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Find closest smaller value for every element in array

  • Last Updated : 25 May, 2021

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.

C++




// C++ program to find closest smaller value for
// every array element
#include <bits/stdc++.h>
using namespace std;
 
void closestSmaller(int arr[], int n)
{
    // Insert all array elements into a TreeSet
    set<int> ts;
    for (int i = 0; i < n; i++)
        ts.insert(arr[i]);
 
    // Find largest smaller element for every
    // array element
    for (int i = 0; i < n; i++)
    {
        auto smaller = ts.lower_bound(arr[i]);
        if (smaller == ts.begin())
            cout << -1 << " ";
        else
            cout << *(--smaller) << " ";
    }
}
 
// Driver Code
int main()
{
    int arr[] = {10, 5, 11, 6, 20, 12};
    int n = sizeof(arr) / sizeof(arr[0]);
 
    closestSmaller(arr, n);
 
    return 0;
}
 
// This code is contributed by
// sanjeev2552

Java




// 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);
    }
}

Python3




# Python3 program to find closest smaller value
# for every array element
import bisect
 
def closestSmaller(arr, n):
     
    # Insert all array elements into a TreeSet
    ts = set()
     
    for i in range(n):
        ts.add(arr[i])
 
    # Find largest smaller element for every
    # array element
    for i in range(n):
        smaller = bisect.bisect_left(list(ts), arr[i])
         
        if (smaller == 0):
            print(-1, end = " ")
        else:
            print((list(ts)[smaller - 1]), end = " ")
            smaller -= 1
 
# Driver Code
arr = [ 10, 5, 11, 6, 20, 12 ]
n = len(arr)
 
closestSmaller(arr, n)
 
# This code is contributed by rohitsingh07052
Output: 
6 -1 10 5 12 11

 

Time Complexity : O(n Log n)
 

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