2620. Counter - Detailed Explanation

Problem Statement

Description:
Implement a function called counter that returns another function (a “counter function”). Each time the returned function is called, it should return an integer that increments by one, starting from 1.

How It Works:

• The first call returns 1.
• The second call returns 2.
• The third call returns 3, and so on.

The key idea is that the returned function must remember the count between calls. This is typically achieved using a closure (or a similar mechanism in languages that do not support closures directly).

Constraints:

• The counter starts at 1.
• The solution should use the idea of closure or an equivalent method to maintain state between calls.
• The function returned by counter should have O(1) time per call.

Example 1:

const counter1 = counter();
console.log(counter1()); // Output: 1
console.log(counter1()); // Output: 2
console.log(counter1()); // Output: 3

Example 2:

const counter2 = counter();
console.log(counter2()); // Output: 1
console.log(counter2()); // Output: 2

Note: Each counter instance maintains its own state.

Hints

• Hint 1: Think about how to use a closure to capture a variable that tracks the current count. In languages like JavaScript and Python, you can define an inner function that accesses a variable defined in an outer function.
• Hint 2: Make sure the counter variable is not re-initialized on every call of the inner function. It must persist between calls.
• Hint 3: In Python, remember to use the nonlocal keyword when modifying a variable defined in an outer (but non-global) scope.

Approaches

Closure-Based Approach (Optimal)

Idea:
Define a function counter that initializes a counter variable (starting at 0) and returns an inner function. This inner function increments the counter variable and returns its value each time it is called.

Steps:

1. In the outer function counter, initialize a variable (e.g., count) to 0.
2. Define an inner function (e.g., increment) that:
   • Increments the count variable.
   • Returns the updated value.
3. Return the inner function from counter. The inner function “remembers” the variable count between calls.

Why It Works:
The inner function has access to the count variable in its lexical scope. Each call to the inner function updates this variable, thus producing the next number in the sequence.

Alternative Variations

• Using a Class or Object:
  Instead of using a closure, you could define a class that encapsulates the count as an instance variable and provides a method (e.g., next()) to increment and return the count. This approach is common in languages without first-class function closures (or if object-oriented design is preferred).

• Functional Programming Variations:
  Some functional languages may use stateful constructs or monads to achieve a similar effect without mutable state.

Detailed Walkthrough (Closure-Based Approach)

Let’s walk through the closure approach using a Python-like pseudocode:

1. Initialization in the Outer Function:

   • Define a variable count and initialize it to 0.

2. Define the Inner Function:

   • The inner function, say increment, uses the variable count from the outer scope.
   • When increment is called, it increases count by 1 and returns the new value.
   • In Python, use the nonlocal keyword to indicate that count is defined in an outer scope.

3. Return the Inner Function:

   • The function counter returns increment, which retains access to the variable count.

4. Example Execution:

   • When you create a counter instance by calling counter(), a new copy of count is created.
   • Calling the returned function repeatedly yields: 1, 2, 3, etc.

Code Implementation

Python Code