Array push and pop in PHP - Time & Space Complexity

Time Complexity: Array push and pop

O(1)

Understanding Time Complexity

We want to understand how fast adding or removing items from the end of an array happens in PHP.

How does the time to push or pop change when the array grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

$array = [];

// Add items to the end
array_push($array, 10);
array_push($array, 20);

// Remove last item
array_pop($array);

This code adds two items to the end of an array and then removes the last item.

Identify Repeating Operations

Look at what repeats or happens often.

• Primary operation: Adding or removing one item at the end of the array.
• How many times: Each push or pop happens once per call, no loops here.

How Execution Grows With Input

Adding or removing one item at the end takes about the same time no matter how big the array is.

Input Size (n)	Approx. Operations
10	1 operation per push or pop
100	1 operation per push or pop
1000	1 operation per push or pop

Pattern observation: The time stays about the same even as the array grows.

Final Time Complexity

Time Complexity: O(1)

This means adding or removing an item at the end takes constant time, no matter the array size.

Common Mistake

[X] Wrong: "Adding an item to the array takes longer as the array gets bigger."

[OK] Correct: Because PHP arrays are implemented as ordered hash tables, adding or removing items at the end is generally efficient and does not grow linearly with array size.

Interview Connect

Knowing that push and pop are fast helps you choose the right data structure and explain your code clearly in interviews.

Self-Check

"What if we added or removed items from the start of the array instead? How would the time complexity change?"

Practice

1. What does the PHP function array_push do to an array?

easy

A. Adds one or more elements to the end of the array

B. Removes the first element from the array

C. Removes the last element from the array

D. Sorts the array in ascending order

Solution

1. Step 1: Understand the purpose of array_push

   array_push is used to add elements to the end of an existing array.

2. Step 2: Compare with other array functions

   Functions like array_pop remove elements, but array_push only adds elements at the end.

3. Final Answer:

   Adds one or more elements to the end of the array -> Option A

4. Quick Check:

   array_push = add elements at end [OK]

Hint: Remember: push means add at the end [OK]

Common Mistakes:

• Confusing array_push with array_pop
• Thinking array_push removes elements
• Assuming array_push sorts the array

2. Which of the following is the correct syntax to add an element 'apple' to the array $fruits using array_push?

easy

A. array_push('apple', $fruits);

B. array_push($fruits['apple']);

C. array_push($fruits => 'apple');

D. array_push($fruits, 'apple');

Solution

1. Step 1: Recall the function signature

   The correct syntax is array_push(array, value1, value2, ...), where the first argument is the array variable.

2. Step 2: Check each option

   array_push($fruits, 'apple'); correctly uses array_push($fruits, 'apple');. Others misuse argument order or syntax.

3. Final Answer:

   array_push($fruits, 'apple'); -> Option D

4. Quick Check:

   array_push(array, value) syntax [OK]

Hint: First argument is array, then values to add [OK]

Common Mistakes:

• Swapping argument order
• Using arrow => instead of comma
• Passing only one argument incorrectly

3. What will be the output of the following PHP code?

$colors = ['red', 'green'];
array_push($colors, 'blue');
$last = array_pop($colors);
print_r($colors);
echo $last;

medium

A. Array ( [0] => red [1] => green [2] => blue ) blue

B. Array ( [0] => red [1] => green ) blue

C. Array ( [0] => red [1] => green ) green

D. Array ( [0] => red [1] => green [2] => blue ) green

Solution

1. Step 1: Understand array_push effect

   array_push adds 'blue' to the end, so array becomes ['red', 'green', 'blue'].

2. Step 2: Understand array_pop effect

   array_pop removes and returns the last element 'blue', so array becomes ['red', 'green'] and $last = 'blue'.

3. Final Answer:

   Array ( [0] => red [1] => green ) blue -> Option B

4. Quick Check:

   push adds, pop removes last [OK]

Hint: Push adds last, pop removes last [OK]

Common Mistakes:

• Thinking pop removes first element
• Expecting array to still have 'blue'
• Confusing printed array and echoed value

4. Identify the error in the following PHP code snippet:

$numbers = [1, 2, 3];
array_pop($numbers, 2);
print_r($numbers);

medium

A. No error, code works fine

B. array_pop should be called before array initialization

C. array_pop accepts only one argument, extra argument causes error

D. array_pop cannot be used on numeric arrays

Solution

1. Step 1: Check array_pop function signature

   array_pop accepts only one argument: the array variable.

2. Step 2: Analyze the code

   Passing a second argument (2) is invalid and will cause an error.

3. Final Answer:

   array_pop accepts only one argument, extra argument causes error -> Option C

4. Quick Check:

   array_pop(array) only one argument [OK]

Hint: array_pop takes exactly one argument [OK]

Common Mistakes:

• Passing multiple arguments to array_pop
• Thinking array_pop removes multiple elements
• Assuming no error on extra arguments

5. Given an empty array $stack = [];, which sequence of PHP statements correctly adds 'first', 'second', then removes the last added element and stores it in $removed?

hard

A. array_push($stack, 'first'); array_push($stack, 'second'); $removed = array_pop($stack);

B. $removed = array_pop($stack); array_push($stack, 'first'); array_push($stack, 'second');

C. array_pop($stack, 'first'); array_pop($stack, 'second'); $removed = array_push($stack);

D. array_push('first', $stack); array_push('second', $stack); $removed = array_pop($stack);

Solution

1. Step 1: Add elements in correct order

   Use array_push($stack, 'first') and then array_push($stack, 'second') to add elements to the stack.

2. Step 2: Remove last element and store it

   Use $removed = array_pop($stack); to remove and save the last added element ('second').

3. Final Answer:

   array_push($stack, 'first'); array_push($stack, 'second'); $removed = array_pop($stack); -> Option A

4. Quick Check:

   Push adds, pop removes last [OK]

Hint: Push then pop to simulate stack behavior [OK]

Common Mistakes:

• Calling array_pop before pushing elements
• Passing arguments in wrong order
• Using array_pop with extra arguments