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Count of Smaller Numbers After Self

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

Write a C# program to implement the CountSmaller(int[] nums) function, which counts for each element in the array how many elements to its right are smaller than it.

Example 1
    

  • Input: nums = [5, 2, 6, 1]
    • 

  • Output: [2, 1, 1, 0]
    • 

  • Explanation:

      

    • Step 1: Process each element from right to left.
      • 

    • Step 2: For each element, count how many smaller elements exist to its right:

        

      • For 5, there are 2 smaller elements to its right (2 and 1)
        • 

      • For 2, there is 1 smaller element to its right (1)
        • 

      • For 6, there is 1 smaller element to its right (1)
        • 

      • For 1, there are 0 smaller elements to its right
        • 

      

      • 

    • Step 3: Store these counts in an array.
      • 

    • Step 4: Return the resulting array [2, 1, 1, 0].
      • 

    •
Example 2
    

  • Input: nums = [2, 0, 1, 0]
    • 

  • Output: [2, 0, 1, 0]
    • 

  • Explanation:

      

    • Step 1: Process each element from right to left.
      • 

    • Step 2: For each element, count how many smaller elements exist to its right:

        

      • For 2, there are 2 smaller elements to its right (0 and 0)
        • 

      • For 0, there are 0 smaller elements to its right (1 is larger)
        • 

      • For 1, there is 1 smaller element to its right (0)
        • 

      • For 0, there are 0 smaller elements to its right
        • 

      

      • 

    • Step 3: Store these counts in an array.
      • 

    • Step 4: Return the resulting array [2, 0, 1, 0].
      • 

    •
Constraints
    

  • 1 ≤ nums.length ≤ 10^5
    • 

  • -10^4 ≤ nums[i] ≤ 10^4
    • 

  • Time Complexity: O(n log n) where n is the length of the input array
    • 

  • Space Complexity: O(n) for storing the result and auxiliary data structures
    •
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Hint
Solution

Solution Hints

    
  
  • Consider using a Binary Search Tree (BST) to keep track of elements
    • 
  
  • Merge sort with counting inversions can be adapted for this problem
    • 
  
  • Binary Indexed Tree (BIT) or Segment Tree can efficiently solve this problem
    • 
  
  • Process the array from right to left for optimal results
    •

Steps to solve by this approach:

 Step 1: Create a modified merge sort algorithm that keeps track of indexes.
 Step 2: Initialize an array to store the count of smaller elements for each number.
 Step 3: Process the array using merge sort, maintaining the original indices.
 Step 4: During the merge operation, when we take an element from the left subarray, increment its count by the number of elements already taken from the right subarray.
 Step 5: Return the array of counts matching the original order of the input array.

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