Predict the Winner Python Solution with Tests

lcpy gen -n 486   # by problem number
lcpy gen -s predict_the_winner   # by problem name

Input: nums = [1,5,2]
Output: false
Explanation: Initially, player 1 can choose between 1 and 2.
If he chooses 2 (or 1), then player 2 can choose from 1 (or 2) and 5. If player 2 chooses 5, then player 1 will be left with 1 (or 2).
So, final score of player 1 is 1 + 2 = 3, and player 2 is 5.
Hence, player 1 will never be the winner and you need to return false.

Input: nums = [1,5,233,7]
Output: true
Explanation: Player 1 first chooses 1. Then player 2 has to choose between 5 and 7. No matter which number player 2 choose, player 1 can choose 233.
Finally, player 1 has more score (234) than player 2 (12), so you need to return True representing player1 can win.

class Solution:
    # Time: O(n^2)
    # Space: O(n^2)
    def predict_the_winner(self, nums: list[int]) -> bool:
        n = len(nums)
        # dp[l][r] is the best score difference (current player minus opponent)
        # achievable on the subarray nums[l:r + 1].
        dp = [[0] * n for _ in range(n)]
        for i in range(n):
            dp[i][i] = nums[i]
        for length in range(2, n + 1):
            for left in range(n - length + 1):
                right = left + length - 1
                take_left = nums[left] - dp[left + 1][right]
                take_right = nums[right] - dp[left][right - 1]
                dp[left][right] = max(take_left, take_right)
        return dp[0][n - 1] >= 0