Previous greater element

Given an array of distinct elements, find previous greater element for every element. If previous greater element does not exist, print -1.

Examples:

Input : arr[] = {10, 4, 2, 20, 40, 12, 30}
Output :         -1, 10, 4, -1, -1, 40, 40

Input : arr[] = {10, 20, 30, 40}
Output :        -1, -1, -1, -1

Input : arr[] = {40, 30, 20, 10}
Output :        -1, 40, 30, 20

Expected time complexity : O(n)



A simple solution is to run two nested loops. The outer loop picks an element one by one. The inner loop, find the previous element that is greater.

C++

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// C++ program previous greater element
// A naive solution to print previous greater
// element for every element in an array.
#include <bits/stdc++.h>
using namespace std;
  
void prevGreater(int arr[], int n)
    // Previous greater for first element never
    // exists, so we print -1.
    cout << "-1, ";
  
    // Let us process remaining elements.
    for (int i = 1; i < n; i++) {
  
        // Find first element on left side
        // that is greater than arr[i].
        int j;
        for (j = i-1; j >= 0; j--) {
            if (arr[i] < arr[j]) {
            cout << arr[j] << ", ";
            break;
            }             
        }
  
        // If all elements on left are smaller.
        if (j == -1)
        cout << "-1, ";
    }
}
// Driver code
int main()
{
    int arr[] = { 10, 4, 2, 20, 40, 12, 30 };
    int n = sizeof(arr) / sizeof(arr[0]);
    prevGreater(arr, n);
    return 0;
}

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Java

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// Java program previous greater element
// A naive solution to print
// previous greater element 
// for every element in an array.
import java.io.*;
import java.util.*;
import java.lang.*;
  
class GFG
{
static void prevGreater(int arr[], 
                        int n)
    // Previous greater for 
    // first element never
    // exists, so we print -1.
    System.out.print("-1, ");
  
    // Let us process 
    // remaining elements.
    for (int i = 1; i < n; i++)
    {
  
        // Find first element on 
        // left side that is 
        // greater than arr[i].
        int j;
        for (j = i-1; j >= 0; j--) 
        {
            if (arr[i] < arr[j]) 
            {
            System.out.print(arr[j] + ", ");
            break;
            }             
        }
  
        // If all elements on 
        // left are smaller.
        if (j == -1)
        System.out.print("-1, ");
    }
}
  
// Driver Code
public static void main(String[] args)
{
    int arr[] = {10, 4, 2, 20, 40, 12, 30};
    int n = arr.length;
    prevGreater(arr, n);
}
}

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Python 3

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# Python 3 program previous greater element
# A naive solution to print previous greater
# element for every element in an array.
def prevGreater(arr, n) :
  
    # Previous greater for first element never
    # exists, so we print -1.
    print("-1",end = ", ")
  
    # Let us process remaining elements.
    for i in range(1, n) :
        flag = 0
  
        # Find first element on left side
        # that is greater than arr[i].
        for j in range(i-1, -1, -1) :
            if arr[i] < arr[j] :
                print(arr[j],end = ", ")
                flag = 1
                break
  
        # If all elements on left are smaller.
        if j == 0 and flag == 0:
            print("-1",end = ", ")
  
  
# Driver code
if __name__ == "__main__" :
    arr = [10, 4, 2, 20, 40, 12, 30]
    n = len(arr)
    prevGreater(arr, n)
  
# This code is contributed by ANKITRAI1

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C#

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// C# program previous greater element
// A naive solution to print
// previous greater element 
// for every element in an array.
  
using System; 
class GFG
{
static void prevGreater(int[] arr, 
                        int n)
    // Previous greater for 
    // first element never
    // exists, so we print -1.
    Console.Write("-1, ");
  
    // Let us process 
    // remaining elements.
    for (int i = 1; i < n; i++)
    {
  
        // Find first element on 
        // left side that is 
        // greater than arr[i].
        int j;
        for (j = i-1; j >= 0; j--) 
        {
            if (arr[i] < arr[j]) 
            {
            Console.Write(arr[j] + ", ");
            break;
            }             
        }
  
        // If all elements on 
        // left are smaller.
        if (j == -1)
        Console.Write("-1, ");
    }
}
  
// Driver Code
public static void Main()
{
    int[] arr = {10, 4, 2, 20, 40, 12, 30};
    int n = arr.Length;
    prevGreater(arr, n);
}
}

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PHP

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<?php
// php program previous greater element
// A naive solution to print previous greater
// element for every element in an array.
  
function prevGreater(&$arr,$n)
    // Previous greater for first element never
    // exists, so we print -1.
    echo( "-1, ");
  
    // Let us process remaining elements.
    for ($i = 1; $i < $n; $i++)
    {
  
        // Find first element on left side
        // that is greater than arr[i].
        for ($j = $i-1; $j >= 0; $j--) 
    {
            if ($arr[$i] < $arr[$j]) 
        {
            echo($arr[$j]); 
        echo( ", ");
            break;
            }             
        }
  
        // If all elements on left are smaller.
        if ($j == -1)
        echo("-1, ");
    }
}
  
// Driver code
$arr = array(10, 4, 2, 20, 40, 12, 30);
$n = sizeof($arr) ;
prevGreater($arr, $n);
  
//This code is contributed by Shivi_Aggarwal.
      
?>

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Output:

-1, 10, 4, -1, -1, 40, 40

An efficient solution is to use stack data structure. If we take a closer look, we can notice that this problem is a variation of stock span problem. We maintain previous greater element in a stack.

C++

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// C++ program previous greater element
// An efficient solution to print previous greater
// element for every element in an array.
#include <bits/stdc++.h>
using namespace std;
  
void prevGreater(int arr[], int n)
{
    // Create a stack and push index of first element 
    // to it
    stack<int> s;
    s.push(arr[0]);
      
    // Previous greater for first element is always -1.
    cout << "-1, ";
  
    // Traverse remaining elements
    for (int i = 1; i < n; i++) {
  
        // Pop elements from stack while stack is not empty 
        // and top of stack is smaller than arr[i]. We 
        // always have elements in decreasing order in a 
        // stack.
        while (s.empty() == false && s.top() < arr[i])
            s.pop();
  
        // If stack becomes empty, then no element is greater
        // on left side. Else top of stack is previous
        // greater.
        s.empty() ? cout << "-1, " : cout << s.top() << ", ";
  
        s.push(arr[i]);
    }
}
// Driver code
int main()
{
    int arr[] = { 10, 4, 2, 20, 40, 12, 30 };
    int n = sizeof(arr) / sizeof(arr[0]);
    prevGreater(arr, n);
    return 0;
}

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Java

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// Java program previous greater element
// An efficient solution to
// print previous greater
// element for every element 
// in an array.
import java.io.*;
import java.util.*;
import java.lang.*;
  
class GFG
{
static void prevGreater(int arr[], 
                        int n)
{
    // Create a stack and push 
    // index of first element 
    // to it
    Stack<Integer> s = new Stack<Integer>();
    s.push(arr[0]);
      
    // Previous greater for 
    // first element is always -1.
    System.out.print("-1, ");
  
    // Traverse remaining elements
    for (int i = 1; i < n; i++) 
    {
  
        // Pop elements from stack 
        // while stack is not empty 
        // and top of stack is smaller 
        // than arr[i]. We always have 
        // elements in decreasing order 
        // in a stack.
        while (s.empty() == false && 
            s.peek() < arr[i])
            s.pop();
  
        // If stack becomes empty, then 
        // no element is greater on left 
        // side. Else top of stack is 
        // previous greater.
        if (s.empty() == true
            System.out.print("-1, ");
        else
            System.out.print(s.peek() + ", ");
  
        s.push(arr[i]);
    }
}
  
// Driver Code
public static void main(String[] args)
{
    int arr[] = { 10, 4, 2, 20, 40, 12, 30 };
    int n = arr.length;
    prevGreater(arr, n);
}
}

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Python3

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# Python3 program to print previous greater element
# An efficient solution to print previous greater
# element for every element in an array.
import math as mt
  
def prevGreater(arr, n):
  
    # Create a stack and push index of 
    # first element to it
    s = list();
    s.append(arr[0])
      
    # Previous greater for first element
    # is always -1.
    print("-1, ", end = "")
  
    # Traverse remaining elements
    for i in range(1, n): 
  
        # Pop elements from stack while stack is 
        # not empty and top of stack is smaller 
        # than arr[i]. We always have elements in 
        # decreasing order in a stack.
        while (len(s) > 0 and s[-1] < arr[i]):
            s.pop()
  
        # If stack becomes empty, then no element 
        # is greater on left side. Else top of stack 
        # is previous greater.
        if len(s) == 0:
            print("-1, ", end = "")
        else:
            print(s[-1], ", ", end = "")
  
        s.append(arr[i])
      
# Driver code
arr = [ 10, 4, 2, 20, 40, 12, 30 ]
n = len(arr)
prevGreater(arr, n)
  
# This code is contributed by
# mohit kumar 29

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Output:

-1, 10, 4, -1, -1, 40, 40

Time Complexity: O(n). It seems more than O(n) at first look. If we take a closer look, we can observe that every element of array is added and removed from stack at most once. So there are total 2n operations at most. Assuming that a stack operation takes O(1) time, we can say that the time complexity is O(n).

Auxiliary Space: O(n) in worst case when all elements are sorted in decreasing order.



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