Codechef Starters 159 | Video Solutions - A to H | by Raghav Goel | TLE Eliminators
Education
Introduction
In this article, we will explore the solutions to the problems presented in Codechef Starters 159. The discussion covers the approach and logic behind each of the problems in an educational manner as shared by Raghav Goel in his video tutorial. Let’s dive into the problems and their solutions.
Problem 1: Election
In the elections problem, we have two candidates A and B competing across n states (where n is odd). A candidate wins if they receive more votes than their opponent, and the candidate who wins in more than half of the states wins the election. Each candidate receives votes represented by two arrays, A and B. Chef has the power to cast X votes in support of candidate A.
Logic: We need to determine if Chef can secure enough state victories with the additional votes. A candidate wins in a state if the votes they have are greater than their opponent. Using a greedy approach, prioritize distributing votes to states where candidate A needs the least votes to win.
Problem 2: Chef and Monsters
In this problem, Chef can multiply his initial health by any integer M (from 1 to K) before battling monsters. After each battle, Chef’s health is reduced to the largest proper divisor of his current health. The goal is to maximize the number of monsters defeated.
Logic: The process is primarily dependent on the prime factorization of Chef’s health. If Chef multiplies his health strategically by a power of 2, he maximizes the number of divisors, leading to defeating more monsters.
Problem 3: Chess Coloring
The chess coloring problem asks us to determine the number of ways to color exactly n² / 2 squares black on a chessboard, ensuring no two black squares share a side.
Logic: Implement a mathematical approach to determine the total state configurations. When n is odd, the configuration allows a combination of colors, resulting in a combinatorial expression to calculate different states.
Problem 4: Random Name
In this game, Alice and Bob roll a die with D faces. The winner is determined by who has more stones removed from their respective piles after a series of rolls.
Logic: The winning probabilities can be effectively calculated using the total space of outcomes from rolling the dice, leading to a formula for the expected number of wins for Alice.
Problem 5: Squid Game Glass Bridge
The problem presents contestants facing susceptibility in a glass bridge scenario, calculating the likelihood of all contestants dying at each step.
Logic: The calculations stem from probabilities derived from each contestant's chances of safety or failure across the glass panels, ultimately calculating cumulative probabilities up to M steps through iterative states.
Problem 6: Crafty Coloring Easy
Alice and Bob take turns coloring a grid's cells either red or blue based on a given sequence. The goal is to determine which color dominates after all moves.
Logic: Each move affects adjacent row and column cells, which lead to the final count of colored squares for Alice and Bob. Counting techniques are used to rapidly calculate outcomes based on how many rounds or moves have been made.
Conclusion
The video by Raghav Goel provides an in-depth discussion of each problem, focusing on approaches, methodologies, and employed strategies to solve the competition at Codechef Starters 159. By understanding each problem and solution, participants in competitive programming can enhance their coding capabilities.
Keyword
Election, Chef and Monsters, Chess Coloring, Random Name, Squid Game, Crafty Coloring, Combinatorial Counting, Prime Factorization, Dynamic Programming, Probability, Competitive Programming.
FAQ
Q1: What is the main focus of Codechef Starters 159?
A1: The main focus is on solving problems related to candidates' votes, health in games, coloring chessboards, and strategic turn-based games.
Q2: How does the problem of "Chef and Monsters" optimize game results?
A2: It maximizes the number of monsters Chef can defeat by choosing the best multiplier for his health.
Q3: What strategies are suggested for the Chess Coloring problem?
A3: The article discusses combinatorial strategies to find different configurations based on the chessboard size.
Q4: How do probabilities come into play in the Random Name problem?
A4: Alice and Bob's win probabilities are calculated based on rolling a die multiple times, with each outcome affecting the next state of the game.
Q5: Can you describe how the Crafty Coloring game concludes?
A5: The game concludes by counting how many cells have been colored by Alice and how many by Bob, determining the winner based on these counts.