Please help (DON'T COPY FROM CHEGG) **2. Enhanced Partition Algorithm**The `PARTITION(A, l, r)` function is designed to select a pivot element, `p`, and return an index, `i`, where elements `A[l..i] ≤ p` and elements `A[i + 1..j] > p`. Generally, when all values in array `A` are unique, this function results in three distinct partitions. However, when `A` contains many duplicate values, the left partition might become excessively large due to many elements equaling `p`.To address this, the task is to develop a modified version of the `PARTITION` pseudocode. This version will divide the array into three separate partitions:1. Elements in `A[l..q] < p`2. Elements in `A[q + 1..t] = p`3. Elements in `A[t + 1..r] > p`The function should return **two values**: `q` and `t`. (Note: Although Java cannot return two values from a function, this pseudocode assumes flexibility similar to Python or allows you to make necessary adjustments).**Example Execution:**- Before partitioning, the array is structured as: `[3, 5, 1, 3, 5, 1, 3]`- The pivot is selected as one of the `3`s.- After applying the enhanced partition algorithm, the array is rearranged into: `[1, 1, 1, 3, 3, 5, 5]` - Indices `q` highlight where elements are less than the pivot: `[1, 1, 1]` - Index `t` shows where elements are equal to the pivot: `[3, 3]` - The elements greater than the pivot are `[5, 5]`**Instruction:**- Implement your pseudocode on scrap paper to ensure it functions correctly.- Submit only the pseudocode.

Answered: 2. The PARTITION (A, 1, r) function…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

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Please help (DON'T COPY FROM CHEGG)

**2. Enhanced Partition Algorithm**

The `PARTITION(A, l, r)` function is designed to select a pivot element, `p`, and return an index, `i`, where elements `A[l..i] ≤ p` and elements `A[i + 1..j] > p`. Generally, when all values in array `A` are unique, this function results in three distinct partitions. However, when `A` contains many duplicate values, the left partition might become excessively large due to many elements equaling `p`.

To address this, the task is to develop a modified version of the `PARTITION` pseudocode. This version will divide the array into three separate partitions:

1. Elements in `A[l..q] < p`
2. Elements in `A[q + 1..t] = p`
3. Elements in `A[t + 1..r] > p`

The function should return **two values**: `q` and `t`. (Note: Although Java cannot return two values from a function, this pseudocode assumes flexibility similar to Python or allows you to make necessary adjustments).

**Example Execution:**

- Before partitioning, the array is structured as:
`[3, 5, 1, 3, 5, 1, 3]`

- The pivot is selected as one of the `3`s.

- After applying the enhanced partition algorithm, the array is rearranged into:
`[1, 1, 1, 3, 3, 5, 5]`

- Indices `q` highlight where elements are less than the pivot: `[1, 1, 1]`
- Index `t` shows where elements are equal to the pivot: `[3, 3]`
- The elements greater than the pivot are `[5, 5]`

**Instruction:**

- Implement your pseudocode on scrap paper to ensure it functions correctly.
- Submit only the pseudocode.

Expert Solution

Step 1

Quick sort

A divide-and-conquer algorithm is quicksort. It operates by choosing one element from the array to serve as the "pivot," and then dividing the remaining components into two sub-arrays based on whether they are less than or greater than the pivot. It is referred to as partition-exchange sort for this reason.