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

The optimal solution has a time complexity of O(n).

What data structures are used to solve Calculate Amount Paid in Taxes?

This problem uses Array, Simulation. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Calculate Amount Paid in Taxes?

Insight 1: Iterating through the brackets: The solution needs to process each tax bracket sequentially, calculating the taxable amount within each bracket and adding the corresponding tax to the total. Insight 2: Handling partial bracket income: The income might not fully utilize the highest tax bracket; it might fall somewhere within a bracket. The solution must handle this partial income correctly.

Which companies ask LeetCode 2303. Calculate Amount Paid in Taxes in interviews?

This problem is frequently asked at Snowflake.

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Calculate Amount Paid in Taxes - LeetCode 2303 Solution

Q: How to solve Calculate Amount Paid in Taxes?

The provided code uses an iterative approach. It starts from the lowest tax bracket and iterates through the `brackets` array. For each bracket, it calculates the taxable income within that bracket by taking the minimum of the remaining `income` and the difference between the current bracket's `upper_bound` and the previous bracket's `upper_bound` (or 0 for the first bracket). The tax for that bracket is calculated and added to the running total. This process repeats until all the income is taxed or all brackets are processed. The function efficiently avoids redundant calculations.

Calculate Amount Paid in Taxes - Complete Solution Guide

Calculate Amount Paid in Taxes is LeetCode problem 2303, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given a 0-indexed 2D integer array brackets where brackets[i] = [upper i , percent i ] means that the i th tax bracket has an upper bound of upper i and is taxed at a rate of percent i . The brackets are sorted by upper bound (i.e. upper i-1 < upper i for 0 < i < brackets.length ). Tax is calculated as follows: The first upper 0 dollars earned are taxed at a rate of percent 0 . The next upper 1 - upper 0 dollars earned are taxed at a rate of percent 1 . The next upper 2 - upper 1 dollars

Detailed Explanation

The problem asks you to calculate the total tax owed on a given income based on a tiered tax bracket system. The input is a 2D array `brackets` where each inner array represents a tax bracket: `[upper_bound, tax_rate]`. `upper_bound` is the maximum income subject to that tax rate, and `tax_rate` is the percentage to apply within that bracket. The brackets are sorted by their upper bounds. The input also includes `income`, the total earnings. The output is the total tax payable, a floating-point number.

Solution Approach

The provided code uses an iterative approach. It starts from the lowest tax bracket and iterates through the `brackets` array. For each bracket, it calculates the taxable income within that bracket by taking the minimum of the remaining `income` and the difference between the current bracket's `upper_bound` and the previous bracket's `upper_bound` (or 0 for the first bracket). The tax for that bracket is calculated and added to the running total. This process repeats until all the income is taxed or all brackets are processed. The function efficiently avoids redundant calculations.

Step-by-Step Algorithm

Step 1: Initialize `tax` to 0.0 and `prev_upper` (or `prev`) to 0. `prev_upper` keeps track of the upper bound of the previously processed bracket.
Step 2: Iterate through the `brackets` array. For each bracket `[upper, percent]`, calculate the `taxable` income within that bracket. This is the minimum of the remaining `income` and (`upper - prev_upper`).
Step 3: Calculate the tax for the current bracket: `taxable * percent / 100.0`. Add this to the running `tax` total.
Step 4: Update the remaining `income`: Subtract the `taxable` amount from the `income`.
Step 5: Update `prev_upper`: Set `prev_upper` to the current bracket's `upper`.
Step 6: If the remaining `income` is 0, exit the loop early.
Step 7: Return the final `tax` value.

Key Insights

Insight 1: Iterating through the brackets: The solution needs to process each tax bracket sequentially, calculating the taxable amount within each bracket and adding the corresponding tax to the total.
Insight 2: Handling partial bracket income: The income might not fully utilize the highest tax bracket; it might fall somewhere within a bracket. The solution must handle this partial income correctly.
Insight 3: Efficient calculation: To minimize calculation, it's crucial to use a running variable to track previously processed income and calculate only the taxable amount within each current bracket

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Simulation.

Companies

Asked at: Snowflake.

Calculate Amount Paid in Taxes | LeetCode 2303

Easy

Array Simulation

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public double calculateTax(int[][] brackets, int income) {
        double tax = 0.0;
        int prev = 0;
        for (int[] bracket : brackets) {
            int upper = bracket[0];
            int percent = bracket[1];
            int taxable = Math.min(income, upper) - prev;
            if (taxable > 0) {
                tax += (double) taxable * percent / 100;
            }
            income -= taxable;
            if (income <= 0) {
                break;
            }
            prev = upper;
        }
        return tax;
    }
}

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Problem Info

Description

Problem 2303: Calculate Amount Paid in Taxes - Detailed explanation and solution approaches.

Topics

Array Simulation

Companies

Snowflake

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2303

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

7 steps

1
Step 1: Initialize `tax` to 0.0 and `prev_upper` (or `prev`) to 0. `prev_upper` keeps track of the upper bound of the previously processed bracket.
2
Step 2: Iterate through the `brackets` array. For each bracket `[upper, percent]`, calculate the `taxable` income within that bracket. This is the minimum of the remaining `income` and (`upper - prev_upper`).
3
Step 3: Calculate the tax for the current bracket: `taxable * percent / 100.0`. Add this to the running `tax` total.
4
Step 4: Update the remaining `income`: Subtract the `taxable` amount from the `income`.
5
Step 5: Update `prev_upper`: Set `prev_upper` to the current bracket's `upper`.
6
Step 6: If the remaining `income` is 0, exit the loop early.
7
Step 7: Return the final `tax` value.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is determined by the single loop that iterates through the `brackets` array. The space complexity is constant because only a few variables are used to store intermediate values.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Prefix Sum

Calculate a prefix sum array to store the cumulative tax rates for each income level. Then use binary search to find the bracket for a given income and directly calculate the tax using the prefix sum.

Time: O(log n + m) where n is the number of tax brackets, and m is the number of incomes.Space: O(n), to store the prefix sum array.

Trade-offs: This approach is better when dealing with many income calculations for the same bracket array. The initial prefix sum calculation adds overhead, so it's less efficient for a single income calculation.

✨

Key Insights

1Insight 1: Iterating through the brackets: The solution needs to process each tax bracket sequentially, calculating the taxable amount within each bracket and adding the corresponding tax to the total.
2Insight 2: Handling partial bracket income: The income might not fully utilize the highest tax bracket; it might fall somewhere within a bracket. The solution must handle this partial income correctly.
3Insight 3: Efficient calculation: To minimize calculation, it's crucial to use a running variable to track previously processed income and calculate only the taxable amount within each current bracket

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Edge case 1: `income` is 0: The code correctly handles this by immediately exiting the loop and returning 0.0.
Edge case 2: `income` is less than the upper bound of the first bracket: The code correctly calculates the tax based on only the first bracket's rate.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrect handling of partial bracket income: Beginners might incorrectly calculate the tax by applying the entire bracket's tax rate to the remaining income even if it's less than the bracket's range.

✗Common mistake 2: Off-by-one errors: Incorrectly managing indices or the boundary conditions of the brackets when calculating the taxable amounts could lead to errors.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Tax calculation software: This algorithm is directly applicable in tax software to calculate the tax owed by individuals based on their income and applicable tax brackets.

🏦Real-world scenario 2: Progressive pricing models: Many subscription services or utility companies use progressive pricing models where the price per unit changes based on the total consumption. This algorithm can be adapted to calculate the total cost based on consumption levels.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: October 22, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 13

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 6

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 29

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Calculate Amount Paid in Taxes"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether simulation techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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