Merge Sort as Divide and Conquer in DSA Java - Build from Scratch

Merge Sort as Divide and Conquer

📖 Scenario: You are working on a program that sorts a list of numbers to help organize data efficiently. Sorting is like arranging books on a shelf in order, so you can find them quickly.

🎯 Goal: Build a Java program that uses the merge sort technique to sort an array of integers. Merge sort works by dividing the list into smaller parts, sorting those parts, and then combining them back together in order.

📋 What You'll Learn

Create an integer array called numbers with the exact values: 38, 27, 43, 3, 9, 82, 10

Create a helper variable n to store the length of the numbers array

Write a mergeSort method that divides the array into halves and sorts them recursively

Write a merge method that combines two sorted halves into one sorted array

Print the sorted array after applying merge sort

💡 Why This Matters

🌍 Real World

Sorting is used in many real-life applications like organizing contacts, searching data quickly, and managing inventories.

💼 Career

Understanding merge sort helps in software development roles where efficient data processing and algorithm optimization are important.

1

Create the initial array

Create an integer array called numbers with these exact values: 38, 27, 43, 3, 9, 82, 10

DSA Java

# Your code here

Hint

Use int[] numbers = {38, 27, 43, 3, 9, 82, 10}; inside the main method.

2

Add array length variable

Create an integer variable called n and set it to the length of the numbers array

DSA Java

public class MergeSort {
    public static void main(String[] args) {
        int[] numbers = {38, 27, 43, 3, 9, 82, 10};
        // Your code here
    }
}

Hint

Use int n = numbers.length; to get the size of the array.

3

Write mergeSort and merge methods

Write a mergeSort method that takes the array arr, a left index, and a right index, and recursively sorts the array by dividing it into halves. Also write a merge method that merges two sorted halves of the array. Use these exact method signatures: public static void mergeSort(int[] arr, int left, int right) and public static void merge(int[] arr, int left, int mid, int right). Call mergeSort(numbers, 0, n - 1) inside main after defining n.

DSA Java

public class MergeSort {
    public static void main(String[] args) {
        int[] numbers = {38, 27, 43, 3, 9, 82, 10};
        int n = numbers.length;
        // Your code here
    }

    // Define mergeSort method here

    // Define merge method here
}

Hint

Use recursion in mergeSort to divide the array and call merge to combine sorted parts.

4

Print the sorted array

Add a for loop to print each element of the numbers array separated by spaces after sorting is complete.

DSA Java

public class MergeSort {
    public static void main(String[] args) {
        int[] numbers = {38, 27, 43, 3, 9, 82, 10};
        int n = numbers.length;
        mergeSort(numbers, 0, n - 1);
        // Your code here
    }

    public static void mergeSort(int[] arr, int left, int right) {
        if (left < right) {
            int mid = left + (right - left) / 2;
            mergeSort(arr, left, mid);
            mergeSort(arr, mid + 1, right);
            merge(arr, left, mid, right);
        }
    }

    public static void merge(int[] arr, int left, int mid, int right) {
        int n1 = mid - left + 1;
        int n2 = right - mid;

        int[] leftArr = new int[n1];
        int[] rightArr = new int[n2];

        for (int i = 0; i < n1; i++)
            leftArr[i] = arr[left + i];
        for (int j = 0; j < n2; j++)
            rightArr[j] = arr[mid + 1 + j];

        int i = 0, j = 0;
        int k = left;

        while (i < n1 && j < n2) {
            if (leftArr[i] <= rightArr[j]) {
                arr[k] = leftArr[i];
                i++;
            } else {
                arr[k] = rightArr[j];
                j++;
            }
            k++;
        }

        while (i < n1) {
            arr[k] = leftArr[i];
            i++;
            k++;
        }

        while (j < n2) {
            arr[k] = rightArr[j];
            j++;
            k++;
        }
    }
}

Hint

Use a for loop to print each element of numbers separated by spaces.

Practice

1. What is the main idea behind the Merge Sort algorithm in the context of divide and conquer?

easy

A. Select a pivot and partition the array around it

B. Sort the array by repeatedly swapping adjacent elements

C. Divide the array into halves, sort each half, then merge them

D. Build a heap and extract elements in sorted order

Solution

1. Step 1: Understand divide and conquer in Merge Sort

   Merge Sort splits the array into two halves recursively until single elements remain.

2. Step 2: Merge sorted halves

   It then merges these sorted halves back together to form a sorted array.

3. Final Answer:

   Divide the array into halves, sort each half, then merge them -> Option C

4. Quick Check:

   Divide and conquer = split, sort, merge [OK]

Hint: Remember: split, sort halves, then merge [OK]

Common Mistakes:

• Confusing Merge Sort with Bubble Sort
• Thinking Merge Sort uses pivot like Quick Sort
• Ignoring the merge step after dividing

2. Which of the following is the correct way to declare the merge function header in Java for merging two sorted subarrays in Merge Sort?

easy

A. int merge(int arr[], int start, int end)

B. void merge(int[] arr, int left, int mid, int right)

C. void merge(int arr[], int low, int high)

D. int merge(int[] arr, int left, int right)

Solution

1. Step 1: Identify parameters needed for merging

   The merge function needs the array and indices: left, mid, right to merge two halves.

2. Step 2: Check method signature correctness

   It returns void and takes int[] arr, int left, int mid, int right as parameters.

3. Final Answer:

   void merge(int[] arr, int left, int mid, int right) -> Option B

4. Quick Check:

   Correct merge signature = void merge(arr, left, mid, right) [OK]

Hint: Merge needs array and three indices: left, mid, right [OK]

Common Mistakes:

• Using wrong parameter names or missing mid index
• Returning int instead of void
• Confusing start/end with left/right without mid

3. What will be the output of the following Java code snippet using Merge Sort on the array [4, 1, 3, 9, 7]?

int[] arr = {4, 1, 3, 9, 7};
mergeSort(arr, 0, arr.length - 1);
System.out.println(Arrays.toString(arr));

medium

A. [1, 4, 3, 7, 9]

B. [4, 1, 3, 7, 9]

C. [9, 7, 4, 3, 1]

D. [1, 3, 4, 7, 9]

Solution

1. Step 1: Apply Merge Sort to the array

   Merge Sort divides and merges to sort: [4,1,3,9,7] -> [1,3,4,7,9]

2. Step 2: Verify final sorted array

   The sorted array is ascending: [1, 3, 4, 7, 9]

3. Final Answer:

   [1, 3, 4, 7, 9] -> Option D

4. Quick Check:

   Sorted array = ascending order [OK]

Hint: Merge Sort always outputs sorted ascending array [OK]

Common Mistakes:

• Confusing merge step output with partial arrays
• Assuming original order remains
• Mixing up ascending and descending order

4. Identify the error in this Merge Sort merge function snippet:

void merge(int[] arr, int left, int mid, int right) {
  int n1 = mid - left;
  int n2 = right - mid;
  int[] L = new int[n1];
  int[] R = new int[n2];
  for (int i = 0; i < n1; i++) L[i] = arr[left + i];
  for (int j = 0; j < n2; j++) R[j] = arr[mid + 1 + j];
  // merging logic follows...
}

medium

A. Incorrect calculation of n1 size

B. Wrong copying of elements into R array

C. Missing return statement in void method

D. Using < instead of <= in for loops

Solution

1. Step 1: Check size calculations for subarrays

   n1 should be mid - left + 1 and n2 should be right - mid to cover all elements.

2. Step 2: Identify impact of wrong sizes

   Incorrect sizes cause array index errors or missing elements during merge.

3. Final Answer:

   Incorrect calculation of n1 size -> Option A

4. Quick Check:

   Sizes must include mid element [OK]

Hint: Remember: n1 = mid-left+1, n2 = right-mid [OK]

Common Mistakes:

• Forgetting +1 in n1 size calculation
• Copying elements starting at wrong index
• Confusing loop bounds with <= instead of <

5. Given an array with many duplicate values, how should the merge step in Merge Sort be adapted to maintain stability (preserve original order of equal elements)?

hard

A. When elements are equal, copy from the left subarray first

B. When elements are equal, copy from the right subarray first

C. Skip duplicates during merge to reduce array size

D. Sort duplicates separately after merge

Solution

1. Step 1: Understand stability in sorting

   Stable sort keeps equal elements in original order.

2. Step 2: Apply stability rule in merge step

   When equal, copy element from left subarray first to preserve order.

3. Final Answer:

   When elements are equal, copy from the left subarray first -> Option A

4. Quick Check:

   Left first on equals = stable merge [OK]

Hint: Copy left element first on equal values to keep stability [OK]

Common Mistakes:

• Copying right element first breaks stability
• Removing duplicates during merge
• Sorting duplicates separately after merge