How do I calculate taxes when income partially fills the last bracket?

Subtract the previous bracket's upper bound from your income within the current bracket, multiply by the rate, and stop accumulating once all income is taxed.

Why track the previous bracket's upper limit in this array simulation?

Tracking prev allows you to compute the taxable portion per bracket correctly, avoiding over-taxing amounts already accounted for.

What if the brackets are not sorted?

You must sort the brackets by upper bound first to ensure the simulation applies tax rates in the correct order.

Can floating point errors affect the final tax?

Yes, use proper decimal arithmetic or floating-point variables to accumulate tax accurately until the final calculation.

Does this problem follow the Array plus Simulation pattern?

Exactly, the problem requires iterating through an array of brackets and simulating tax computation, making it a classic Array plus Simulation use case.

#2303

Easy

auto_awesome数组·模拟

LeetCode 题解工作台

计算应缴税款总额

给你一个下标从 0 开始的二维整数数组 brackets ，其中 brackets[i] = [upper i , percent i ] ，表示第 i 个税级的上限是 upper i ，征收的税率为 percent i 。税级按上限从低到高排序（在满足 0 的前提下， upper i-1 i …

数组模拟

题目描述

给你一个下标从 0 开始的二维整数数组 brackets ，其中 brackets[i] = [upper_i, percent_i] ，表示第 i 个税级的上限是 upper_i ，征收的税率为 percent_i 。税级按上限 从低到高排序（在满足 0 < i < brackets.length 的前提下，upper_i-1 < upper_i）。

税款计算方式如下：

不超过 upper₀ 的收入按税率 percent₀ 缴纳
接着 upper₁ - upper₀ 的部分按税率 percent₁ 缴纳
然后 upper₂ - upper₁ 的部分按税率 percent₂ 缴纳
以此类推

给你一个整数 income 表示你的总收入。返回你需要缴纳的税款总额。与标准答案误差不超 10^-5 的结果将被视作正确答案。

示例 1：

输入：brackets = [[3,50],[7,10],[12,25]], income = 10
输出：2.65000
解释：
前 $3 的税率为 50% 。需要支付税款 $3 * 50% = $1.50 。
接下来 $7 - $3 = $4 的税率为 10% 。需要支付税款 $4 * 10% = $0.40 。
最后 $10 - $7 = $3 的税率为 25% 。需要支付税款 $3 * 25% = $0.75 。
需要支付的税款总计 $1.50 + $0.40 + $0.75 = $2.65 。

示例 2：

输入：brackets = [[1,0],[4,25],[5,50]], income = 2
输出：0.25000
解释：
前 $1 的税率为 0% 。需要支付税款 $1 * 0% = $0 。
剩下 $1 的税率为 25% 。需要支付税款 $1 * 25% = $0.25 。
需要支付的税款总计 $0 + $0.25 = $0.25 。

示例 3：

输入：brackets = [[2,50]], income = 0
输出：0.00000
解释：
没有收入，无需纳税，需要支付的税款总计 $0 。

提示：

1 <= brackets.length <= 100
1 <= upper_i <= 1000
0 <= percent_i <= 100
0 <= income <= 1000
upper_i 按递增顺序排列
upper_i 中的所有值 互不相同
最后一个税级的上限大于等于 income

lightbulb

解题思路

方法一：模拟

我们遍历 brackets，对于每个税级，计算该税级的税额，然后累加即可。

时间复杂度 $O(n)$ ，其中 $n$ 为 brackets 的长度。空间复杂度 $O(1)$ 。

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class Solution:
    def calculateTax(self, brackets: List[List[int]], income: int) -> float:
        ans = prev = 0
        for upper, percent in brackets:
            ans += max(0, min(income, upper) - prev) * percent
            prev = upper
        return ans / 100

speed

复杂度分析

指标	值
时间	complexity is O(n) where n is the number of tax brackets, since each bracket is processed once. Space complexity is O(1) because only a few variables like prev and total tax are needed.
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
They may ask you to explain why you track the previous bracket's upper bound.
question_mark
They might probe your handling of income that exactly matches a bracket's upper bound.
question_mark
They could test understanding of precision by providing rates or income that produce fractional taxes.

warning

常见陷阱

外企场景

error
Forgetting to subtract the previous upper bound when calculating the taxable portion in a bracket.
error
Continuing to compute tax for brackets when income is already fully taxed.
error
Rounding intermediate calculations instead of maintaining precision until the final total.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Compute taxes with brackets given in descending order, requiring sorting first.
arrow_right_alt
Calculate tax when brackets may overlap or have missing ranges, requiring conditional checks.
arrow_right_alt
Determine total after applying deductions before applying the bracketed tax simulation.

help

常见问题

外企场景

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