Intersection types in PHP - Time & Space Complexity

Time Complexity: Intersection types

O(n)

Understanding Time Complexity

When using intersection types in PHP, it's important to understand how checking multiple type conditions affects performance.

We want to know how the time to verify these types grows as we add more types to check.

Scenario Under Consideration

Analyze the time complexity of the following PHP code that checks intersection types.

function checkIntersection(object $obj): bool {
    return $obj instanceof InterfaceA
        && $obj instanceof InterfaceB
        && $obj instanceof InterfaceC;
}
    

This function checks if an object implements all three interfaces using intersection types.

Identify Repeating Operations

Look at what repeats when checking intersection types.

• Primary operation: Three separate instanceof checks.
• How many times: Each check runs once per function call, so 3 times total.

How Execution Grows With Input

As the number of interfaces to check grows, the number of instanceof checks grows too.

Number of Interfaces (n)	Approx. Checks
3	3 checks
10	10 checks
100	100 checks

Pattern observation: The checks increase directly with the number of interfaces to verify.

Final Time Complexity

Time Complexity: O(n)

This means the time to check intersection types grows linearly with how many types you check.

Common Mistake

[X] Wrong: "Checking multiple interfaces is done all at once, so it takes the same time as one check."

[OK] Correct: Each interface check runs separately, so more interfaces mean more checks and more time.

Interview Connect

Understanding how intersection type checks scale helps you write clear and efficient code, showing you know how PHP handles multiple type conditions.

Self-Check

"What if we used union types instead of intersection types? How would the time complexity change?"