Buy Candy - JavaScript Solution and Time Complexity Analysis

A box of candy costs price dollars. You have balance dollars. Compute the number of boxes of candy you can buy and return how many more dollars you need to buy one more box of candy.

Example:

Input: price = 4, balance = 9

Output: 3

Explanation:
You can buy two boxes of candy that costs 4 * 2 = 8 dollars.
If you would have 12 dollars you could buy 3 boxes (one more), so you would need 3 more dollars.

Understanding the Problem

The core challenge of this problem is to determine how many boxes of candy you can buy with a given amount of money and how much more money you would need to buy one additional box. This problem is straightforward but requires careful handling of integer division and basic arithmetic operations.

Common applications of this problem include budgeting scenarios, resource allocation, and financial planning where you need to determine how much more of a resource is required to achieve a goal.

Potential pitfalls include incorrect handling of integer division and not properly calculating the additional amount needed for one more box.

Approach

To solve this problem, we can break it down into the following steps:

Calculate the number of boxes you can buy with the given balance.
Determine the total cost if you were to buy one more box.
Calculate the difference between the required amount for one more box and the current balance.

Let's start with a naive solution and then optimize it.

Naive Solution

The naive solution involves directly performing the calculations as described. This approach is simple and works well for this problem since the operations involved are basic arithmetic.

Optimized Solution

The optimized solution follows the same steps but ensures that the calculations are done efficiently and correctly. Given the simplicity of the problem, the naive solution is already optimal.

Algorithm

Here is a step-by-step breakdown of the algorithm:

Calculate the number of boxes you can buy: boxes = Math.floor(balance / price).
Calculate the total cost for one more box: balanceNeeded = (boxes + 1) * price.
Calculate the additional amount needed: additionalAmount = balanceNeeded - balance.

Code Implementation

// Function to calculate the number of boxes and additional amount needed
function buyCandy(price, balance) {
    // Calculate the number of boxes that can be bought
    const boxes = Math.floor(balance / price);
    
    // Calculate the total cost for one more box
    const balanceNeeded = (boxes + 1) * price;
    
    // Calculate the additional amount needed
    const additionalAmount = balanceNeeded - balance;
    
    // Return the additional amount needed
    return additionalAmount;
}

// Example usage:
const price = 4;
const balance = 9;
console.log(buyCandy(price, balance)); // Output: 3

Complexity Analysis

The time complexity of this solution is O(1) because it involves a constant number of arithmetic operations. The space complexity is also O(1) as it uses a fixed amount of additional space for variables.

Edge Cases

Potential edge cases include:

balance is less than price: The function should correctly return the difference between price and balance.
balance is exactly a multiple of price: The function should return the price as the additional amount needed.

Examples:

buyCandy(4, 3); // Output: 1
buyCandy(4, 8); // Output: 4

Testing

To test the solution comprehensively, consider the following test cases:

Simple cases where balance is less than, equal to, and greater than price.
Edge cases where balance is zero or a negative number (if applicable).
Large values of price and balance to ensure the solution handles them correctly.

Example test cases:

console.log(buyCandy(4, 3)); // Output: 1
console.log(buyCandy(4, 8)); // Output: 4
console.log(buyCandy(4, 0)); // Output: 4
console.log(buyCandy(4, 12)); // Output: 4

Thinking and Problem-Solving Tips

When approaching such problems, consider the following tips:

Break down the problem into smaller, manageable steps.
Think about edge cases and how your solution handles them.
Write pseudo-code or diagrams to visualize the problem and solution.
Test your solution with a variety of inputs to ensure its correctness.

To improve problem-solving skills, practice solving similar problems and study different algorithms and their applications.

Conclusion

In this blog post, we discussed how to solve the problem of determining how many boxes of candy you can buy with a given balance and how much more money you need to buy one more box. We provided a detailed explanation of the algorithm, code implementation, complexity analysis, and testing strategies. Understanding and solving such problems is crucial for developing strong problem-solving skills and improving algorithmic thinking.

Additional Resources

For further reading and practice problems, consider the following resources: