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Implement Merge Sort Algorithm

Certification: Intermediate Level Accuracy: 100% Submissions: 1 Points: 15

Write a Python program that implements the Merge Sort algorithm to sort a list of integers in ascending order. Merge Sort is a divide-and-conquer algorithm that divides the input array into two halves, recursively sorts them, and then merges the sorted halves.

Example 1
    
  
  • Input: [38, 27, 43, 3, 9, 82, 10]
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  • Output: [3, 9, 10, 27, 38, 43, 82]
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  • Explanation: 
    
      
      
    • Step 1: Take the input array [38, 27, 43, 3, 9, 82, 10].
      • 
      
    • Step 2: Divide the array into two halves: [38, 27, 43, 3] and [9, 82, 10].
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    • Step 3: Further divide and recursively sort each half.
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    • Step 4: Merge the sorted halves back together, comparing elements.
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    • Step 5: Continue merging until the entire array is sorted.
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    • Step 6: Return the sorted array [3, 9, 10, 27, 38, 43, 82].
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Example 2
    
  
  • Input: [5, 2, 4, 7, 1, 3, 2, 6]
    • 
  
  • Output: [1, 2, 2, 3, 4, 5, 6, 7]
    • 
  
  • Explanation: 
    
      
      
    • Step 1: Take the input array [5, 2, 4, 7, 1, 3, 2, 6].
      • 
      
    • Step 2: Divide the array into two halves: [5, 2, 4, 7] and [1, 3, 2, 6].
      • 
      
    • Step 3: Further divide and recursively sort each half.
      • 
      
    • Step 4: Merge the sorted halves back together, comparing elements.
      • 
      
    • Step 5: Continue merging until the entire array is sorted.
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    • Step 6: Return the sorted array [1, 2, 2, 3, 4, 5, 6, 7].
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Constraints
    
  
  • 1 ≤ len(arr) ≤ 10^5
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  • -10^6 ≤ arr[i] ≤ 10^6
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  • Time Complexity: O(n log n), where n is the length of the array
    • 
  
  • Space Complexity: O(n)
    •
ArraysNumberRecursionEYAdobe
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Hint
Solution

Solution Hints

    
  
  • Divide the array into two halves recursively until each subarray has only one element
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  • Merge the subarrays by comparing elements from both subarrays
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  • Use a temporary array to store the merged results
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  • Implement a merge function to combine two sorted subarrays
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  • The base case of the recursion is when the subarray has one or zero elements
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  • The merge function should compare elements from both subarrays and place them in sorted order
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  • The recursion depth is log(n), where n is the length of the array
    •

Steps to solve by this approach:

 Step 1: Create a copy of the input array to avoid modifying the original.
 Step 2: Define the base case: if array has 0 or 1 element, it's already sorted.
 Step 3: Divide the array into two halves at the midpoint.
 Step 4: Recursively sort the left half and right half.
 Step 5: Define a merge function to combine two sorted subarrays.
 Step 6: Merge the sorted halves by comparing elements and adding them in order.
 Step 7: Return the final merged and sorted array.

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