Alice and Bob take turns playing a game, with Alice starting first.
\r\n\r\nThere are n stones arranged in a row. On each player's turn, while the number of stones is more than one, they will do the following:
x > 1, and remove the leftmost x stones from the row.The game stops when only one stone is left in the row.
\r\n\r\nThe score difference between Alice and Bob is (Alice's score - Bob's score). Alice's goal is to maximize the score difference, and Bob's goal is the minimize the score difference.
Given an integer array stones of length n where stones[i] represents the value of the ith stone from the left, return the score difference between Alice and Bob if they both play optimally.
\r\n
Example 1:
\r\n\r\n\r\nInput: stones = [-1,2,-3,4,-5]\r\nOutput: 5\r\nExplanation:\r\n- Alice removes the first 4 stones, adds (-1) + 2 + (-3) + 4 = 2 to her score, and places a stone of\r\n value 2 on the left. stones = [2,-5].\r\n- Bob removes the first 2 stones, adds 2 + (-5) = -3 to his score, and places a stone of value -3 on\r\n the left. stones = [-3].\r\nThe difference between their scores is 2 - (-3) = 5.\r\n\r\n\r\n
Example 2:
\r\n\r\n\r\nInput: stones = [7,-6,5,10,5,-2,-6]\r\nOutput: 13\r\nExplanation:\r\n- Alice removes all stones, adds 7 + (-6) + 5 + 10 + 5 + (-2) + (-6) = 13 to her score, and places a\r\n stone of value 13 on the left. stones = [13].\r\nThe difference between their scores is 13 - 0 = 13.\r\n\r\n\r\n
Example 3:
\r\n\r\n\r\nInput: stones = [-10,-12]\r\nOutput: -22\r\nExplanation:\r\n- Alice can only make one move, which is to remove both stones. She adds (-10) + (-12) = -22 to her\r\n score and places a stone of value -22 on the left. stones = [-22].\r\nThe difference between their scores is (-22) - 0 = -22.\r\n\r\n\r\n
\r\n
Constraints:
\r\n\r\nn == stones.length2 <= n <= 105-104 <= stones[i] <= 104Compiled with clang 11 using the latest C++ 20 standard.
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