<p>Alice and Bob take turns playing a game, with <strong>Alice starting first</strong>.</p>

<p>There are <code>n</code> stones arranged in a row. On each player&#39;s turn, they can <strong>remove</strong> either the leftmost stone or the rightmost stone from the row and receive points equal to the <strong>sum</strong> of the remaining stones&#39; values in the row. The winner is the one with the higher score when there are no stones left to remove.</p>

<p>Bob found that he will always lose this game (poor Bob, he always loses), so he decided to <strong>minimize the score&#39;s difference</strong>. Alice&#39;s goal is to <strong>maximize the difference</strong> in the score.</p>

<p>Given an array of integers <code>stones</code> where <code>stones[i]</code> represents the value of the <code>i<sup>th</sup></code> stone <strong>from the left</strong>, return <em>the <strong>difference</strong> in Alice and Bob&#39;s score if they both play <strong>optimally</strong>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> stones = [5,3,1,4,2]
<strong>Output:</strong> 6
<strong>Explanation:</strong> 
- Alice removes 2 and gets 5 + 3 + 1 + 4 = 13 points. Alice = 13, Bob = 0, stones = [5,3,1,4].
- Bob removes 5 and gets 3 + 1 + 4 = 8 points. Alice = 13, Bob = 8, stones = [3,1,4].
- Alice removes 3 and gets 1 + 4 = 5 points. Alice = 18, Bob = 8, stones = [1,4].
- Bob removes 1 and gets 4 points. Alice = 18, Bob = 12, stones = [4].
- Alice removes 4 and gets 0 points. Alice = 18, Bob = 12, stones = [].
The score difference is 18 - 12 = 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> stones = [7,90,5,1,100,10,10,2]
<strong>Output:</strong> 122</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == stones.length</code></li>
	<li><code>2 &lt;= n &lt;= 1000</code></li>
	<li><code>1 &lt;= stones[i] &lt;= 1000</code></li>
</ul>

# class Solution:
#     def stoneGameVII(self, stones: List[int]) -> int:
#         @lru_cache(None)
#         def minimax(left, right, isPlayerOne, remain):
#             if left > right:
#                 return 0
            
#             if isPlayerOne:
#                 takeLeft = remain - stones[left] + minimax(left + 1, right, False, remain - stones[left])
#                 takeRight = remain - stones[right] + minimax(left, right - 1, False, remain - stones[right])
#                 return max(takeLeft, takeRight)

#             else:
#                 takeLeft = stones[left] - remain + minimax(left + 1, right, True, remain - stones[left])
#                 takeRight = stones[right] - remain + minimax(left, right - 1, True, remain - stones[right])
#                 return min(takeLeft, takeRight)

#         return minimax(0, len(stones)-1, True, sum(stones))

class Solution:
    def stoneGameVII(self, stones: List[int]) -> int:
        n = len(stones)
        flag = 1
        lis = list(stones)
        for i in range(1,n):
            for j in range(n - i):
                if flag:
                    lis[j] = max(lis[j],lis[j+1])
                else:
                    lis[j] = min(lis[j] + stones[j + i],lis[j+1] + stones[j])
            flag ^= 1
            #print(lis)
        return lis[0] if not flag else sum(stones) - lis[0]
        
17848