<p>You are given an array of integers <code>stones</code> where <code>stones[i]</code> is the weight of the <code>i<sup>th</sup></code> stone.</p>

<p>We are playing a game with the stones. On each turn, we choose any two stones and smash them together. Suppose the stones have weights <code>x</code> and <code>y</code> with <code>x &lt;= y</code>. The result of this smash is:</p>

<ul>
	<li>If <code>x == y</code>, both stones are destroyed, and</li>
	<li>If <code>x != y</code>, the stone of weight <code>x</code> is destroyed, and the stone of weight <code>y</code> has new weight <code>y - x</code>.</li>
</ul>

<p>At the end of the game, there is <strong>at most one</strong> stone left.</p>

<p>Return <em>the smallest possible weight of the left stone</em>. If there are no stones left, return <code>0</code>.</p>

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

<pre>
<strong>Input:</strong> stones = [2,7,4,1,8,1]
<strong>Output:</strong> 1
<strong>Explanation:</strong>
We can combine 2 and 4 to get 2, so the array converts to [2,7,1,8,1] then,
we can combine 7 and 8 to get 1, so the array converts to [2,1,1,1] then,
we can combine 2 and 1 to get 1, so the array converts to [1,1,1] then,
we can combine 1 and 1 to get 0, so the array converts to [1], then that&#39;s the optimal value.
</pre>

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

<pre>
<strong>Input:</strong> stones = [31,26,33,21,40]
<strong>Output:</strong> 5
</pre>

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

<ul>
	<li><code>1 &lt;= stones.length &lt;= 30</code></li>
	<li><code>1 &lt;= stones[i] &lt;= 100</code></li>
</ul>

class Solution:
    def lastStoneWeightII(self, stones: List[int]) -> int:
        sum_stones = sum(stones)
        target = sum_stones//2
        rem = target
        @lru_cache(maxsize =None )
        def helper(target,i):
            if target <= 0:
                temp = abs(target)+ rem
                return abs(sum_stones - temp - temp)

            elif i == len(stones):
                return float('inf')
  
            return min(helper(target,i+1),helper(target-stones[i],i+1))
        
        return helper(target, 0)


"""
        class Solution:
    def lastStoneWeightII(self, stones: List[int]) -> int:
        dp = {}
        target = ceil(sum(stones) / 2)

        def helper(total, i):
            if (total, i) in dp:
                return dp[(total, i)]
            if total >= target or i >= len(stones):
                return abs(total - (sum(stones) - total))

            dp[(total, i)] = min(helper(total, i + 1), helper(total + stones[i], i + 1))
            return dp[(total, i)]
        
        return helper(0, 0)


        """
        
            








        
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