Problem Description

This problem asks you to implement a Calculator class that supports basic mathematical operations and method chaining.

The Calculator class should:

1. Initialize with a starting value: The constructor takes a number that becomes the initial result value.

2. Support five mathematical operations, each returning the Calculator instance for chaining:

   • add(value): Adds value to the current result
   • subtract(value): Subtracts value from the current result
   • multiply(value): Multiplies the current result by value
   • divide(value): Divides the current result by value (must throw error "Division by zero is not allowed" if value is 0)
   • power(value): Raises the current result to the power of value

3. Provide a way to retrieve the result: The getResult() method returns the current calculated value.

4. Enable method chaining: All operation methods return this (the Calculator instance), allowing consecutive operations like:

   calculator.add(5).multiply(2).subtract(3).getResult()

The solution uses a private property x to store the current result. Each operation method modifies x and returns this to enable chaining. The divide method includes validation to prevent division by zero. The getResult method simply returns the current value of x.

Results within 10^-5 of the actual answer are considered correct, accounting for floating-point precision issues.

Intuition

The key insight for this problem is recognizing that method chaining requires each method to return the object itself. When we call calculator.add(5).multiply(2), the add(5) method must return the calculator object so that we can immediately call multiply(2) on it.

To achieve this pattern, we need:

1. State preservation: A single variable to hold the running result throughout all operations. This is why we use a private property x to maintain the current value across method calls.

2. Return this pattern: Each operation method performs its calculation on the stored value and then returns this (the current instance). This is the fundamental pattern that enables method chaining - by returning the object itself, we allow the next method to be called on the same object.

3. Mutating operations: Instead of creating new Calculator instances, we modify the existing instance's state. This makes sense because we want a continuous calculation flow where each operation builds upon the previous result.

The design follows the Fluent Interface pattern, commonly used in builder patterns and query builders. The idea is to make the code read more naturally, almost like a sentence: "take this number, add 5, multiply by 2, subtract 3, and give me the result."

For the division by zero check, we handle this explicitly before performing the division since JavaScript would return Infinity for division by zero, which isn't the desired behavior. By throwing an error with the exact message required, we prevent invalid mathematical operations while maintaining the chainable interface (the error stops the chain execution).

The getResult() method breaks the chain by returning a number instead of the Calculator instance, which makes logical sense as it's the terminating operation to retrieve our final answer.

Solution Approach

The implementation uses a class-based approach with a single private property to maintain state and instance methods that return this for chaining.

Core Structure:

1. Private property x: Stores the current calculation result. Using a private property ensures encapsulation and prevents external modification.

2. Constructor: Initializes the x property with the provided starting value:

   constructor(value: number) {
       this.x = value;
   }

Implementation of Each Operation:

Each arithmetic method follows the same pattern:

• Perform the operation on this.x
• Return this to enable chaining

1. Addition: this.x += value adds the value to the current result

2. Subtraction: this.x -= value subtracts the value from the current result

3. Multiplication: this.x *= value multiplies the current result by the value

4. Division:

   divide(value: number): Calculator {
       if (value === 0) {
           throw new Error('Division by zero is not allowed');
       }
       this.x /= value;
       return this;
   }

   First checks for zero to prevent invalid operations, then performs this.x /= value

5. Power: this.x **= value raises the current result to the given power using the exponentiation operator

Result Retrieval: The getResult() method simply returns the current value of x without modifying it:

getResult(): number {
    return this.x;
}

Method Chaining Mechanism: By returning this from each operation method, we enable consecutive method calls:

new Calculator(10)
    .add(5)      // x becomes 15, returns this
    .multiply(2) // x becomes 30, returns this
    .divide(3)   // x becomes 10, returns this
    .getResult() // returns 10

The solution is straightforward and efficient with O(1) time complexity for each operation and O(1) space complexity for the entire calculator instance.

Example Walkthrough

Let's walk through a calculation step-by-step: new Calculator(2).add(5).multiply(3).subtract(4).divide(2).getResult()

Step 1: Initialize

new Calculator(2)

• Creates a new Calculator instance
• Sets internal property x = 2
• Current state: x = 2

Step 2: Add 5

.add(5)

• Executes: this.x = this.x + 5 = 2 + 5 = 7
• Returns this (the Calculator instance)
• Current state: x = 7

Step 3: Multiply by 3

.multiply(3)

• Executes: this.x = this.x * 3 = 7 * 3 = 21
• Returns this (the Calculator instance)
• Current state: x = 21

Step 4: Subtract 4

.subtract(4)

• Executes: this.x = this.x - 4 = 21 - 4 = 17
• Returns this (the Calculator instance)
• Current state: x = 17

Step 5: Divide by 2

.divide(2)

• First checks: Is value === 0? No, proceed
• Executes: this.x = this.x / 2 = 17 / 2 = 8.5
• Returns this (the Calculator instance)
• Current state: x = 8.5

Step 6: Get Result

.getResult()

• Returns the current value of x
• Final answer: 8.5

Key Points:

• Each operation method modifies the same internal variable x
• Each operation returns this, allowing the next method to be called immediately
• The chain continues until getResult() is called, which returns a number instead of the Calculator instance
• If we tried .divide(0) at any point, it would throw an error and stop execution

Solution Implementation

Time and Space Complexity

Time Complexity: Each method (add, subtract, multiply, divide, power, getResult) performs a constant-time operation. The arithmetic operations and the assignment take O(1) time. The constructor also runs in O(1) time as it only initializes a single variable. Therefore, each individual method call has a time complexity of O(1).

For a chain of n method calls (e.g., calculator.add(5).multiply(2).subtract(3)...), the total time complexity would be O(n), where n is the number of operations performed.

Space Complexity: The Calculator class stores only a single number x as its state, regardless of how many operations are performed. The space used remains constant throughout the lifetime of the object. Each method returns this (a reference to the same object), so no additional Calculator objects are created during method chaining. Therefore, the space complexity is O(1).

The method chaining pattern (fluent interface) doesn't create new objects but modifies and returns the same instance, maintaining constant space usage.

Common Pitfalls

1. Global State Management Issues

The Python implementation uses a global variable calculator_value, which creates several problems:

• No support for multiple calculator instances: You can't have two calculators running independently
• State persistence between tests: The global value persists across different test cases, leading to incorrect results
• Thread safety concerns: Global state is not thread-safe for concurrent operations

Example of the problem:

initialize_calculator(10)
add(5)  # calculator_value = 15
# Start a "new" calculator
initialize_calculator(20)
# But if someone forgets to initialize, they get the old value!

2. Loss of Method Chaining

The provided Python solution doesn't support method chaining as required by the problem. You can't write:

# This won't work with the global function approach
result = Calculator(10).add(5).multiply(2).getResult()

3. Floating-Point Precision Issues

When performing division and power operations, floating-point arithmetic can introduce precision errors that might exceed the 10^-5 tolerance:

# Example: 0.1 + 0.2 != 0.3 in floating-point
calculator_value = 0.1
add(0.2)  # Might not exactly equal 0.3

Solution

Here's a proper class-based implementation that addresses these pitfalls:

class Calculator:
    def __init__(self, value: float):
        """Initialize calculator with a starting value"""
        self._result = float(value)  # Ensure float for consistency
  
    def add(self, value: float):
        """Add value to current result"""
        self._result += value
        return self  # Enable chaining
  
    def subtract(self, value: float):
        """Subtract value from current result"""
        self._result -= value
        return self
  
    def multiply(self, value: float):
        """Multiply current result by value"""
        self._result *= value
        return self
  
    def divide(self, value: float):
        """Divide current result by value"""
        if value == 0:
            raise ValueError('Division by zero is not allowed')
        self._result /= value
        return self
  
    def power(self, value: float):
        """Raise current result to the power of value"""
        self._result **= value
        return self
  
    def getResult(self) -> float:
        """Get the current result"""
        # Round to handle floating-point precision within 10^-5
        return round(self._result, 10)

# Usage example with proper chaining:
calc = Calculator(10)
result = calc.add(5).multiply(2).divide(3).getResult()
print(result)  # Output: 10.0

# Multiple independent instances work correctly:
calc1 = Calculator(10)
calc2 = Calculator(20)
calc1.add(5)
calc2.subtract(5)
print(calc1.getResult())  # 15.0
print(calc2.getResult())  # 15.0

Key improvements:

1. Instance-based state: Each Calculator object has its own _result property
2. Method chaining support: All operation methods return self
3. Proper encapsulation: Using _result as a private property
4. Floating-point handling: Converting input to float and rounding output for precision
5. Multiple instances: Can create and use multiple calculators independently