How do you solve Number of Ways to Buy Pens and Pencils on LeetCode?

Number of Ways to Buy Pens and Pencils (LeetCode #2240) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Fixing one variable (pencils or pens) allows for a more efficient calculation of the other.

What is the brute force solution for Number of Ways to Buy Pens and Pencils?

The brute force approach for Number of Ways to Buy Pens and Pencils is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying every possible combination of pens and pencils you can buy with the given total amount. This means iterating through all possible quantities of pens and calculating how many pencils can be bought with the remaining money. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Number of Ways to Buy Pens and Pencils?

Number of Ways to Buy Pens and Pencils uses the following concepts: Math, Enumeration. The recommended patterns to study are: Enumeration, Dynamic Programming.

What are the interview tips for Number of Ways to Buy Pens and Pencils?

Always start with a brute force solution to understand the problem better. Look for patterns in how the quantities of items relate to the total money available. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Number of Ways to Buy Pens and Pencils?

Not considering the case where no items can be bought (i.e., when total is less than both costs). Overcomplicating the counting logic by not simplifying the problem into manageable parts.

#2240

Number of Ways to Buy Pens and Pencils

Medium

MathEnumerationEnumerationDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution leverages the idea of fixing the number of pencils and calculating the maximum number of pens that can be bought with the remaining money. This reduces the number of iterations significantly.

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Algorithm

5 steps

1Step 1: Initialize a counter for the number of ways.
2Step 2: Loop through all possible quantities of pencils you can buy (from 0 to total // cost2).
3Step 3: For each quantity of pencils, calculate the remaining money and determine how many pens can be bought with that money.
4Step 4: For each valid quantity of pens, increment the counter.
5Step 5: Return the counter as the result.

solution.py6 lines

1def countWays(total, cost1, cost2):
2    count = 0
3    for pencils in range(total // cost2 + 1):
4        remaining = total - pencils * cost2
5        count += remaining // cost1 + 1
6    return count

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Complexity note: The time complexity is O(n) because we only loop through the number of pencils, and for each pencil count, we perform a constant time operation to calculate the number of pens.

1Fixing one variable (pencils or pens) allows for a more efficient calculation of the other.
2Understanding the relationship between total money and the costs of items is crucial for optimizing the solution.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.