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Merge K Sorted Arrays into One Sorted Array

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 12

Write a C# program to implement the MergeKSortedArrays function, which merges k sorted arrays into one sorted array. The function should take a jagged array (array of arrays) as input and return a single sorted array containing all elements from the input arrays.

Example 1
    
  
  • Input: arrays = [[1,4,5],[1,3,4],[2,6]]
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  • Output: [1,1,2,3,4,4,5,6]
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  • Explanation: 
      
      
    • The input contains 3 sorted arrays:
      • 
      
    • [1,4,5], [1,3,4], and [2,6]
      • 
      
    • When merged, they form [1,1,2,3,4,4,5,6]
      • 
    
    •
Example 2
    
  
  • Input: arrays = [[10,15,30],[12],[5,8,20,25]]
    • 
  
  • Output: [5,8,10,12,15,20,25,30]
    • 
  
  • Explanation: 
      
      
    • The input contains 3 sorted arrays:
      • 
      
    • [10,15,30], [12], and [5,8,20,25]
      • 
      
    • When merged, they form [5,8,10,12,15,20,25,30]
      • 
    
    •
Constraints
    
  
  • 1 ≤ k ≤ 10^4 (where k is the number of arrays)
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  • 0 ≤ arrays[i].length ≤ 500
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  • -10^4 ≤ arrays[i][j] ≤ 10^4
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  • Each arrays[i] is sorted in ascending order
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  • Time Complexity: O(n log k) where n is the total number of elements across all arrays
    • 
  
  • Space Complexity: O(n)
    •
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Hint
Solution

Solution Hints

    
  
  • Consider using a min-heap (priority queue) to efficiently merge the arrays
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  • Keep track of which array each element came from
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  • Maintain pointers to the current position in each array
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  • Extract the minimum element from the heap, then add the next element from the same array
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  • Use C#'s built-in PriorityQueue class or implement your own
    •

Steps to solve by this approach:

 Step 1: Create a priority queue (min-heap) to keep track of the smallest elements
 Step 2: Initialize the heap with the first element from each array along with information about which array it came from
 Step 3: Extract the minimum element from the heap and add it to the result array
 Step 4: After extracting an element, add the next element from the same array to the heap
 Step 5: Repeat steps 3 and 4 until the heap is empty
 Step 6: Return the result array containing all elements in sorted order
 Step 7: Time complexity is O(n log k) where n is the total number of elements and k is the number of arrays

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