Account Balance After Rounded Purchase

Difficulty: Easy | Acceptance: 56.40% | Paid: No Topics: Math

Initially, you have a bank account balance of 100 dollars.

You are given an integer purchaseAmount representing the amount you will spend on a single purchase in dollars.

At the store where you will make the purchase, the amount is rounded to the nearest multiple of 10. If the number ends in a 5 or greater, it is rounded up. If it ends in 4 or less, it is rounded down.

Return an integer representing the balance that remains in your bank account after your purchase.

• Examples
• Constraints
• Mathematical Rounding
• Modulo Arithmetic
• String Manipulation

Examples

Example 1

Input:

purchaseAmount = 9

Output:

90

Explanation: The nearest multiple of 10 to 9 is 10. So your account balance becomes 100 - 10 = 90.

Example 2

Input:

purchaseAmount = 15

Output:

80

Explanation: The nearest multiple of 10 to 15 is 20. So your account balance becomes 100 - 20 = 80.

Example 3

Input:

purchaseAmount = 10

Output:

90

Explanation: 10 is a multiple of 10 itself. So your account balance becomes 100 - 10 = 90.

Constraints

1 <= purchaseAmount <= 100

Mathematical Rounding

Intuition Use integer arithmetic to round the purchase amount to the nearest multiple of 10 by adding 5 and then dividing by 10.

Steps

• Add 5 to the purchase amount
• Perform integer division by 10
• Multiply by 10 to get the rounded amount
• Subtract from 100 to get the remaining balance

class Solution:
    def accountBalanceAfterPurchase(self, purchaseAmount: int) -> int:
        rounded = ((purchaseAmount + 5) // 10) * 10
        return 100 - rounded

Complexity

• Time: O(1)
• Space: O(1)
• Notes: Most efficient approach with constant time operations

Modulo Arithmetic

Intuition Extract the last digit using modulo operation and apply rounding rules based on whether it’s 5 or greater.

Steps

• Get the last digit using purchaseAmount % 10
• If last digit is 5 or more, round up by adding (10 - last digit)
• If last digit is less than 5, round down by subtracting last digit
• Return 100 minus the rounded amount

class Solution:
    def accountBalanceAfterPurchase(self, purchaseAmount: int) -> int:
        last_digit = purchaseAmount % 10
        if last_digit >= 5:
            rounded = purchaseAmount + (10 - last_digit)
        else:
            rounded = purchaseAmount - last_digit
        return 100 - rounded

Complexity

• Time: O(1)
• Space: O(1)
• Notes: Slightly more verbose but equally efficient

String Manipulation

Intuition Convert the number to a string to extract the last digit and apply rounding logic.

Steps

• Convert purchaseAmount to string
• Extract the last character and convert back to integer
• Apply rounding rules based on the last digit
• Return 100 minus the rounded amount

class Solution:
    def accountBalanceAfterPurchase(self, purchaseAmount: int) -> int:
        s = str(purchaseAmount)
        last_digit = int(s[-1])
        if last_digit >= 5:
            rounded = purchaseAmount + (10 - last_digit)
        else:
            rounded = purchaseAmount - last_digit
        return 100 - rounded

Complexity

• Time: O(1) - String operations are constant time for fixed-size integers
• Space: O(1) - String representation is bounded by input size
• Notes: Less efficient due to string conversion overhead