Bag of Tokens

class Solution {
public:
    int maxScore(vector<int>& coins, int energy) {
        int points = 0;
        sort(coins.begin(), coins.end());
        deque<int> tokenDeck(coins.begin(), coins.end());

        while (!tokenDeck.empty()) {
            if (energy >= tokenDeck.front()) {
                energy -= tokenDeck.front();
                tokenDeck.pop_front();
                points += 1;
            } else if (tokenDeck.size() > 1 && points > 0) {
                energy += tokenDeck.back();
                tokenDeck.pop_back();
                points -= 1;
            } else {
                return points;
            }
        }
        return points;
    }
};

This solution involves a problem where you are aiming to maximize your score by manipulating tokens with different energy values. The approach is implemented in C++ and relies on sorting, deque utilization, and a while-loop control structure to manage token operations efficiently.

• Start by initializing a points variable to zero to keep track of the score.
• Sort the coins vector to arrange token values in increasing order to simplify decision-making regarding token use.
• Convert the sorted vector into a deque named tokenDeck to gain efficient access to both the smallest and largest elements, crucial for the strategy involved.
• Enter a while-loop that continues until tokenDeck is empty.
  • If the current energy level is sufficient to purchase the least expensive token (tokenDeck.front()), use some energy to buy the token, remove it from the deque, and increment the points.
  • If energy is insufficient but there are at least two tokens left and the score is greater than zero, regain some energy by trading in the most expensive token (tokenDeck.back()), remove it, and decrement the points.
  • If neither operation is feasible, exit the loop and return the collected points.
• The final score, after processing all possible operations within the limits of available energy and tokens, is returned.

This algorithm efficiently balances the management of resources (energy) and objectives (points) through strategic token trades, ensuring the maximum possible score under given constraints.

public class Solution {
    public int tokensGame(int[] tokens, int energy) {
        int points = 0;
        Arrays.sort(tokens);
        Deque<Integer> dequeTokens = new LinkedList<>();

        for (int t : tokens) {
            dequeTokens.add(t);
        }

        while (!dequeTokens.isEmpty()) {
            // Play token face-up if enough energy
            if (energy >= dequeTokens.peekFirst()) {
                energy -= dequeTokens.pollFirst();
                points++;
            } 
            // If insufficient energy but can play face-down
            else if (dequeTokens.size() > 1 && points > 0) {
                energy += dequeTokens.pollLast();
                points--;
            } 
            // Cannot play further
            else {
                return points;
            }
        }
        return points;
    }
}

The given Java solution manages a game involving tokens and energy with the objective of maximizing the player's points. The method tokensGame(int[] tokens, int energy) operates by following these steps:

1. Sort the array of tokens in ascending order. This allows strategizing the game play starting with the smallest (least energy consuming) tokens.
2. Convert the sorted token array into a deque (double-ended queue) to facilitate easy addition and removal of elements from both ends.
3. Initialize the points to zero. This will keep a count of the player's points.
4. Use a loop to iterate while the deque is not empty, indicating that tokens are available for play.
5. Within the loop, check if the available energy is sufficient to play the token with the least energy requirement (front of the deque). If yes, use up the energy required for this token, remove the token from the deque and increment the points.
6. If there's not enough energy but the deque has more than one token and the player already has points, attempt to gain more energy by playing tokens face-down, starting from the token with the highest energy requirement (back of the deque). This yields more energy for future plays and decrements the points by one.
7. End the game either when all tokens are played or when no further moves can be made (i.e., there aren't enough tokens to play face-down and insufficient energy to play any token face-up).

This approach thus balances the strategy of gaining points by clearing tokens with minimal energy requirements and regaining energy by sacrificing points when necessary. This algorithm ensures that points are maximized based on the initial set of tokens and available energy.