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Find the nearest smaller numbers on left side in an array
  • Difficulty Level : Medium
  • Last Updated : 13 Apr, 2021

Given an array of integers, find the nearest smaller number for every element such that the smaller element is on left side.

Examples: 

Input:  arr[] = {1, 6, 4, 10, 2, 5}
Output:         {_, 1, 1,  4, 1, 2}
First element ('1') has no element on left side. For 6, 
there is only one smaller element on left side '1'. 
For 10, there are three smaller elements on left side (1,
6 and 4), nearest among the three elements is 4.

Input: arr[] = {1, 3, 0, 2, 5}
Output:        {_, 1, _, 0, 2}

Expected time complexity is O(n). 

A Simple Solution is to use two nested loops. The outer loop starts from second element, the inner loop goes to all elements on left side of the element picked by outer loop and stops as soon as it finds a smaller element.  

C++




// C++ implementation of simple algorithm to find
// smaller element on left side
#include <iostream>
using namespace std;
 
// Prints smaller elements on left side of every element
void printPrevSmaller(int arr[], int n)
{
    // Always print empty or '_' for first element
    cout << "_, ";
 
    // Start from second element
    for (int i=1; i<n; i++)
    {
        // look for smaller element on left of 'i'
        int j;
        for (j=i-1; j>=0; j--)
        {
            if (arr[j] < arr[i])
            {
                cout << arr[j] << ", ";
                break;
            }
        }
 
        // If there is no smaller element on left of 'i'
        if (j == -1)
           cout << "_, " ;
    }
}
 
/* Driver program to test insertion sort */
int main()
{
    int arr[] = {1, 3, 0, 2, 5};
    int n = sizeof(arr)/sizeof(arr[0]);
    printPrevSmaller(arr, n);
    return 0;
}

Java




// Java implementation of simple
// algorithm to find smaller
// element on left side
import java.io.*;
class GFG {
 
// Prints smaller elements on
// left side of every element
static void printPrevSmaller(int []arr, int n)
{
     
    // Always print empty or '_'
    // for first element
    System.out.print( "_, ");
 
    // Start from second element
    for (int i = 1; i < n; i++)
    {
        // look for smaller
        // element on left of 'i'
        int j;
        for(j = i - 1; j >= 0; j--)
        {
            if (arr[j] < arr[i])
            {
                System.out.print(arr[j] + ", ");
                break;
            }
        }
 
        // If there is no smaller
        // element on left of 'i'
        if (j == -1)
        System.out.print( "_, ") ;
    }
}
 
    // Driver Code
    public static void main (String[] args)
    {
        int []arr = {1, 3, 0, 2, 5};
        int n = arr.length;
        printPrevSmaller(arr, n);
    }
}
 
// This code is contributed by anuj_67.

Python3




# Python 3 implementation of simple
# algorithm to find smaller element
# on left side
 
# Prints smaller elements on left
# side of every element
def printPrevSmaller(arr, n):
 
    # Always print empty or '_' for
    # first element
    print("_, ", end="")
 
    # Start from second element
    for i in range(1, n ):
     
        # look for smaller element
        # on left of 'i'
        for j in range(i-1 ,-2 ,-1):
         
            if (arr[j] < arr[i]):
             
                print(arr[j] ,", ",
                            end="")
                break
 
        # If there is no smaller
        # element on left of 'i'
        if (j == -1):
            print("_, ", end="")
 
# Driver program to test insertion
# sort
arr = [1, 3, 0, 2, 5]
n = len(arr)
printPrevSmaller(arr, n)
 
# This code is contributed by
# Smitha

C#




// C# implementation of simple
// algorithm to find smaller
// element on left side
using System;
 
class GFG {
 
    // Prints smaller elements on
    // left side of every element
    static void printPrevSmaller(int []arr,
                                    int n)
    {
         
        // Always print empty or '_'
        // for first element
        Console.Write( "_, ");
     
        // Start from second element
        for (int i = 1; i < n; i++)
        {
            // look for smaller
            // element on left of 'i'
            int j;
            for(j = i - 1; j >= 0; j--)
            {
                if (arr[j] < arr[i])
                {
                    Console.Write(arr[j]
                                + ", ");
                    break;
                }
            }
     
            // If there is no smaller
            // element on left of 'i'
            if (j == -1)
            Console.Write( "_, ") ;
        }
    }
 
    // Driver Code
    public static void Main ()
    {
        int []arr = {1, 3, 0, 2, 5};
        int n = arr.Length;
        printPrevSmaller(arr, n);
    }
}
 
// This code is contributed by anuj_67.

PHP




<?php
// PHP implementation of simple
// algorithm to find smaller
// element on left side
 
// Prints smaller elements on
// left side of every element
function printPrevSmaller( $arr, $n)
{
     
    // Always print empty or
    // '_' for first element
    echo "_, ";
 
    // Start from second element
    for($i = 1; $i < $n; $i++)
    {
         
        // look for smaller
        // element on left of 'i'
        $j;
        for($j = $i - 1; $j >= 0; $j--)
        {
            if ($arr[$j] < $arr[$i])
            {
                echo $arr[$j] , ", ";
                break;
            }
        }
 
        // If there is no smaller
        // element on left of 'i'
        if ($j == -1)
        echo "_, " ;
    }
}
 
    // Driver Code
    $arr = array(1, 3, 0, 2, 5);
    $n = count($arr);
    printPrevSmaller($arr, $n);
 
// This code is contributed by anuj_67.
?>

Javascript




<script>
 
 
// Javascript implementation
// of simple algorithm to find
// smaller element on left side
 
 
// Prints smaller elements on
// left side of every element
function printPrevSmaller( arr, n)
{
    // Always print empty or '_' for first element
    document.write("_, ");
 
    // Start from second element
    for (let i=1; i<n; i++)
    {
        // look for smaller element on left of 'i'
        let j;
        for (j=i-1; j>=0; j--)
        {
            if (arr[j] < arr[i])
            {
                 document.write(arr[j] + ", ");
                break;
            }
        }
 
        // If there is no smaller element on left of 'i'
        if (j == -1)
           document.write("_, ");
    }
}
 
    // Driver program
     
    let arr = [ 1, 3, 0, 2, 5 ];
    let n = arr.length;
    printPrevSmaller(arr, n);
     
</script>

Output: 



_, 1, _, 0, 2, ,

Time complexity of the above solution is O(n2).
  
There can be an Efficient Solution that works in O(n) time. The idea is to use a stack. Stack is used to maintain a subsequence of the values that have been processed so far and are smaller than any later value that has already been processed.
Below is stack based algorithm 

Let input sequence be 'arr[]' and size of array be 'n'

1) Create a new empty stack S

2) For every element 'arr[i]' in the input sequence 'arr[]',
   where 'i' goes from 0 to n-1.
    a) while S is nonempty and the top element of 
       S is greater than or equal to 'arr[i]':
           pop S
    
    b) if S is empty:
           'arr[i]' has no preceding smaller value
    c) else:
           the nearest smaller value to 'arr[i]' is 
           the top element of S

    d) push 'arr[i]' onto S

Below is the implementation of above algorithm. 

C++




// C++ implementation of efficient algorithm to find
// smaller element on left side
#include <iostream>
#include <stack>
using namespace std;
 
// Prints smaller elements on left side of every element
void printPrevSmaller(int arr[], int n)
{
    // Create an empty stack
    stack<int> S;
 
    // Traverse all array elements
    for (int i=0; i<n; i++)
    {
        // Keep removing top element from S while the top
        // element is greater than or equal to arr[i]
        while (!S.empty() && S.top() >= arr[i])
            S.pop();
 
        // If all elements in S were greater than arr[i]
        if (S.empty())
            cout << "_, ";
        else  //Else print the nearest smaller element
            cout << S.top() << ", ";
 
        // Push this element
        S.push(arr[i]);
    }
}
 
/* Driver program to test insertion sort */
int main()
{
    int arr[] = {1, 3, 0, 2, 5};
    int n = sizeof(arr)/sizeof(arr[0]);
    printPrevSmaller(arr, n);
    return 0;
}

Java




import java.util.Stack;
 
//Java implementation of efficient algorithm to find
// smaller element on left side
class GFG {
 
// Prints smaller elements on left side of every element
    static void printPrevSmaller(int arr[], int n) {
        // Create an empty stack
        Stack<Integer> S = new Stack<>();
 
        // Traverse all array elements
        for (int i = 0; i < n; i++) {
            // Keep removing top element from S while the top
            // element is greater than or equal to arr[i]
            while (!S.empty() && S.peek() >= arr[i]) {
                S.pop();
            }
 
            // If all elements in S were greater than arr[i]
            if (S.empty()) {
                System.out.print("_, ");
            } else //Else print the nearest smaller element
            {
                System.out.print(S.peek() + ", ");
            }
 
            // Push this element
            S.push(arr[i]);
        }
    }
 
    /* Driver program to test insertion sort */
    public static void main(String[] args) {
        int arr[] = {1, 3, 0, 2, 5};
        int n = arr.length;
        printPrevSmaller(arr, n);
    }
}

Python3




# Python3 implementation of efficient
# algorithm to find smaller element
# on left side
import math as mt
 
# Prints smaller elements on left
# side of every element
def printPrevSmaller(arr, n):
 
    # Create an empty stack
    S = list()
 
    # Traverse all array elements
    for i in range(n):
     
        # Keep removing top element from S
        # while the top element is greater
        # than or equal to arr[i]
        while (len(S) > 0 and S[-1] >= arr[i]):
            S.pop()
 
        # If all elements in S were greater
        # than arr[i]
        if (len(S) == 0):
            print("_, ", end = "")
        else: # Else print the nearest
              # smaller element
            print(S[-1], end = ", ")
 
        # Push this element
        S.append(arr[i])
     
# Driver Code
arr = [ 1, 3, 0, 2, 5]
n = len(arr)
printPrevSmaller(arr, n)
 
# This code is contributed by
# Mohit kumar 29

C#




// C# implementation of efficient algorithm to find
// smaller element on left side
using System;
using System.Collections.Generic;
     
public class GFG
{
 
    // Prints smaller elements on left side of every element
    static void printPrevSmaller(int []arr, int n)
    {
        // Create an empty stack
        Stack<int> S = new Stack<int>();
 
        // Traverse all array elements
        for (int i = 0; i < n; i++)
        {
            // Keep removing top element from S while the top
            // element is greater than or equal to arr[i]
            while (S.Count != 0 && S.Peek() >= arr[i])
            {
                S.Pop();
            }
 
            // If all elements in S were greater than arr[i]
            if (S.Count == 0)
            {
                Console.Write("_, ");
            }
            else //Else print the nearest smaller element
            {
                Console.Write(S.Peek() + ", ");
            }
 
            // Push this element
            S.Push(arr[i]);
        }
    }
 
    /* Driver code */
    public static void Main(String[] args)
    {
        int []arr = {1, 3, 0, 2, 5};
        int n = arr.Length;
        printPrevSmaller(arr, n);
    }
}
 
// This code is contributed by Princi Singh

Javascript




<script>
 
// Javascript implementation of efficient
// algorithm to find smaller element on left side
 
// Prints smaller elements on left
// side of every element
function printPrevSmaller(arr, n)
{
     
    // Create an empty stack
    let S = [];
 
    // Traverse all array elements
    for(let i = 0; i < n; i++)
    {
         
        // Keep removing top element from S
        // while the top element is greater
        // than or equal to arr[i]
        while ((S.length != 0) &&
             (S[S.length - 1] >= arr[i]))
        {
            S.pop();
        }
 
        // If all elements in S were
        // greater than arr[i]
        if (S.length == 0)
        {
            document.write("_, ");
        }
         
        // Else print the nearest smaller element
        else
        {
            document.write(S[S.length - 1] + ", ");
        }
 
        // Push this element
        S.push(arr[i]);
    }
}
 
// Driver code
let arr = [ 1, 3, 0, 2, 5 ];
let n = arr.length;
 
printPrevSmaller(arr, n);
 
// This code is contributed by divyeshrabadiya07
 
</script>

Output: 

_, 1, _, 0, 2,

Time complexity of above program is O(n) as every element is pushed and popped at most once to the stack. So overall constant number of operations are performed per element. 
This article is contributed by Ashish Kumar Singh. Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.
 

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