Prototype chain in Javascript - Time & Space Complexity

Time Complexity: Prototype chain

O(n)

Understanding Time Complexity

When we use the prototype chain in JavaScript, the computer looks up properties step by step along linked objects.

We want to know how the time to find a property changes as the chain gets longer.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

const grandparent = { a: 1 };
const parent = Object.create(grandparent);
parent.b = 2;
const child = Object.create(parent);
child.c = 3;

console.log(child.a); // looks up prototype chain
console.log(child.b);
console.log(child.c);
    

This code creates a chain of objects and accesses properties that may be on the object or its prototypes.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Searching for a property by checking each object in the prototype chain one by one.
• How many times: At most, the number of objects in the chain until the property is found or the chain ends.

How Execution Grows With Input

As the prototype chain gets longer, the time to find a property grows roughly in a straight line with the chain length.

Input Size (chain length)	Approx. Operations (property checks)
10	Up to 10 checks
100	Up to 100 checks
1000	Up to 1000 checks

Pattern observation: The time grows linearly as the chain length increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to find a property grows directly with the number of objects in the prototype chain.

Common Mistake

[X] Wrong: "Looking up a property is always instant, no matter how long the chain is."

[OK] Correct: The computer checks each object one by one until it finds the property, so longer chains take more time.

Interview Connect

Understanding how prototype chains affect lookup time helps you write efficient code and explain how JavaScript works under the hood.

Self-Check

"What if the property is always found on the first object in the chain? How would the time complexity change?"

Practice

1. What does the prototype chain in JavaScript help with?

easy

A. Sharing properties and methods between objects

B. Creating new variables automatically

C. Running code faster

D. Stopping code execution

Solution

1. Step 1: Understand prototype chain purpose

   The prototype chain allows objects to share properties and methods by linking them.

2. Step 2: Identify correct description

   Sharing properties and methods matches the prototype chain's role, unlike other options.

3. Final Answer:

   Sharing properties and methods between objects -> Option A

4. Quick Check:

   Prototype chain = Sharing properties and methods [OK]

Hint: Prototype chain shares properties/methods between objects [OK]

Common Mistakes:

• Thinking it creates variables
• Assuming it speeds up code
• Believing it stops code

2. Which of the following is the correct way to create an object with a specific prototype in JavaScript?

easy

A. let obj = prototypeObj.create();

B. let obj = Object.create(prototypeObj);

C. let obj = new Object(prototypeObj);

D. let obj = Object.prototype(prototypeObj);

Solution

1. Step 1: Recall Object.create syntax

   Object.create(prototypeObj) creates a new object with prototypeObj as its prototype.

2. Step 2: Check other options

   Other options use incorrect syntax or methods that don't exist.

3. Final Answer:

   let obj = Object.create(prototypeObj); -> Option B

4. Quick Check:

   Object.create() creates object with prototype [OK]

Hint: Use Object.create(prototype) to set prototype correctly [OK]

Common Mistakes:

• Using new Object() with prototype argument
• Calling create() on prototype object
• Trying to call Object.prototype as a function

3. What will be the output of this code?

const parent = { greet() { return 'Hello'; } };
const child = Object.create(parent);
console.log(child.greet());

medium

A. undefined

B. null

C. TypeError

D. 'Hello'

Solution

1. Step 1: Understand prototype lookup

   child has no greet method, so JavaScript looks up to parent where greet exists.

2. Step 2: Call greet method from parent

   Calling child.greet() runs parent.greet(), returning 'Hello'.

3. Final Answer:

   'Hello' -> Option D

4. Quick Check:

   Prototype lookup finds greet() = 'Hello' [OK]

Hint: If property missing, JS checks prototype chain [OK]

Common Mistakes:

• Expecting undefined because child lacks greet
• Thinking it causes error
• Assuming null is returned

4. Find the error in this code snippet:

const animal = { eats: true };
const rabbit = Object.create(animal);
rabbit.eats = false;
console.log(rabbit.eats);
console.log(animal.eats);

medium

A. No error; output is as expected

B. Object.create should not be used here

C. rabbit.eats does not override animal.eats

D. animal.eats is changed to false

Solution

1. Step 1: Understand property shadowing

   Setting rabbit.eats creates a new property on rabbit, shadowing animal.eats.

2. Step 2: Check outputs

   rabbit.eats logs false; animal.eats remains true. This is expected behavior.

3. Final Answer:

   No error; output is as expected -> Option A

4. Quick Check:

   Property shadowing works correctly [OK]

Hint: Setting property on child shadows parent's property [OK]

Common Mistakes:

• Thinking parent's property changes
• Believing Object.create is wrong here
• Expecting error from property override

5. You want to create a chain where child inherits from parent, and parent inherits from grandparent. Which code correctly sets this prototype chain?

hard

A. const grandparent = {};
const parent = Object.create(child);
const child = Object.create(parent);

B. const grandparent = {};
const parent = {};
const child = Object.create(parent);
child.__proto__ = grandparent;

C. const grandparent = {};
const parent = Object.create(grandparent);
const child = Object.create(parent);

D. const grandparent = {};
const parent = Object.create(grandparent);
const child = Object.create(grandparent);

Solution

1. Step 1: Set parent prototype to grandparent

   Using Object.create(grandparent) for parent sets grandparent as prototype.

2. Step 2: Set child prototype to parent

   Using Object.create(parent) for child sets parent as prototype, completing chain.

3. Step 3: Check other options

   B incorrectly overrides child's prototype to grandparent using __proto__, skipping parent; C creates a circular reference (child not defined when creating parent); D sets child directly to grandparent, skipping parent.

4. Final Answer:

   const grandparent = {}; const parent = Object.create(grandparent); const child = Object.create(parent); -> Option C

5. Quick Check:

   Prototype chain: child -> parent -> grandparent [OK]

Hint: Use Object.create in order from top to bottom [OK]

Common Mistakes:

• Setting child prototype to grandparent directly
• Reversing prototype chain order
• Using __proto__ instead of Object.create