LeetCode #2303 — EASY

Calculate Amount Paid in Taxes

Build confidence with an intuition-first walkthrough focused on array fundamentals.

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The Problem

Problem Statement

You are given a 0-indexed 2D integer array brackets where brackets[i] = [upperi, percenti] means that the ith tax bracket has an upper bound of upperi and is taxed at a rate of percenti. The brackets are sorted by upper bound (i.e. upperi-1 < upperi for 0 < i < brackets.length).

Tax is calculated as follows:

  • The first upper0 dollars earned are taxed at a rate of percent0.
  • The next upper1 - upper0 dollars earned are taxed at a rate of percent1.
  • The next upper2 - upper1 dollars earned are taxed at a rate of percent2.
  • And so on.

You are given an integer income representing the amount of money you earned. Return the amount of money that you have to pay in taxes. Answers within 10-5 of the actual answer will be accepted.

Example 1:

Input: brackets = [[3,50],[7,10],[12,25]], income = 10
Output: 2.65000
Explanation:
Based on your income, you have 3 dollars in the 1st tax bracket, 4 dollars in the 2nd tax bracket, and 3 dollars in the 3rd tax bracket.
The tax rate for the three tax brackets is 50%, 10%, and 25%, respectively.
In total, you pay $3 * 50% + $4 * 10% + $3 * 25% = $2.65 in taxes.

Example 2:

Input: brackets = [[1,0],[4,25],[5,50]], income = 2
Output: 0.25000
Explanation:
Based on your income, you have 1 dollar in the 1st tax bracket and 1 dollar in the 2nd tax bracket.
The tax rate for the two tax brackets is 0% and 25%, respectively.
In total, you pay $1 * 0% + $1 * 25% = $0.25 in taxes.

Example 3:

Input: brackets = [[2,50]], income = 0
Output: 0.00000
Explanation:
You have no income to tax, so you have to pay a total of $0 in taxes.

Constraints:

  • 1 <= brackets.length <= 100
  • 1 <= upperi <= 1000
  • 0 <= percenti <= 100
  • 0 <= income <= 1000
  • upperi is sorted in ascending order.
  • All the values of upperi are unique.
  • The upper bound of the last tax bracket is greater than or equal to income.

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given a 0-indexed 2D integer array brackets where brackets[i] = [upperi, percenti] means that the ith tax bracket has an upper bound of upperi and is taxed at a rate of percenti. The brackets are sorted by upper bound (i.e. upperi-1 < upperi for 0 < i < brackets.length). Tax is calculated as follows: The first upper0 dollars earned are taxed at a rate of percent0. The next upper1 - upper0 dollars earned are taxed at a rate of percent1. The next upper2 - upper1 dollars earned are taxed at a rate of percent2. And so on. You are given an integer income representing the amount of money you earned. Return the amount of money that you have to pay in taxes. Answers within 10-5 of the actual answer will be accepted.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

[[3,50],[7,10],[12,25]]
10

Example 2

[[1,0],[4,25],[5,50]]
2

Example 3

[[2,50]]
0
Step 02

Core Insight

What unlocks the optimal approach

  • As you iterate through the tax brackets, keep track of the previous tax bracket’s upper bound in a variable called prev. If there is no previous tax bracket, use 0 instead.
  • The amount of money in the ith tax bracket is min(income, upperi) - prev.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2303: Calculate Amount Paid in Taxes
class Solution {
    public double calculateTax(int[][] brackets, int income) {
        int ans = 0, prev = 0;
        for (var e : brackets) {
            int upper = e[0], percent = e[1];
            ans += Math.max(0, Math.min(income, upper) - prev) * percent;
            prev = upper;
        }
        return ans / 100.0;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(1)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED
O(n) time
O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.