Multidimensional arrays in PHP - Time & Space Complexity

Time Complexity: Multidimensional arrays

O(n * m)

Understanding Time Complexity

When working with multidimensional arrays, it is important to understand how the time to process them grows as the array size increases.

We want to know how the number of steps changes when we access or loop through all elements in these arrays.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

$matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
];

foreach ($matrix as $row) {
    foreach ($row as $value) {
        echo $value . " ";
    }
}

This code loops through a 2D array (a matrix) and prints each value.

Identify Repeating Operations

• Primary operation: Nested loops over rows and columns of the array.
• How many times: Outer loop runs once per row, inner loop runs once per element in each row.

How Execution Grows With Input

As the number of rows and columns grows, the total steps grow by multiplying these sizes.

Input Size (rows x columns)	Approx. Operations
10 x 10	100
100 x 100	10,000
1000 x 1000	1,000,000

Pattern observation: The total operations grow by the product of rows and columns, so doubling both makes the work much larger.

Final Time Complexity

Time Complexity: O(n * m)

This means the time grows proportionally to the number of rows times the number of columns in the array.

Common Mistake

[X] Wrong: "The time complexity is just O(n) because there is only one loop inside the other."

[OK] Correct: Each element in every row is visited, so the total steps multiply, not add. The nested loops multiply the work.

Interview Connect

Understanding how nested loops affect time helps you explain and optimize code that works with tables, grids, or matrices in real projects.

Self-Check

"What if the inner arrays had different lengths? How would the time complexity change?"

Practice

1. What is a multidimensional array in PHP?

easy

A. An array containing one or more arrays inside it

B. An array with only string keys

C. An array that can only hold numbers

D. An array that cannot be changed after creation

Solution

1. Step 1: Understand array nesting

   A multidimensional array is an array that contains other arrays as its elements.

2. Step 2: Identify the correct definition

   An array containing one or more arrays inside it correctly describes this nesting, while others describe unrelated properties.

3. Final Answer:

   An array containing one or more arrays inside it -> Option A

4. Quick Check:

   Multidimensional array = nested arrays [OK]

Hint: Think of arrays inside arrays like boxes within boxes [OK]

Common Mistakes:

• Confusing multidimensional arrays with simple arrays
• Thinking keys must be strings only
• Believing arrays cannot be changed

2. Which of the following is the correct way to access the element 'blue' in this array?

$colors = [['red', 'green'], ['blue', 'yellow']];

easy

A. $colors[1][0]

B. $colors[0][2]

C. $colors[2][1]

D. $colors[1][1]

Solution

1. Step 1: Identify the position of 'blue'

   'blue' is in the second inner array (index 1) and is the first element (index 0) there.

2. Step 2: Use correct indices to access

   Accessing $colors[1][0] retrieves 'blue'. Other options point to wrong indices or elements.

3. Final Answer:

   $colors[1][0] -> Option A

4. Quick Check:

   Second array, first element = 'blue' [OK]

Hint: Count arrays and elements starting at zero [OK]

Common Mistakes:

• Using wrong index numbers
• Confusing first and second arrays
• Trying to access non-existing elements

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

$matrix = [[1, 2], [3, 4]];
echo $matrix[0][1] + $matrix[1][0];

medium

A. 9

B. 7

C. 5

D. Error

Solution

1. Step 1: Identify the values at given indices

   $matrix[0][1] is 2 and $matrix[1][0] is 3.

2. Step 2: Calculate the sum

   2 + 3 equals 5, so the output is 5.

3. Final Answer:

   5 -> Option C

4. Quick Check:

   2 + 3 = 5 [OK]

Hint: Add values at given indices carefully [OK]

Common Mistakes:

• Mixing up indices
• Adding wrong elements
• Expecting string output

4. Find the error in this code snippet:

$arr = [[1, 2], [3, 4];
echo $arr[1][1];

medium

A. Missing closing bracket for the first array

B. Missing closing bracket for the outer array

C. Incorrect index used to access element

D. Missing semicolon after echo statement

Solution

1. Step 1: Check array syntax

   The array starts with [[ but only one closing bracket ] is present before the semicolon.

2. Step 2: Identify missing bracket

   The outer array requires a closing bracket ], so the code should end with ]];

3. Final Answer:

   Missing closing bracket for the outer array -> Option B

4. Quick Check:

   Outer array brackets must match [OK]

Hint: Count opening and closing brackets carefully [OK]

Common Mistakes:

• Confusing inner and outer brackets
• Ignoring syntax errors
• Assuming semicolon fixes bracket issues

5. Given this multidimensional array representing students and their scores:
<pre>$students = [
['name' => 'Alice', 'scores' => [85, 90]],
['name' => 'Bob', 'scores' => [78, 82]],
['name' => 'Charlie', 'scores' => [92, 88]]
];

Which code correctly calculates and prints the average score of Bob?

hard

A. $avg = array_sum($students[2]['scores']) / count($students[2]['scores']);echo $avg;

B. $avg = array_sum($students['Bob']['scores']) / count($students['Bob']['scores']);echo $avg;

C. $avg = array_sum($students[1]['score']) / count($students[1]['score']);echo $avg;

D. $avg = array_sum($students[1]['scores']) / count($students[1]['scores']);echo $avg;

Solution

1. Step 1: Locate Bob's data in the array

   Bob is at index 1, and his scores are under the key 'scores'.

2. Step 2: Calculate average correctly

   Use array_sum and count on $students[1]['scores'] to get average. $avg = array_sum($students[1]['scores']) / count($students[1]['scores']);
   echo $avg; does this correctly.

3. Final Answer:

   $avg = array_sum($students[1]['scores']) / count($students[1]['scores']); echo $avg; -> Option D

4. Quick Check:

   Index 1 and 'scores' key used correctly [OK]

Hint: Use numeric index for array, string keys for inner arrays [OK]

Common Mistakes:

• Using string key for outer array
• Misspelling 'scores' key
• Using wrong index for Bob