Code Implementation
Token Strategy Game Implementation
Below is the implementation of the token strategy game:
12345678910111213141516171819202122232425262728293031323334353637383940/** * Greedy Approach with Sorting * Time Complexity: O(n log n) - Sorting the tokens takes O(n log n) time * Space Complexity: O(1) - We only use a constant amount of extra space * * @param {number[]} tokens - Array of token values * @param {number} power - Initial power * @return {number} - Maximum score achievable */function bagOfTokensScore(tokens, power) { // Sort tokens in ascending order tokens.sort((a, b) => a - b); let left = 0; let right = tokens.length - 1; let score = 0; let maxScore = 0; while (left <= right) { // If we can play the smallest token face up if (power >= tokens[left]) { power -= tokens[left]; left++; score++; maxScore = Math.max(maxScore, score); } // If we can play the largest token face down else if (score > 0) { power += tokens[right]; right--; score--; } // If we can't make any move else { break; } } return maxScore;}Step-by-Step Explanation
Let's break down the implementation:
- 1. Understand the Problem: First, understand that we need to maximize our score by strategically playing tokens either face up or face down.
- 2. Sort the Tokens: Sort the tokens in ascending order to easily access the smallest and largest tokens.
- 3. Use Two Pointers: Use two pointers to track the smallest and largest tokens that haven't been played yet.
- 4. Implement the Greedy Strategy: Play the smallest tokens face up and the largest tokens face down, always choosing the move that maximizes our score.
- 5. Track the Maximum Score: Keep track of the maximum score achieved during the game, as we might temporarily decrease our score to gain more power.
- 6. Handle Edge Cases: Consider edge cases such as empty token arrays or when we don't have enough power to play any token.
- 7. Test the Solution: Verify the solution with the provided examples and additional test cases.
String Problems
Learning Objective
Implement the token strategy game solution in different programming languages.
Token Strategy Game Implementation
Below is the implementation of the token strategy game in different programming languages. Select a language tab to view the corresponding code.
12345678910111213141516171819202122232425262728293031323334353637383940/** * Greedy Approach with Sorting * Time Complexity: O(n log n) - Sorting the tokens takes O(n log n) time * Space Complexity: O(1) - We only use a constant amount of extra space * * @param {number[]} tokens - Array of token values * @param {number} power - Initial power * @return {number} - Maximum score achievable */function bagOfTokensScore(tokens, power) { // Sort tokens in ascending order tokens.sort((a, b) => a - b); let left = 0; let right = tokens.length - 1; let score = 0; let maxScore = 0; while (left <= right) { // If we can play the smallest token face up if (power >= tokens[left]) { power -= tokens[left]; left++; score++; maxScore = Math.max(maxScore, score); } // If we can play the largest token face down else if (score > 0) { power += tokens[right]; right--; score--; } // If we can't make any move else { break; } } return maxScore;}Step-by-Step Explanation
11. Understand the Problem
First, understand that we need to maximize our score by strategically playing tokens either face up or face down.
22. Sort the Tokens
Sort the tokens in ascending order to easily access the smallest and largest tokens.
33. Use Two Pointers
Use two pointers to track the smallest and largest tokens that haven't been played yet.
44. Implement the Greedy Strategy
Play the smallest tokens face up and the largest tokens face down, always choosing the move that maximizes our score.
55. Track the Maximum Score
Keep track of the maximum score achieved during the game, as we might temporarily decrease our score to gain more power.
66. Handle Edge Cases
Consider edge cases such as empty token arrays or when we don't have enough power to play any token.
77. Test the Solution
Verify the solution with the provided examples and additional test cases.
Language-Specific Notes
javascript
- JavaScript's sort() method with a custom comparator is used to sort the tokens in ascending order.
- Math.max() is used to keep track of the maximum score achieved during the game.
- The solution uses a two-pointer approach to efficiently access the smallest and largest tokens.
python
- Python's built-in sort() method is used to sort the tokens in ascending order.
- The max() function is used to keep track of the maximum score achieved during the game.
- Python's clean syntax makes the two-pointer approach easy to implement and understand.
java
- Java's Arrays.sort() method is used to sort the tokens in ascending order.
- Math.max() is used to keep track of the maximum score achieved during the game.
- The solution includes a main method with test cases to demonstrate the functionality.
cpp
- C++'s std::sort() function is used to sort the tokens in ascending order.
- std::max() is used to keep track of the maximum score achieved during the game.
- The solution uses references to avoid unnecessary copying of the tokens array.
Key Takeaways
- Sorting the tokens is crucial for implementing the greedy strategy efficiently.
- The optimal strategy is to play the smallest tokens face up and the largest tokens face down.
- Sometimes, it's beneficial to temporarily decrease our score to gain more power, which can lead to a higher final score.
- The two-pointer approach allows us to efficiently access the smallest and largest tokens at each step.
- Not all tokens need to be played to achieve the maximum score.
- This problem demonstrates the effectiveness of greedy algorithms for certain optimization problems.
Try It Yourself
Modify the code to implement an alternative approach and test it with the same examples.
Challenge:
Implement a function that solves the token strategy game problem using a different approach than shown above.
Common Edge Cases
Empty Token Array
If there are no tokens, the maximum score is 0.
Insufficient Initial Power
If the initial power is less than the smallest token value, we can't play any token face up initially.
All Tokens Playable Face Up
If we have enough power to play all tokens face up, the maximum score is the number of tokens.
Strategic Face Down Play
Sometimes, it's beneficial to temporarily decrease our score by playing a token face down to gain more power.