Math Problem Statement

numbers:

68

99

33

43

45

MergeSort(numbers, 0, 4) is called. Merge() is called to merge the following partitions:

Merge call #Left partition Right partition

1

(a)

(b)

2

68, 99

33

3

43

45

4

(c)

(d)

Fill in the missing values.

(a)

(b)

(c)

(d)

(commas between values, if applicable)

Solution

The MergeSort algorithm works by recursively dividing the list into smaller sublists (partitions) and then merging them back in a sorted order. Based on the details provided, let's analyze and fill in the missing values:

Steps and Partitions:

  1. Merge call #1:

    • Left partition (a): 68
    • Right partition (b): 99
  2. Merge call #2:

    • Left partition: 68, 99 (result from merging 68 and 99)
    • Right partition: 33
  3. Merge call #3:

    • Left partition (c): 43
    • Right partition (d): 45
  4. Final Merge:

    • Left partition: 33, 68, 99 (result of merging from call #2)
    • Right partition: 43, 45 (result of merging from call #3)

Missing Values:

  1. (a) = 68
  2. (b) = 99
  3. (c) = 43
  4. (d) = 45

Would you like me to go into more detail about how the merging process works or clarify anything?

Questions:

  1. Can you explain how MergeSort divides the list recursively?
  2. How is the merge operation different from the divide operation?
  3. Why does MergeSort have a time complexity of O(n log n)?
  4. How does MergeSort compare to other sorting algorithms, such as QuickSort?
  5. Could this same method work on linked lists instead of arrays?

Tip:

MergeSort is a stable sorting algorithm, meaning it preserves the relative order of equal elements. This is useful for applications where stability matters.

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Math Problem Analysis

Mathematical Concepts

Sorting Algorithms
MergeSort
Recursion

Formulas

Divide-and-conquer methodology

Theorems

Time complexity of MergeSort: O(n log n)

Suitable Grade Level

Grades 10-12