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This approach involves using a two-pointer technique to process the tokens. By sorting the tokens array, we aim to utilize the smallest possible tokens first to maximize score when power allows, and then balance power by utilizing score if achievable.
Start by sorting the tokens array. Maintain two pointers: one at the start to play face-up when you have enough power, and the other at the end to play face-down when a score can be sacrificed to gain more power. Keep track of the current score and maximum score achieved. This greedy approach helps in maximizing score by trying to play as many tokens face-up as possible while being able to trade score for power when needed.
The time complexity is O(n log n) due to sorting the tokens array. The space complexity is O(1) as no additional space besides variables is used.
1#include <stdio.h>
2#include <stdlib.h>
3
4int compare(const void *a, const void *b) {
The implementation begins by sorting the tokens array using qsort. Two pointers, left and right, are initialized to keep track of which tokens to consider for playing face-up or face-down. If the power is enough to play the token at the left pointer face-up, the player does so and increments the score. Otherwise, if the score allows it, the player can play the token at the right pointer face-down to increase power. The loop continues until no more moves are possible. The maximum score obtained is returned.
In the dynamic programming approach, we consider decisions at each token in terms of playing face-up or face-down, and store results for subproblems to optimize the score obtained.
The dynamic programming table, dp[i][j], keeps track of the maximum score achievable with the first i tokens and with j power. For each token, either spend or gain power while adjusting the score, and calculate the best possible outcome for each state.
The time complexity is O(n * m) where n is the number of tokens and m is the initial power range explored. The space complexity is also O(n * m) due to the DP table usage.
In the JavaScript dynamic programming solution, a 2D array dp is used to track the optimal score outcomes available with varying amounts of power and tokens utilized. The logic expands power or adjusts score, ensuring the possible highest score is accounted for and output.