Merge Sort

Write a C++ program that implements the merge sort algorithm. The program should take an unsorted array of integers and sort it in ascending order using the divide-and-conquer approach.

Example 1

Input: array = [38, 27, 43, 3, 9, 82, 10]
Output: [3, 9, 10, 27, 38, 43, 82]
Explanation: 
  

    
Step 1: Divide the array into two halves
      

        
Left half: [38, 27, 43, 3]
        
Right half: [9, 82, 10]
      
    
    
Step 2: Recursively divide the left half
      

        
Left: [38, 27]
        
Right: [43, 3]
      
    
    
Step 3: Recursively divide until single elements
    
Step 4: Merge back in sorted order
      

        
Merge [38] and [27] → [27, 38]
        
Merge [43] and [3] → [3, 43]
        
Merge [27, 38] and [3, 43] → [3, 27, 38, 43]
      
    
    
Step 5: Similarly sort right half [9, 82, 10] → [9, 10, 82]
    
Step 6: Merge [3, 27, 38, 43] and [9, 10, 82] → [3, 9, 10, 27, 38, 43, 82]
    
Step 7: Return sorted array [3, 9, 10, 27, 38, 43, 82]
  

Example 2

Input: array = [8, 4, 2, 1]
Output: [1, 2, 4, 8]
Explanation: 
  

    
Step 1: Divide the array into two halves
      

        
Left half: [8, 4]
        
Right half: [2, 1]
      
    
    
Step 2: Recursively divide until single elements
    
Step 3: Merge back in sorted order
      

        
Merge [8] and [4] → [4, 8]
        
Merge [2] and [1] → [1, 2]
      
    
    
Step 4: Merge [4, 8] and [1, 2] → [1, 2, 4, 8]
    
Step 5: Return sorted array [1, 2, 4, 8]
  

Constraints

1 ≤ array.length ≤ 10^5
-10^6 ≤ array[i] ≤ 10^6
Time Complexity: O(n log n), where n is the length of the array
Space Complexity: O(n)