We often encounter game problems with specific rules in coding tests. In this lecture, we will cover a problem related to card games. Card game problems are a good example that can be effectively solved using algorithms and data structures.
Problem Description
Two players are playing a card game. Each player has unique cards labeled with numbers from 1 to N. Players take turns picking one card at a time. Each player earns points equal to the number on the card they pick.
Problem: Implement a function to maximize the scores that both players can achieve while playing the game and calculate the final score. The following conditions apply:
- Each player can select cards from 1 to N.
- Each player can select one card at a time, and a card cannot be selected again.
- The final score is the sum of the cards chosen by each player.
Input
- An integer N (1 ≤ N ≤ 100) – the number of cards
Output
- The total score of both players
Algorithmic Approach
This problem requires simple score calculations and optimizations based on card selection. We will solve the problem with the following approach:
- Create a list of card numbers for the players to choose from.
- Define how each player can calculate their card scores.
- Simulate the card selections of both players to calculate the final scores.
Code Implementation
Now, let’s implement the code to solve the problem. Below is the Python code for solving the problem:
def card_game(n):
# Generate card numbers.
cards = list(range(1, n + 1))
# Initialize player scores
player1_score = 0
player2_score = 0
# Players take turns selecting cards
turn = 0
while cards:
# Current player's selection
if turn % 2 == 0: # Player 1's turn
chosen_card = max(cards) # Select the highest value
player1_score += chosen_card
else: # Player 2's turn
chosen_card = min(cards) # Select the lowest value
player2_score += chosen_card
# Remove the chosen card
cards.remove(chosen_card)
turn += 1
return player1_score + player2_score
# Example
n = 5
print("Final score:", card_game(n))
Code Explanation
Let me briefly explain the code we wrote:
def card_game(n):
– Defines the card game function. It takes N as input.cards = list(range(1, n + 1))
– Creates a list of cards from 1 to N.player1_score
andplayer2_score
– Initializes the scores for both players.while cards:
– Continues to loop while there are cards left.if turn % 2 == 0:
– Checks the player’s turn and selects cards alternately.- Depending on the player’s selection, either the maximum card or the minimum card is chosen and added to the score.
cards.remove(chosen_card)
– Removes the chosen card from the card list.- Finally, it returns the sum of the scores of both players.
Test Cases
Let’s test the function that calculates the final score. We’ll create various test cases to observe different results:
print("N=3:", card_game(3)) # Output: 6
print("N=4:", card_game(4)) # Output: 10
print("N=5:", card_game(5)) # Output: 15
print("N=10:", card_game(10)) # Output: 55
Conclusion
In this lecture, we learned the basic uses of algorithms and data structures through a simple card game problem. We saw how one must strategically think about score accumulation with each card selection.
Such card game problems help develop algorithmic thinking and can be practiced through various variations. You can apply the problem discussed in this lecture to explore more complex card games or different types of problems. I hope you continue to enhance your skills through a variety of algorithm problem-solving!