Smallest Greater Element on Right Side

Given an array of distinct elements, print the closest greater element for every element. The closest greater element for an element x is the smallest element on the right side of x in array which is greater than x. Elements for which no greater element exist, consider next greater element as -1.

Examples:

Input: arr[] = {4, 5, 2, 25}
Output: 
Element       NGE
   4      -->   5
   5      -->   25
   2      -->   25
   25     -->   -1

Input: arr[] = {4, 10, 7}
Output: 
Element       NGE
   4       -->  7
   10      -->   -1
   7       -->   -1

Approach: In this post, we will be discussing how to find the Next Greater Element using C++ STL(set).
Finding the smallest greater element on the right side will be like finding the first greater element of the current element in a list that is sorted.
Consider example 1, The sorted list would look like 2, 4, 5, 25.
Here for element 4, the greater element is 5 as it is next to it, so we print 5 and remove 4 because it would not be greater to the other elements since it is no longer on anyone’s right.
Similarly, for 5 it is 25 and we remove 5 from the list, as 5 will not be on the right side of 2 or 25, so it can be deleted.



Given below are the steps to find the Next Greater Element of every index element.

  • Insert all the elements in a Set, it will store all the elements in an increasing order.
  • Iterate on the array of elements, and for each index, find the upper_bound of the current index element. The upper_bound() returns an iterator which can point to the following position.
    1. If the iterator is pointing to a position past the last element, then there exists no NGE to the current index element.
    2. If the iterator points to a position referring to an element, then that element is the NGE to the current index element.
  • Find the position of current index element at every traversal and remove it from the set using >lower_bound() and erase() functions of set.

Below is the implementation of the above approach.

C/C++

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// C++ program to print the
// NGE's of array elements using
// C++ STL
#include <bits/stdc++.h>
using namespace std;
  
// Function to print the NGE
void printNGE(int a[], int n)
{
  
    set<int> ms;
  
    // insert in the multiset container
    for (int i = 0; i < n; i++)
        ms.insert(a[i]);
  
    cout << "Element   "
         << "NGE";
  
    // traverse for all array elements
    for (int i = 0; i < n; i++) {
  
        // find the upper_bound in set
        auto it = ms.upper_bound(a[i]);
  
        // if points to the end, then
        // no NGE of that element
        if (it == ms.end()) {
            cout << "\n   " << a[i]
                 << " ----> " << -1;
        }
  
        // print the element at that position
        else {
            cout << "\n   " << a[i]
                 << " ----> " << *it;
        }
  
        // find the first occurrence of
        // the index element and delete it
        it = ms.lower_bound(a[i]);
  
        // delete one occurrence
        // from the container
        ms.erase(it);
    }
}
  
// Driver Code
int main()
{
    int a[] = { 4, 5, 2, 25 };
    int n = sizeof(a) / sizeof(a[0]);
  
    // Function call to print the NGE
    printNGE(a, n);
    return 0;
}

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Java

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// C++ program to print the
// NGE's of array elements using
import java.util.TreeSet;
  
class Geeks {
  
    // Function to print the NGE
    static void printNGE(int[] a, int n)
    {
  
        // Tree Set is an ordered set used to
        // store elements in a sorted manner
        TreeSet<Integer> t = new TreeSet<>();
  
        // Adding elements into the set
        for (int i = 0; i < n; i++)
            t.add(a[i]);
  
        System.out.println("ELEMENT     NGE");
  
        for (int i = 0; i < n; i++) {
  
            // If the elements does not have an upper bound
            // or an element greater than it,
            // higher method of TreeSet class will return NULL
            if (t.higher(a[i]) == null)
                System.out.println(a[i] + " ----> "
                                   + "-1");
  
            // Otherwise print the upper bound of that element
            else
                System.out.println(a[i] + " ----> " + t.higher(a[i]));
  
            // Remove the current element from the set
            t.remove(a[i]);
        }
    }
  
    // Driver code
    public static void main(String[] args)
    {
  
        int a[] = { 4, 5, 2, 25 };
        int n = a.length;
  
        printNGE(a, n);
    }
}

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Python3

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# Python3 program to print the
# NGE's of array elements
from bisect import bisect_right as upper_bound, \
                   bisect_left as lower_bound
  
# Function to print the NGE
def printNGE(a: list, n):
    ms = set()
  
    # insert in the multiset container
    for i in range(n):
        ms.add(a[i])
  
    print("Element NGE", end = "")
  
    # Required because Python sets
    # are not sorted
    new_arr = list(ms)
    new_arr.sort()
  
    # traverse for all array elements
    for i in range(n):
  
        # find the upper_bound in set
        it = upper_bound(new_arr, a[i])
  
        # if points to the end, then
        # no NGE of that element
        if (it == len(new_arr)):
            print("\n %d ----> -1" % a[i], end = "")
  
        # print the element at that position
        else:
            print("\n %d ----> %d" % (a[i], 
                    new_arr[it]), end = "")
  
        # find the first occurrence of
        # the index element and delete it
        it = lower_bound(new_arr, a[i])
  
        # delete one occurrence
        # from the container
        new_arr.remove(new_arr[it])
  
# Driver Code
if __name__ == "__main__":
    a = [4, 5, 2, 25]
    n = len(a)
  
    # Function call to print the NGE
    printNGE(a, n)
  
# This code is contributed by
# sanjeev2552

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Output:

Element   NGE
   4 ----> 5
   5 ----> 25
   2 ----> 25
   25 ----> -1

Time Complexity: O(N log N)

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