How do you solve Calculate Amount Paid in Taxes on LeetCode?

Calculate Amount Paid in Taxes (LeetCode #2303) 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: Understanding how tax brackets work is crucial for calculating taxes accurately.

What is the time complexity of Calculate Amount Paid in Taxes?

The optimal solution for Calculate Amount Paid in Taxes runs in O(n) time and uses O(1) space. The complexity is O(n) because we only loop through the brackets once, making it efficient for larger inputs.

What is the brute force solution for Calculate Amount Paid in Taxes?

The brute force approach for Calculate Amount Paid in Taxes is Brute Force, with O(n²) time complexity and O(1) space complexity. In this approach, we will iterate through each tax bracket and calculate the tax for each segment of income. This method is straightforward but inefficient as it checks each bracket even if the income is lower than the upper limit of some brackets. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Calculate Amount Paid in Taxes?

Calculate Amount Paid in Taxes uses the following concepts: Array, Simulation. The recommended patterns to study are: Array, Simulation.

What are the interview tips for Calculate Amount Paid in Taxes?

Clarify the problem statement and ask about edge cases. Think aloud while coding to show your thought process. Test your solution with different inputs to ensure accuracy.

What are common mistakes when solving Calculate Amount Paid in Taxes?

Not accounting for the case when income is less than the first bracket. Failing to break the loop once the income is fully taxed.

#2303

Calculate Amount Paid in Taxes

Easy

ArraySimulationArraySimulation

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)

This approach efficiently calculates the tax by iterating through the brackets just once, using a single loop. We keep track of the previous upper limit and only calculate the taxable income for the relevant brackets.

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Algorithm

4 steps

1Step 1: Initialize a variable 'tax' to 0 and 'prev' to 0.
2Step 2: Loop through each bracket, calculating the taxable income based on the current income and the previous upper limit.
3Step 3: If the income exceeds the current bracket's upper limit, calculate the tax for that segment and update 'prev'.
4Step 4: If the income is less than the current bracket's upper limit, calculate the tax for the remaining income and break the loop.

solution.py11 lines

1def calculateTax(brackets, income):
2    tax = 0
3    prev = 0
4    for upper, percent in brackets:
5        if income > prev:
6            taxable_income = min(income, upper) - prev
7            tax += taxable_income * (percent / 100)
8            prev = upper
9        else:
10            break
11    return tax

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Complexity note: The complexity is O(n) because we only loop through the brackets once, making it efficient for larger inputs.

1Understanding how tax brackets work is crucial for calculating taxes accurately.
2The order of brackets matters; they must be processed sequentially.

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