Next Greater Element

Difficulty Level : Medium
Last Updated : 26 Jul, 2021

Given an array, print the Next Greater Element (NGE) for every element. The Next greater Element for an element x is the first greater element on the right side of x in the array. Elements for which no greater element exist, consider the next greater element as -1.

Examples:

For an array, the rightmost element always has the next greater element as -1.
For an array that is sorted in decreasing order, all elements have the next greater element as -1.
For the input array [4, 5, 2, 25], the next greater elements for each element are as follows.

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

d) For the input array [13, 7, 6, 12}, the next greater elements for each element are as follows.

  Element        NGE
   13      -->    -1
   7       -->     12
   6       -->     12
   12      -->     -1

Method 1 (Simple)
Use two loops: The outer loop picks all the elements one by one. The inner loop looks for the first greater element for the element picked by the outer loop. If a greater element is found then that element is printed as next, otherwise, -1 is printed.

Below is the implementation of the above approach:

C++

// Simple C++ program to print
// next greater elements in a
// given array
#include<iostream>
using namespace std;
 
/* prints element and NGE pair
for all elements of arr[] of size n */
void printNGE(int arr[], int n)
{
    int next, i, j;
    for (i = 0; i < n; i++)
    {
        next = -1;
        for (j = i + 1; j < n; j++)
        {
            if (arr[i] < arr[j])
            {
                next = arr[j];
                break;
            }
        }
        cout << arr[i] << " -- "
             << next << endl;
    }
}
 
// Driver Code
int main()
{
    int arr[] = {11, 13, 21, 3};
    int n = sizeof(arr)/sizeof(arr[0]);
    printNGE(arr, n);
    return 0;
}
 
// This code is contributed
// by Akanksha Rai(Abby_akku)

C

// Simple C program to print next greater elements
// in a given array
#include<stdio.h>
 
/* prints element and NGE pair for all elements of
arr[] of size n */
void printNGE(int arr[], int n)
{
    int next, i, j;
    for (i=0; i<n; i++)
    {
        next = -1;
        for (j = i+1; j<n; j++)
        {
            if (arr[i] < arr[j])
            {
                next = arr[j];
                break;
            }
        }
        printf("%d -- %dn", arr[i], next);
    }
}
 
int main()
{
    int arr[]= {11, 13, 21, 3};
    int n = sizeof(arr)/sizeof(arr[0]);
    printNGE(arr, n);
    return 0;
}

Java

// Simple Java program to print next
// greater elements in a given array
 
class Main
{
    /* prints element and NGE pair for
     all elements of arr[] of size n */
    static void printNGE(int arr[], int n)
    {
        int next, i, j;
        for (i=0; i<n; i++)
        {
            next = -1;
            for (j = i+1; j<n; j++)
            {
                if (arr[i] < arr[j])
                {
                    next = arr[j];
                    break;
                }
            }
            System.out.println(arr[i]+" -- "+next);
        }
    }
      
    public static void main(String args[])
    {
        int arr[]= {11, 13, 21, 3};
        int n = arr.length;
        printNGE(arr, n);
    }
}

Python

# Function to print element and NGE pair for all elements of list
def printNGE(arr):
 
    for i in range(0, len(arr), 1):
 
        next = -1
        for j in range(i+1, len(arr), 1):
            if arr[i] < arr[j]:
                next = arr[j]
                break
             
        print(str(arr[i]) + " -- " + str(next))
 
# Driver program to test above function
arr = [11,13,21,3]
printNGE(arr)
 
# This code is contributed by Sunny Karira

C#

// Simple C# program to print next
// greater elements in a given array
using System;
 
class GFG
{
     
    /* prints element and NGE pair for
    all elements of arr[] of size n */
    static void printNGE(int []arr, int n)
    {
        int next, i, j;
        for (i = 0; i < n; i++)
        {
            next = -1;
            for (j = i + 1; j < n; j++)
            {
                if (arr[i] < arr[j])
                {
                    next = arr[j];
                    break;
                }
            }
            Console.WriteLine(arr[i] + " -- " + next);
        }
    }
     
    // driver code
    public static void Main()
    {
        int []arr= {11, 13, 21, 3};
        int n = arr.Length;
         
        printNGE(arr, n);
    }
}
 
// This code is contributed by Sam007

PHP

<?php
// Simple PHP program to print next
// greater elements in a given array
 
/* prints element and NGE pair for
   all elements of arr[] of size n */
function printNGE($arr, $n)
{
    for ($i = 0; $i < $n; $i++)
    {
        $next = -1;
        for ($j = $i + 1; $j < $n; $j++)
        {
            if ($arr[$i] < $arr[$j])
            {
                $next = $arr[$j];
                break;
            }
        }
        echo $arr[$i]." -- ". $next."\n";
         
    }
}
 
    // Driver Code
    $arr= array(11, 13, 21, 3);
    $n = count($arr);
    printNGE($arr, $n);
     
// This code is contributed by Sam007
?>

Javascript

<script>
      // Simple JavaScript program to print
      // next greater elements in a
      // given array
 
      /* prints element and NGE pair
      for all elements of arr[] of size n */
      function printNGE(arr, n)
      {
        var next, i, j;
        for (i = 0; i < n; i++)
        {
          next = -1;
          for (j = i + 1; j < n; j++)
          {
            if (arr[i] < arr[j])
            {
              next = arr[j];
              break;
            }
          }
          document.write(arr[i] + " -- " + next);
          document.write("<br>");
        }
      }
 
      // Driver Code
      var arr = [11, 13, 21, 3];
      var n = arr.length;
      printNGE(arr, n);
       
      // This code is contributed by rdtank.
    </script>

Output

11 -- 13
13 -- 21
21 -- -1
3 -- -1

Time Complexity: O(N²)
Auxiliary Space: O(1)

Method 2 (Using Stack)

Push the first element to stack.
Pick rest of the elements one by one and follow the following steps in loop.
1. Mark the current element as next.
2. If stack is not empty, compare top element of stack with next.
3. If next is greater than the top element, Pop element from stack. next is the next greater element for the popped element.
4. Keep popping from the stack while the popped element is smaller than next. next becomes the next greater element for all such popped elements.
Finally, push the next in the stack.
After the loop in step 2 is over, pop all the elements from the stack and print -1 as the next element for them.

Below image is a dry run of the above approach:

Below is the implementation of the above approach:

C++

// A Stack based C++ program to find next
// greater element for all array elements.
#include <bits/stdc++.h>
using namespace std;
 
/* prints element and NGE pair for all
elements of arr[] of size n */
void printNGE(int arr[], int n)
{
    stack<int> s;
 
    /* push the first element to stack */
    s.push(arr[0]);
 
    // iterate for rest of the elements
    for (int i = 1; i < n; i++)
    {
 
        if (s.empty()) {
            s.push(arr[i]);
            continue;
        }
 
        /* if stack is not empty, then
           pop an element from stack.
           If the popped element is smaller
           than next, then
        a) print the pair
        b) keep popping while elements are
        smaller and stack is not empty */
        while (s.empty() == false
               && s.top() < arr[i])
        {
            cout << s.top()
                 << " --> " << arr[i] << endl;
            s.pop();
        }
 
        /* push next to stack so that we can find
        next greater for it */
        s.push(arr[i]);
    }
 
    /* After iterating over the loop, the remaining
    elements in stack do not have the next greater
    element, so print -1 for them */
    while (s.empty() == false) {
        cout << s.top() << " --> " << -1 << endl;
        s.pop();
    }
}
 
/* Driver code */
int main()
{
    int arr[] = { 11, 13, 21, 3 };
    int n = sizeof(arr) / sizeof(arr[0]);
    printNGE(arr, n);
    return 0;
}

C

// A Stack based C program to find next
//  greater element for all array elements.
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#define STACKSIZE 100
 
// stack structure
struct stack {
    int top;
    int items[STACKSIZE];
};
 
// Stack Functions to be used by printNGE()
void push(struct stack* ps, int x)
{
    if (ps->top == STACKSIZE - 1) {
        printf("Error: stack overflown");
        getchar();
        exit(0);
    }
    else {
        ps->top += 1;
        int top = ps->top;
        ps->items[top] = x;
    }
}
 
bool isEmpty(struct stack* ps)
{
    return (ps->top == -1) ? true : false;
}
 
int pop(struct stack* ps)
{
    int temp;
    if (ps->top == -1) {
        printf("Error: stack underflow n");
        getchar();
        exit(0);
    }
    else {
        int top = ps->top;
        temp = ps->items[top];
        ps->top -= 1;
        return temp;
    }
}
 
/* prints element and NGE pair for all elements of
arr[] of size n */
void printNGE(int arr[], int n)
{
    int i = 0;
    struct stack s;
    s.top = -1;
    int element, next;
 
    /* push the first element to stack */
    push(&s, arr[0]);
 
    // iterate for rest of the elements
    for (i = 1; i < n; i++) {
        next = arr[i];
 
        if (isEmpty(&s) == false)
        {
            // if stack is not empty, then pop an element
            // from stack
            element = pop(&s);
 
            /* If the popped element is smaller than next,
               then a) print the pair b) keep popping while
               elements are smaller and stack is not empty
             */
            while (element < next) {
                printf("n %d --> %d", element, next);
                if (isEmpty(&s) == true)
                    break;
                element = pop(&s);
            }
 
            /* If element is greater than next, then push
               the element back */
            if (element > next)
                push(&s, element);
        }
 
        /* push next to stack so that we can find
           next greater for it */
        push(&s, next);
    }
 
    /* After iterating over the loop, the remaining
       elements in stack do not have the next greater
       element, so print -1 for them */
    while (isEmpty(&s) == false)
    {
        element = pop(&s);
        next = -1;
        printf("n %d --> %d", element, next);
    }
}
 
/* Driver code */
int main()
{
    int arr[] = { 11, 13, 21, 3 };
    int n = sizeof(arr) / sizeof(arr[0]);
    printNGE(arr, n);
    getchar();
    return 0;
}

Java

// Java program to print next
// greater element using stack
 
public class NGE {
    static class stack {
        int top;
        int items[] = new int[100];
 
        // Stack functions to be used by printNGE
        void push(int x)
        {
            if (top == 99)
            {
                System.out.println("Stack full");
            }
            else
            {
                items[++top] = x;
            }
        }
 
        int pop()
        {
            if (top == -1)
            {
                System.out.println("Underflow error");
                return -1;
            }
            else {
                int element = items[top];
                top--;
                return element;
            }
        }
 
        boolean isEmpty()
        {
            return (top == -1) ? true : false;
        }
    }
 
    /* prints element and NGE pair for
       all elements of arr[] of size n */
    static void printNGE(int arr[], int n)
    {
        int i = 0;
        stack s = new stack();
        s.top = -1;
        int element, next;
 
        /* push the first element to stack */
        s.push(arr[0]);
 
        // iterate for rest of the elements
        for (i = 1; i < n; i++)
        {
            next = arr[i];
 
            if (s.isEmpty() == false)
            {
 
                // if stack is not empty, then
                // pop an element from stack
                element = s.pop();
 
                /* If the popped element is smaller than
                   next, then a) print the pair b) keep
                   popping while elements are smaller and
                   stack is not empty */
                while (element < next)
                {
                    System.out.println(element + " --> "
                                       + next);
                    if (s.isEmpty() == true)
                        break;
                    element = s.pop();
                }
 
                /* If element is greater than next, then
                   push the element back */
                if (element > next)
                    s.push(element);
            }
 
            /* push next to stack so that we can find next
               greater for it */
            s.push(next);
        }
 
        /* After iterating over the loop, the remaining
           elements in stack do not have the next greater
           element, so print -1 for them */
        while (s.isEmpty() == false)
        {
            element = s.pop();
            next = -1;
            System.out.println(element + " -- " + next);
        }
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int arr[] = { 11, 13, 21, 3 };
        int n = arr.length;
        printNGE(arr, n);
    }
}
 
// Thanks to Rishabh Mahrsee for contributing this code

Python

# Python program to print next greater element using stack
 
# Stack Functions to be used by printNGE()
 
 
def createStack():
    stack = []
    return stack
 
 
def isEmpty(stack):
    return len(stack) == 0
 
 
def push(stack, x):
    stack.append(x)
 
 
def pop(stack):
    if isEmpty(stack):
        print("Error : stack underflow")
    else:
        return stack.pop()
 
 
'''prints element and NGE pair for all elements of
   arr[] '''
 
 
def printNGE(arr):
    s = createStack()
    element = 0
    next = 0
 
    # push the first element to stack
    push(s, arr[0])
 
    # iterate for rest of the elements
    for i in range(1, len(arr), 1):
        next = arr[i]
 
        if isEmpty(s) == False:
 
            # if stack is not empty, then pop an element from stack
            element = pop(s)
 
            '''If the popped element is smaller than next, then
                a) print the pair
                b) keep popping while elements are smaller and
                   stack is not empty '''
            while element < next:
                print(str(element) + " -- " + str(next))
                if isEmpty(s) == True:
                    break
                element = pop(s)
 
            '''If element is greater than next, then push
               the element back '''
            if element > next:
                push(s, element)
 
        '''push next to stack so that we can find
           next greater for it '''
        push(s, next)
 
    '''After iterating over the loop, the remaining
       elements in stack do not have the next greater
       element, so print -1 for them '''
 
    while isEmpty(s) == False:
        element = pop(s)
        next = -1
        print(str(element) + " -- " + str(next))
 
 
# Driver code
arr = [11, 13, 21, 3]
printNGE(arr)
 
# This code is contributed by Sunny Karira

C#

using System;
 
// c# program to print next
// greater element using stack
 
public class NGE {
    public class stack {
        public int top;
        public int[] items = new int[100];
 
        // Stack functions to be used by printNGE
        public virtual void push(int x)
        {
            if (top == 99) {
                Console.WriteLine("Stack full");
            }
            else {
                items[++top] = x;
            }
        }
 
        public virtual int pop()
        {
            if (top == -1) {
                Console.WriteLine("Underflow error");
                return -1;
            }
            else {
                int element = items[top];
                top--;
                return element;
            }
        }
 
        public virtual bool Empty
        {
            get { return (top == -1) ? true : false; }
        }
    }
 
    /* prints element and NGE pair for
       all elements of arr[] of size n */
    public static void printNGE(int[] arr, int n)
    {
        int i = 0;
        stack s = new stack();
        s.top = -1;
        int element, next;
 
        /* push the first element to stack */
        s.push(arr[0]);
 
        // iterate for rest of the elements
        for (i = 1; i < n; i++) {
            next = arr[i];
 
            if (s.Empty == false) {
 
                // if stack is not empty, then
                // pop an element from stack
                element = s.pop();
 
                /* If the popped element is smaller than
                   next, then a) print the pair b) keep
                   popping while elements are smaller and
                   stack is not empty */
                while (element < next) {
                    Console.WriteLine(element + " --> "
                                      + next);
                    if (s.Empty == true) {
                        break;
                    }
                    element = s.pop();
                }
 
                /* If element is greater than next, then
                   push the element back */
                if (element > next) {
                    s.push(element);
                }
            }
 
            /* push next to stack so that we can find next
               greater for it */
            s.push(next);
        }
 
        /* After iterating over the loop, the remaining
           elements in stack do not have the next greater
           element, so print -1 for them */
        while (s.Empty == false) {
            element = s.pop();
            next = -1;
            Console.WriteLine(element + " -- " + next);
        }
    }
 
    // Driver Code
    public static void Main(string[] args)
    {
        int[] arr = new int[] { 11, 13, 21, 3 };
        int n = arr.Length;
        printNGE(arr, n);
    }
}
 
// This code is contributed by Shrikant13

Javascript

<script>
 
// A Stack based Javascript program to find next
// greater element for all array elements.
 
/* prints element and NGE pair for all
elements of arr[] of size n */
function printNGE(arr, n)
{
    var s = [];
 
    /* push the first element to stack */
    s.push(arr[0]);
 
    // iterate for rest of the elements
    for (var i = 1; i < n; i++)
    {
 
        if (s.length == 0) {
            s.push(arr[i]);
            continue;
        }
 
        /* if stack is not empty, then
           pop an element from stack.
           If the popped element is smaller
           than next, then
        a) print the pair
        b) keep popping while elements are
        smaller and stack is not empty */
        while (s.length ==0 == false
               && s[s.length-1] < arr[i])
        {
            document.write( s[s.length-1]
                 + " --> " + arr[i]+"<br>");
            s.pop();
        }
 
        /* push next to stack so that we can find
        next greater for it */
        s.push(arr[i]);
    }
 
    /* After iterating over the loop, the remaining
    elements in stack do not have the next greater
    element, so print -1 for them */
    while (s.length !=0) {
        document.write( s[s.length-1] + " --> " + -1+ "<br>" );
        s.pop();
    }
}
 
/* Driver code */
var arr = [11, 13, 21, 3];
var n = arr.length;
printNGE(arr, n);
 
</script>

Output

11 --> 13
13 --> 21
3 --> -1
21 --> -1

Time Complexity: O(N)
Auxiliary Space: O(N)

The worst case occurs when all elements are sorted in decreasing order. If elements are sorted in decreasing order, then every element is processed at most 4 times.

Initially pushed to the stack.
Popped from the stack when next element is being processed.
Pushed back to the stack because the next element is smaller.
Popped from the stack in step 3 of the algorithm.

How to get elements in the same order as input?

The above approach may not produce output elements in the same order as the input. To achieve the same order, we can traverse the same in reverse order

Below is the implementation of the above approach:

C++

// A Stack based C++ program to find next
// greater element for all array elements
// in same order as input.
#include <bits/stdc++.h>
 
using namespace std;
 
/* prints element and res pair for all
elements of arr[] of size n */
void printNGE(int arr[], int n)
{
    stack<int> s;
    int res[n];
    for (int i = n - 1; i >= 0; i--) {
        /* if stack is not empty, then
        pop an element from stack.
        If the popped element is smaller
        than next, then
        a) print the pair
        b) keep popping while elements are
        smaller and stack is not empty */
        if (!s.empty()) {
            while (!s.empty() && s.top() <= arr[i]) {
                s.pop();
            }
        }
        res[i] = s.empty() ? -1 : s.top();
        s.push(arr[i]);
    }
    for (int i = 0; i < n; i++)
        cout << arr[i] << " --> " << res[i] << endl;
}
// Driver Code
int main()
{
    int arr[] = { 11, 13, 21, 3 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    // Function call
    printNGE(arr, n);
    return 0;
}

Java

// A Stack based Java program to find next
// greater element for all array elements
// in same order as input.
import java.util.Stack;
 
class NextGreaterElement {
 
    static int arr[] = { 11, 13, 21, 3 };
 
    /* prints element and NGE pair for all
    elements of arr[] of size n */
    public static void printNGE()
    {
        Stack<Integer> s = new Stack<>();
        int nge[] = new int[arr.length];
 
        // iterate for rest of the elements
        for (int i = arr.length - 1; i >= 0; i--)
        {
            /* if stack is not empty, then
            pop an element from stack.
            If the popped element is smaller
            than next, then
            a) print the pair
            b) keep popping while elements are
            smaller and stack is not empty */
            if (!s.empty())
            {
                while (!s.empty()
                       && s.peek() <= arr[i])
                {
                    s.pop();
                }
            }
            nge[i] = s.empty() ? -1 : s.peek();
            s.push(arr[i]);
        }
        for (int i = 0; i < arr.length; i++)
            System.out.println(arr[i] +
                               " --> " + nge[i]);
    }
 
    /* Driver Code */
    public static void main(String[] args)
    {
        // NextGreaterElement nge = new
        // NextGreaterElement();
        printNGE();
    }
}

C#

// A Stack based C# program to find next
// greater element for all array elements
// in same order as input.
using System;
using System.Collections.Generic;
 
class GFG {
    private int[] arr = new int[] { 11, 13, 21, 3 };
 
    /* prints element and NGE pair for all
    elements of arr[] of size n */
    private void printNGE()
    {
        Stack<int> s = new Stack<int>();
        int[] nge = new int[arr.Length];
 
        // iterate for rest of the elements
        for (int i = arr.Length - 1; i >= 0; i--)
        {
 
            /* if stack is not empty, then
            pop an element from stack.
            If the popped element is smaller
            than next, then
            a) print the pair
            b) keep popping while elements are
            smaller and stack is not empty */
            if (s.Count > 0)
            {
                while (s.Count > 0
                       && s.Peek() <= arr[i])
                {
                    s.Pop();
                }
            }
            nge[i] = s.Count == 0 ? -1 : s.Peek();
            s.Push(arr[i]);
        }
        for (int i = 0; i < arr.Length; i++)
        {
            Console.WriteLine(arr[i] + " --> " + nge[i]);
        }
    }
 
    // Driver Code
    public static void Main(string[] args)
    {
        GFG nge = new GFG();
        nge.printNGE();
    }
}

Output

11 ---> 13
13 ---> 21
21 ---> -1
3 ---> -1

Time Complexity: O(N)
Auxiliary Space: O(N)

Method 3:

1. This is same as above method but the elements are pushed and popped only once into the stack. The array is changed in place. The array elements are pushed into the stack until it finds a greatest element in the right of array. In other words the elements are popped from stack when top of the stack value is smaller in the current array element.

2. Once all the elements are processed in the array but stack is not empty. The left out elements in the stack doesn’t encounter any greatest element . So pop the element from stack and change it’s index value as -1 in the array.

Python3

# Python3 code
class Solution:
    def nextLargerElement(self,arr,n):
        #code here
        s=[]
        for i in range(len(arr)):
            while s and s[-1].get("value") < arr[i]:
                d = s.pop()
                arr[d.get("ind")] = arr[i]
            s.append({"value": arr[i], "ind": i})
        while s:
            d = s.pop()
            arr[d.get("ind")] = -1
        return arr
         
if __name__ == "__main__":
    print(Solution().nextLargerElement([6,8,0,1,3],5))

Output

[8, -1, 1, 3, -1]

Time Complexity: O(N)
Auxiliary Space: O(N)

Please see for an optimized solution for printing in same order.

Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.

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