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

Time Complexity: Next Greater Element Using Stack

O(n)

Understanding Time Complexity

We want to understand how the time taken grows when finding the next greater element for each item in a list using a stack.

How does the number of steps change as the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func nextGreaterElement(nums []int) []int {
    result := make([]int, len(nums))
    stack := []int{}
    for i := len(nums) - 1; i >= 0; i-- {
        for len(stack) > 0 && stack[len(stack)-1] <= nums[i] {
            stack = stack[:len(stack)-1]
        }
        if len(stack) == 0 {
            result[i] = -1
        } else {
            result[i] = stack[len(stack)-1]
        }
        stack = append(stack, nums[i])
    }
    return result
}
    

This code finds the next greater element for each number in the list by scanning from right to left using a stack.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: A single loop runs through the list once from right to left.
• Inner operation: The inner loop pops elements from the stack while they are smaller or equal to the current number.
• How many times: Each element is pushed and popped at most once, so the total inner loop operations across all iterations are limited.

How Execution Grows With Input

As the list size grows, each element is processed once and pushed or popped from the stack at most once.

Input Size (n)	Approx. Operations
10	About 20 (push + pop per element)
100	About 200
1000	About 2000

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

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "The inner loop makes this algorithm O(n²) because it can run many times inside the outer loop."

[OK] Correct: Each element is pushed and popped only once, so the total inner loop operations across all iterations add up to n, not n squared.

Interview Connect

Understanding this pattern helps you solve many problems involving next greater or smaller elements efficiently, a common skill interviewers look for.

Self-Check

"What if we changed the input to a circular list where the search wraps around? How would the time complexity change?"

Practice

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

easy

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

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

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

D. The last 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 track elements for which we haven't found a greater element yet, efficiently finding the next greater element to the right.

3. Final Answer:

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

4. Quick Check:

   NGE = first greater element on right [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 sums elements instead of finding one

2. Which Go code snippet correctly initializes an empty stack to use for Next Greater Element logic?

easy

A. stack := 0

B. stack := make(map[int]int)

C. stack := new(int)

D. stack := []int{}

Solution

1. Step 1: Identify stack data structure in Go

   Stacks can be implemented using slices in Go. An empty stack is an empty slice of ints: []int{}.

2. Step 2: Check other options

   stack := make(map[int]int) is a map, not a stack. stack := new(int) is a pointer to int, not a stack. stack := 0 is an int variable, not a stack.

3. Final Answer:

   stack := []int{} -> Option D

4. Quick Check:

   Stack as slice = []int{} [OK]

Hint: Use empty int slice for stack in Go [OK]

Common Mistakes:

• Using map instead of slice for stack
• Using pointer instead of slice
• Initializing stack as int variable

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

medium

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

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

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

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

Solution

1. Step 1: Trace the array elements with stack

   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: Form the output array

   Output is [5, 25, 25, -1].

3. Final Answer:

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

4. Quick Check:

   Next greater elements found correctly [OK]

Hint: Check each element's right side for bigger number [OK]

Common Mistakes:

• Assigning -1 too early
• Mixing up indices in output
• Ignoring last element's -1

4. Given the following Go code snippet for Next Greater Element, what is the bug?

func nextGreater(arr []int) []int {
  stack := []int{}
  result := make([]int, len(arr))
  for i := len(arr) - 1; i >= 0; i-- {
    for len(stack) > 0 && stack[len(stack)-1] <= arr[i] {
      stack = stack[:len(stack)-1]
    }
    if len(stack) == 0 {
      result[i] = 0
    } else {
      result[i] = stack[len(stack)-1]
    }
    stack = append(stack, arr[i])
  }
  return result
}

medium

A. Stack is not initialized properly

B. Loop iterates in wrong direction

C. Result uses 0 instead of -1 for no greater element

D. Comparison operator should be >= instead of <=

Solution

1. Step 1: Identify the no greater element marker

   The code assigns 0 when no greater element is found, but the standard is to use -1.

2. Step 2: Check other parts

   Stack initialization and loop direction are correct. Comparison operator <= is correct for popping smaller or equal elements.

3. Final Answer:

   Result uses 0 instead of -1 for no greater element -> Option C

4. Quick Check:

   No greater element should be -1 [OK]

Hint: Use -1 for no next greater element, not 0 [OK]

Common Mistakes:

• Returning 0 instead of -1 for no greater element
• Changing loop direction incorrectly
• Wrong comparison operator causing wrong pops

5. You have an array [13, 7, 6, 12]. Using the Next Greater Element stack approach, what is the output array?

hard

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

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

C. [ 12, 13, 7, -1 ]

D. [ 7, 6, 12, -1 ]

Solution

1. Step 1: Find next greater for each element

   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 output array

   Output is [-1, 12, 12, -1].

3. Final Answer:

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

4. Quick Check:

   Check right side for bigger numbers [OK]

Hint: Check each element's right side for bigger number [OK]

Common Mistakes:

• Assigning wrong next greater for 7 and 6
• Confusing output with input order
• Using 0 instead of -1 for no greater element