0600EasyArraySimulation

Graduated Service Levy

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Trains the technique from

LeetCode 2303Calculate Amount Paid in Taxes

This is an original problem, written from a brief that listed the technique, the difficulty, the topics, the function shape and the input bounds — none of that problem's wording, examples, hints or editorials. The link is there so you can map your practice onto the standard set.

Same function shape, different story and different numbers.

A credit union bills its members a graduated service levy against their declared annual income.

You are handed the schedule as brackets. Entry i of it holds two numbers: a ceiling upper_i followed by a rate percent_i, and together they describe the i-th band of the schedule. The bands are listed with upper_i increasing. Band 0 covers income from 0 up to and including upper_0. For i > 0, band i covers the income above upper_(i-1) up to and including upper_i. Whatever portion of the income lands inside band i is billed at percent_i percent of that portion.

Given a member's income, return the levy owed on it.

The levy always works out to a whole number of hundredths of a currency unit. Return it as a decimal number; an answer is accepted when it is within 10^-5 of the correct levy.

Examples

Example 1

Input: brackets = [[3, 50], [7, 10], [12, 25]], income = 10
Output: 2.65

The first 3 of income is billed at 50 percent, giving 1.5. The next 4 is billed at 10 percent, giving 0.4. The remaining 3 falls in the third band at 25 percent, giving 0.75. Altogether that is 2.65.

Example 2

Input: brackets = [[4, 0], [9, 100]], income = 9
Output: 5.0

The first 4 of income attracts nothing, and the remaining 5 is billed in full, so the levy is 5.0.

Example 3

Input: brackets = [[500, 20], [1000, 40]], income = 100
Output: 20.0

All 100 of income sits inside the first band, so it is billed at 20 percent for a levy of 20.0. The second band is never reached.

Constraints

1 <= brackets.length <= 100
1 <= upper_i <= 1000
0 <= percent_i <= 100
0 <= income <= 1000
upper_i is sorted in ascending order.
All the values of upper_i are unique.
The upper bound of the last band is greater than or equal to income.

The signature

The editor is preloaded with this. It matches the parent problem's shape, so a solution that works here transfers to a judge unchanged.

Python

def calculate_tax(brackets: list[list[int]], income: int) -> float:

Java

public double calculateTax(int[][] brackets, int income)

The intended approach

Time O(b) where b is the number of bands.Space O(1) beyond the input.

Walk the bands in the order given, remembering the top of the previous band as the floor of the current one. The portion charged in a band is the band's top, clipped at the member's income, minus that floor; once the clipped top no longer rises above the floor the income is exhausted and the walk stops. Each portion contributes `portion * percent` hundredths of a unit, kept as a whole number so nothing is rounded mid-way, and the single division by 100 happens at the end.

Pythonentry point: calculate_tax

def calculate_tax(brackets, income):
    # O(b) time, O(1) space. Accumulate the levy in hundredths as a whole number
    # so nothing is rounded on the way, and divide by 100 exactly once at the end.
    hundredths = 0
    floor = 0
    for upper, percent in brackets:
        ceiling = upper if upper < income else income
        width = ceiling - floor
        if width <= 0:
            break
        hundredths += width * percent
        floor = upper
    return hundredths / 100.0

The obvious version

Charge the income one whole unit at a time: for each unit from 1 to income, scan the bands to find the first whose top is at least that unit, and add that band's percent to a running count of hundredths. Divide by 100 at the end.

This is not filler. It was written independently of the fast solution and the two were run against thousands of random inputs to confirm they agree — which is how the answer above is known to be right. Read it when the intended approach feels like a rabbit pulled out of a hat.

Python

def bf_calculate_tax(brackets, income):
    hundredths = 0
    for unit in range(1, income + 1):
        for upper, percent in brackets:
            if unit <= upper:
                hundredths += percent
                break
    return hundredths / 100.0

How this problem was checked

Reference solution executed against 12 test cases — 12 passed
3 worked examples confirmed by running the code
0 eight-word sequences shared with the parent problem's text
Agrees with an independent brute-force implementation on random inputs
Test set proven to catch deliberately broken solutions
Reviewed by a separate quality pass
Function arity matches the parent problem's

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