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

Time Complexity: Next Greater Element Using Stack

O(n)

Understanding Time Complexity

We want to understand how the time needed to find the next greater element changes as the input size grows.

How does the algorithm handle larger arrays efficiently?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void nextGreaterElement(int arr[], int n, int result[]) {
    int stack[n];
    int top = -1;
    for (int i = n - 1; i >= 0; i--) {
        while (top != -1 && stack[top] <= arr[i]) {
            top--;
        }
        result[i] = (top == -1) ? -1 : stack[top];
        stack[++top] = arr[i];
    }
}
    

This code finds the next greater element for each item in the array using a stack.

Identify Repeating Operations

• Primary operation: A single loop running from the end to the start of the array.
• How many times: The loop runs once for each element, so n times.
• Inside the loop: The while loop pops elements from the stack, but each element is pushed and popped at most once.

How Execution Grows With Input

As the input size grows, each element is processed once, and stack operations happen at most once per element.

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

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

Final Time Complexity

Time Complexity: O(n)

This means the time to find the next greater element grows linearly with the number of elements.

Common Mistake

[X] Wrong: "The nested while loop makes this algorithm O(n²)."

[OK] Correct: Each element is pushed and popped only once, so the total work inside the while loops across all iterations is still proportional to n.

Interview Connect

Understanding this linear time stack approach shows you can solve problems efficiently by avoiding repeated work, a key skill in coding interviews.

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 (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 last element in the array

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

Solution

1. Step 1: Understand the problem definition

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

2. Step 2: Identify the role of the stack

   The stack helps efficiently find this next greater element by storing candidates and popping smaller elements.

3. Final Answer:

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

4. Quick Check:

   Next Greater Element = first greater right element [OK]

Hint: Look right for the first bigger number using a 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 of the following C code snippets correctly initializes an empty stack for Next Greater Element problem?

easy

A. int stack[100]; int top = -1;

B. int stack[] = {0}; int top = 0;

C. int *stack; int top = NULL;

D. stack = new int[100]; top = -1;

Solution

1. Step 1: Check valid C array and top initialization

   int stack[100]; int top = -1; declares a fixed size array and sets top to -1 indicating empty stack.

2. Step 2: Identify invalid syntax or semantics in other options

   int stack[] = {0}; int top = 0; initializes top to 0 which means stack is not empty; int *stack; int top = NULL; uses NULL for int top which is invalid; stack = new int[100]; top = -1; uses 'new' which is C++ syntax, not C.

3. Final Answer:

   int stack[100]; int top = -1; -> Option A

4. Quick Check:

   Stack array + top = -1 means empty [OK]

Hint: Use array and top = -1 for empty stack in C [OK]

Common Mistakes:

• Using C++ 'new' keyword in C code
• Initializing top to 0 instead of -1
• Using pointer without allocation

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

medium

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

B. [5, 2, 25, -1]

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

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

Solution

1. Step 1: Process each element to find next greater

   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: Confirm output array

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

3. Final Answer:

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

4. Quick Check:

   Next greater elements match output [OK]

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

Common Mistakes:

• Assigning smaller or wrong next greater values
• Using -1 for elements that do have greater elements
• Confusing order of output

4. Identify the bug in this C code snippet for Next Greater Element using stack:

for (int i = 0; i < n; i++) {
  while (top != -1 && arr[stack[top]] < arr[i]) {
    result[stack[top]] = arr[i];
    top--;
  }
  stack[++top] = i;
}
while (top != -1) {
  result[stack[top]] = 0;
  top--;
}

medium

A. Using post-increment instead of pre-increment on stack index

B. Assigning 0 instead of -1 for elements with no greater element

C. Incorrect loop condition causing infinite loop

D. Not initializing top before loop

Solution

1. Step 1: Check final assignment for elements with no next greater

   The code assigns 0 instead of -1, which is incorrect as per problem definition.

2. Step 2: Verify other parts of code

   Stack index increment and loop conditions are correct; top is assumed initialized before.

3. Final Answer:

   Assigning 0 instead of -1 for elements with no greater element -> Option B

4. Quick Check:

   No greater element should be -1, not 0 [OK]

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

Common Mistakes:

• Using 0 instead of -1 for no next greater
• Forgetting to initialize top
• Wrong increment operator on stack

5. Given the array [13, 7, 6, 12], what is the Next Greater Element array using the stack approach? Also, explain why the last element's next greater is -1.

hard

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

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

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

D. [ -1, 12, 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: Explain last element's next greater

   The last element 12 has no elements to its right, so no next greater element exists, hence -1.

3. Final Answer:

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

4. Quick Check:

   Last element no right neighbor = -1 [OK]

Hint: Last element always has -1 as no elements to right [OK]

Common Mistakes:

• Assigning next greater to last element
• Mixing up next greater for middle elements
• Confusing output order