Next Greater Element

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:
a) For any array, rightmost element always has next greater element as -1.
b) For an array which is sorted in decreasing order, all elements have next greater element as -1.
c) 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 outer loop. If a greater element is found then that element is printed as next, otherwise -1 is printed.

Thanks to Sachin for providing following code.

C++



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// 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)

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C

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// 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;
}

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Java

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// 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);
    }
}

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Python

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# 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

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C#

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// 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

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PHP

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<?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
?>

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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)
1) Push the first element to stack.
2) Pick rest of the elements one by one and follow following steps in loop.
….a) Mark the current element as next.
….b) If stack is not empty, then pop an element from stack and compare it with next.
….c) If next is greater than the popped element, then next is the next greater element for the popped element.
….d) Keep popping from the stack while the popped element is smaller than next. next becomes the next greater element for all such popped elements
3) After the loop in step 2 is over, pop all the elements from stack and print -1 as next element for them.

Below is the implementation of above approach:

C++

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// 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;
}

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C

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// 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;
}

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//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 

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Python

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# 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

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C#

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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

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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.
a) Initially pushed to the stack.
b) Popped from the stack when next element is being processed.
c) Pushed back to the stack because next element is smaller.
d) Popped from the stack in step 3 of algo.


How to get elements in same order as input?

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

Below is the implementation of above approach:

C++

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// 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 NGE pair for all 
elements of arr[] of size n */
void printNGE(int arr[], int n) 
    stack<int> s; 
    unordered_map<int, int> mp; 
  
    /* 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]) { 
            mp[s.top()] = arr[i]; 
            s.pop(); 
        
  
        /* push next to stack so that we can find 
    next smaller for it */
        s.push(arr[i]); 
    
  
    /* After iterating over the loop, the remaining 
elements in stack do not have the next smaller 
element, so print -1 for them */
    while (s.empty() == false) { 
        mp[s.top()] = -1; 
        s.pop(); 
    
  
    for (int i=0; i<n; i++) 
    cout << arr[i] << " ---> " << mp[arr[i]] << endl; 
  
/* 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; 
}

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Java

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// 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 program to test above functions */
    public static void main(String[] args)
    {
        //NextGreaterElement nge = new NextGreaterElement();
        printNGE();
    }
}
// This code is contributed by Ashish Goyal

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C#

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// 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();
}
}
  
// This code is contributed 
// by Shrikant13

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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.



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