Next Greater Element Using Stack in DSA Python - Time & Space Complexity

Time Complexity: Next Greater Element Using Stack

O(n)

Understanding Time Complexity

We want to understand how the time needed changes when we find the next greater element for each item in a list using a stack.

How does the number of steps grow as the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

def next_greater_element(arr):
    stack = []
    result = [-1] * len(arr)
    for i, value in enumerate(arr):
        while stack and arr[stack[-1]] < value:
            index = stack.pop()
            result[index] = value
        stack.append(i)
    return result

This code finds the next greater number for each element in the list using a stack to keep track of indices.

Identify Repeating Operations

• Primary operation: The for-loop goes through each element once, and the while-loop pops elements from the stack when the current element is greater.
• How many times: Each element is pushed and popped at most once, so the total number of stack operations is at most 2n.

How Execution Grows With Input

As the list size grows, each element is handled a limited number of times.

Input Size (n)	Approx. Operations
10	About 20 stack operations
100	About 200 stack operations
1000	About 2000 stack operations

Pattern observation: The operations grow roughly in a straight line with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time needed grows directly in proportion to the number of elements in the list.

Common Mistake

[X] Wrong: "The nested while-loop makes this algorithm O(n²) because it looks like a loop inside a loop."

[OK] Correct: Each element is pushed and popped only once, so the total work inside the while-loop across the whole run is limited to n operations, not n².

Interview Connect

Understanding this pattern helps you solve many problems efficiently by using stacks to track previous elements, a skill often valued in coding challenges.

Self-Check

What if we changed the input to a linked list instead of an array? How would the time complexity change?

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