Next Greater Element Using Stack in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Next Greater Element (NGE) for an element in an array?

The Next Greater Element for an element is the first element to the right of it in the array that is greater than it. If no such element exists, the NGE is -1.

intermediate

Why do we use a stack to find the Next Greater Element efficiently?

A stack helps keep track of elements for which we haven't found the NGE yet. It allows us to compare the current element with the top of the stack and find NGEs in a single pass, making the solution efficient.

intermediate

What is the time complexity of the Next Greater Element algorithm using a stack?

The time complexity is O(n) because each element is pushed and popped from the stack at most once during the single pass through the array.

intermediate

In the Next Greater Element algorithm, what do you do when the current element is greater than the element at the top of the stack?

You pop the top element from the stack and assign the current element as its Next Greater Element. Repeat this until the stack is empty or the top element is greater than or equal to the current element.

beginner

What value do you assign as the Next Greater Element if no greater element exists to the right?

You assign -1 to indicate that there is no Next Greater Element for that position.

What data structure is best suited for solving the Next Greater Element problem efficiently?

A Hash Map

B Queue

C Stack

D Linked List

A stack allows us to keep track of elements waiting for their Next Greater Element and process them efficiently in one pass.

What is the Next Greater Element for the last element in any array?

A -1

B The element itself

C The first element

D The previous element

The last element has no elements to its right, so its Next Greater Element is always -1.

If the current element is smaller than the top of the stack, what should you do in the NGE algorithm?

A Push the current element onto the stack

B Pop the stack

C Ignore the current element

D Replace the top of the stack

If the current element is smaller, push it onto the stack to find its NGE later.

What is the time complexity of the Next Greater Element algorithm using a stack?

A O(n^2)

B O(log n)

C O(n log n)

D O(n)

Each element is pushed and popped at most once, so the algorithm runs in linear time O(n).

What does the stack store during the Next Greater Element algorithm?

A All elements in sorted order

B Indices or values of elements waiting for their NGE

C Only the maximum element

D Elements that already have their NGE

The stack stores elements (or their indices) for which we haven't found the Next Greater Element yet.

Explain step-by-step how to find the Next Greater Element for each element in an array using a stack.

Think about how the stack helps track elements waiting for their NGE.

Why is the Next Greater Element algorithm using a stack more efficient than a brute force approach?

Compare how many times each element is checked in both methods.

Practice

1. What does the Next Greater Element problem using a stack help you find for each element in an array?

easy

A. The first smaller element to the left of each element

B. The first greater element to the right of each element

C. The sum of all elements greater than the current element

D. The index of the largest element in the array

Solution

1. Step 1: Understand the problem goal

   The Next Greater Element problem asks to find, for each element, the first element to its right that is greater than it.

2. Step 2: Recognize the stack usage

   A stack helps efficiently track elements waiting for their next greater element to appear on the right.

3. Final Answer:

   The first greater element to the right of each element -> Option B

4. Quick Check:

   Next Greater Element = first bigger right element [OK]

Hint: Look right for first bigger number using stack [OK]

Common Mistakes:

• Confusing next greater with next smaller element
• Looking to the left instead of right
• Thinking it finds the largest element overall

2. Which of the following is the correct way to initialize an empty stack in Python for solving Next Greater Element?

easy

A. stack = []

B. stack = {}

C. stack = ()

D. stack = None

Solution

1. Step 1: Identify stack data structure in Python

   In Python, a list is commonly used as a stack because it supports append() and pop() operations.

2. Step 2: Check initialization syntax

   An empty list is created with square brackets []. Curly braces {} create a dictionary, parentheses () create a tuple, and None is a null value.

3. Final Answer:

   stack = [] -> Option A

4. Quick Check:

   Empty stack = empty list [] [OK]

Hint: Use list [] for stack in Python [OK]

Common Mistakes:

• Using {} which creates a dictionary
• Using () which creates a tuple
• Assigning None instead of a list

3. What is the output of the Next Greater Element for the array [4, 5, 2, 25]?

medium

A. [25, 25, -1, -1]

B. [5, -1, 25, -1]

C. [5, 25, 25, -1]

D. [-1, -1, -1, -1]

Solution

1. Step 1: Find next greater for each element

   For 4, next greater is 5; for 5, next greater is 25; for 2, next greater is 25; for 25, no greater element, so -1.

2. Step 2: Write the output array

   The output array is [5, 25, 25, -1].

3. Final Answer:

   [5, 25, 25, -1] -> Option C

4. Quick Check:

   Check each element's next bigger right = output [OK]

Hint: Scan right for bigger number or -1 if none [OK]

Common Mistakes:

• Putting -1 too early for elements that have bigger right
• Confusing order of output elements
• Missing last element's -1

4. Given the code snippet below, what is the error?

def next_greater(arr):
    stack = []
    result = [-1] * len(arr)
    for i in range(len(arr)):
        while stack and arr[stack[-1]] < arr[i]:
            result[stack.pop()] = arr[i]
        stack.append(i)
    return result

print(next_greater([2, 7, 3, 5, 4, 6, 8]))

medium

A. No error, code runs correctly

B. IndexError due to wrong stack usage

C. SyntaxError because of missing colon

D. TypeError due to wrong list initialization

Solution

1. Step 1: Analyze the code logic

   The code uses a stack to store indices and updates the result list with next greater elements correctly.

2. Step 2: Check for syntax and runtime errors

   All syntax is correct, stack usage is proper, and list initialization is valid.

3. Final Answer:

   No error, code runs correctly -> Option A

4. Quick Check:

   Stack and result used correctly, no errors [OK]

Hint: Trace stack push/pop carefully to spot errors [OK]

Common Mistakes:

• Assuming index errors without checking stack conditions
• Confusing syntax errors with logic errors
• Misreading list initialization syntax

5. You have an array [13, 7, 6, 12]. Using the Next Greater Element approach with a stack, what will be the final output array?

hard

A. [7, 12, 12, -1]

B. [13, 12, 12, -1]

C. [-1, -1, 12, -1]

D. [-1, 12, 12, -1]

Solution

1. Step 1: Find next greater element for each index

   For 13, no greater element to right, so -1; for 7, next greater is 12; for 6, next greater is 12; for 12, no greater element, so -1.

2. Step 2: Write the output array

   The output is [-1, 12, 12, -1].

3. Final Answer:

   [-1, 12, 12, -1] -> Option D

4. Quick Check:

   Check each element's next bigger right = output [OK]

Hint: Remember last element always -1 if no bigger right [OK]

Common Mistakes:

• Assuming first element has a bigger next element incorrectly
• Mixing values with indices in output
• Forgetting to put -1 when no greater element exists