9. [10] Let h be the height of a quicksort recursion tree on an array of size n that is obtained as follows: (a) For the first h/2 levels, the pivot always partitions the array into a left subarray of one-third the size and a right subarray of two-thirds the size. (b) And for the next h/2 levels, the pivot always partitions the array into a left subarray of one-fourth the size and a right subarray of three-fourths the size. At the end of this process, the rightmost path in the recursion tree results in an array of size exactly 1. Derive an equation that expresses the height h of the quicksort recursion tree as a function of n. Show all steps to receive full credit, including drawing the recursion tree if it helps with your analysis. 9. [10] Let h be the height of a quicksort recursion tree on an array of size n that is obtained as follows: (a) For the first h/2 levels, the pivot always partitions the array into a left subarray of one-third the size and a right subarray of two-thirds the size. (b) And for the next h/2 levels, the pivot always partitions the array into a left subarray of one-fourth the size and a right subarray of three-fourths the size. At the end of this process, the rightmost path in the recursion tree results in an array of size exactly 1. Derive an equation that expresses the height h of the quicksort recursion tree as a function of n. Show all steps to receive full credit, including drawing the recursion tree if it helps with your analysis