math plus simulation Pattern
15 problems
Pattern pages help build reusable solving frames. Identify signals first, then explain state, transition, and edge handling.
Recognition Signals
- Candidate should show understanding of basic digit operations and how to optimize them.
- Look for recognition of number properties like digital roots and their use in optimization.
- Candidate should focus on simulating the candy distribution step by step.
Solve Flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common Misses
- Misunderstanding the problem and applying unnecessary loops or calculations.
- Misunderstanding the cyclical distribution process and giving candies in the wrong order.
- Failing to correctly simulate the bottle exchange and drinking process.
Recommended Ladder
Add Digits
Add Digits involves repeatedly summing digits of a number until a single digit is obtained.
Distribute Candies to People
Distribute candies to people in a way that follows a mathematical pattern, ensuring the distribution is correct.
Water Bottles
Maximize the number of water bottles you can drink by simulating the exchange process between full and empty bottles.
Count of Matches in Tournament
Calculate the total matches in a tournament by simulating rounds and applying simple math rules for advancing teams.
Incremental Memory Leak
Solve Incremental Memory Leak by simulating each second carefully and using math to reason about the crash time bound.
Count Operations to Obtain Zero
Simulate operations on two integers until one becomes zero, counting how many steps it takes to achieve the result.
Find Three Consecutive Integers That Sum to a Given Number
Given a number, find three consecutive integers that sum to it, or return an empty array if no such integers exist.
Count Integers With Even Digit Sum
Solve this Easy Math plus Simulation problem by counting numbers whose digit sums are even up to a given limit efficient…
Smallest Value After Replacing With Sum of Prime Factors
Replace a number with the sum of its prime factors until it stabilizes, and return the smallest value.
Pass the Pillow
Pass the Pillow simulates the process of passing an item through a line of people, adjusting the direction based on time…
Total Distance Traveled
Calculate the maximum distance a truck can travel using main and additional fuel tanks with controlled transfers.
Water Bottles II
Compute the maximum number of water bottles you can drink by simulating exchanges with step-by-step math logic.
Find the Child Who Has the Ball After K Seconds
Find the child who holds the ball after k seconds of passing in a queue, considering reversals at both ends.
Find the Winning Player in Coin Game
In this game between Alice and Bob, players must pick coins summing to 115. Alice starts, and the goal is to determine t…
Stone Removal Game
Alice and Bob play a game of stone removal. Alice goes first, and the winner is the player who can make a move until the…