Next Greater Element

Difficulty Level : Medium
Last Updated : 24 Jul, 2019

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 array. Elements for which no greater element exist, consider next greater element as -1.

Examples:

For any array, rightmost element always has next greater element as -1.
For an array which is sorted in decreasing order, all elements have 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

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

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.

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 
?> 

Output:

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

Time Complexity: O(n^2). The worst case occurs when all elements are sorted in decreasing order.

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 stack and print -1 as 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 program to test above functions */
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<stdio.h> 
#include<stdlib.h> 
#include<stdbool.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 program to test above functions */
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); 
        } 
    } 
  
    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 program to test above functions 
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); 
        } 
    } 
  
    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 

Output:

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

Time Complexity: 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 algorithm.

Please see for 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.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes

Related Articles

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

C++

C

Java

Python

C#

PHP

C++

C

Java

Python

C#