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Smallest Range Covering Elements

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to find the smallest range that includes at least one number from each of the k lists. You have k lists of sorted integers in non-decreasing order. Find the smallest range [a, b] such that a <= b and for each list, there is at least one number x such that a <= x <= b.

Example 1
    
  
  • Input: nums = [[4,10,15,24,26],[0,9,12,20],[5,18,22,30]]
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  • Output: [20,24]
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  • Explanation: 
    • We need to pick one element from each list: [4,10,15,24,26], [0,9,12,20], [5,18,22,30]. 
    • One possible combination is 20 (from list 2), 22 (from list 3), and 24 (from list 1). 
    • The range [20,24] covers all three elements and has length 4, which is the smallest possible.
    •
Example 2
    
  
  • Input: nums = [[1,2,3],[1,2,3],[1,2,3]]
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  • Output: [1,1]
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  • Explanation: 
    • We can pick 1 from each list. 
    • The range [1,1] covers all elements and has length 0. 
    • This is the smallest possible range.
    •
Constraints
    
  
  • nums.length == k
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  • 1 <= k <= 3500
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  • 1 <= nums[i].length <= 50
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  • -10^5 <= nums[i][j] <= 10^5
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  • nums[i] is sorted in non-decreasing order
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  • Time Complexity: O(n * log k) where n is total number of elements
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  • Space Complexity: O(k)
    •
HeapTCS (Tata Consultancy Services)Airbnb
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Hint
Solution

Solution Hints

    
  
  • Use a min-heap to keep track of the smallest element from each list
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  • Keep track of the maximum element among current candidates
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  • Initially, add the first element from each list to the heap
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  • The current range is [min_element, max_element]
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  • Remove the minimum element and add the next element from the same list
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  • Update the range if the new range is smaller
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  • Continue until one of the lists is exhausted
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Steps to solve by this approach:

 Step 1: Create a min-heap to store elements with their values, list indices, and element indices
 Step 2: Initialize the heap with the first element from each of the k lists
 Step 3: Keep track of the maximum value among all current elements in the heap
 Step 4: The current range is [min_heap_top, max_value] - update the smallest range if this is better
 Step 5: Remove the minimum element from heap and add the next element from the same list (if available)
 Step 6: Update the maximum value if the newly added element is larger
 Step 7: Continue until we can't maintain elements from all k lists, then return the smallest range found

Submitted Code :