level of the recursion tree at which the array contains the elements in the order: 2, 4, 5, 7, 1, 8, 3, 6. To find ℓ, we need to understand how the merge-sort algorithm works and how the recursion tree is built.

In the merge-sort algorithm, the array is repeatedly divided into halves until each half contains only one element. Then, the smaller arrays are merged back together in a sorted manner. Each division and merging process represents a level in the recursion tree.

By analyzing the given order of the elements, we can determine that after level 2 of the recursion tree, the array contains the desired order. Therefore, the value of ℓ is c. 2.