Find closest smaller value for every element in array

Given an array of integers, find the closest smaller element for every element. If there is no smaller element then print -1

Examples:

Input : arr[] = {10, 5, 11, 6, 20, 12}
Output : 6, -1, 10, 5, 12, 11

Input : arr[] = {10, 5, 11, 10, 20, 12}
Output : 5 -1 10 5 12 11

A simple solution is to run two nested loops. We pick an outer element one by one. For every picked element, we traverse remaining array and find closest smaller element. Time complexity of this solution is O(n*n)

A better solution is to use sorting. We sort all elements, then for every element, traverse toward left until we find a smaller element (Note that there can be multiple occurrences of an element).

An efficient solution is to use Self Balancing BST (Implemented as set in C++ and TreeSet in Java). In a Self Balancing BST, we can do both insert and closest smaller operations in O(Log n) time.

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// Java program to find closest smaller value for
// every array element
import java.util.*;
  
class TreeSetDemo {
    public static void closestSmaller(int[] arr)
    {
        // Insert all array elements into a TreeSet
        TreeSet<Integer> ts = new TreeSet<Integer>();
        for (int i = 0; i < arr.length; i++)
            ts.add(arr[i]);
  
        // Find largest smaller element for every
        // array element
        for (int i = 0; i < arr.length; i++) {
            Integer smaller = ts.lower(arr[i]);
            if (smaller == null)
                System.out.print(-1 + " ");
            else
                System.out.print(smaller + " ");
        }
    }
  
    public static void main(String[] args)
    {
        int[] arr = { 10, 5, 11, 6, 20, 12 };
        closestSmaller(arr);
    }
}

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Output:


6 -1 10 5 12 11





Time Complexity : O(n Log n)



          
          
          
          

            

    

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