<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:
        S=sum(stones)
        n=len(stones)
        dp=[]
        for i in range(n+1):
            row=[]
            for j in range(S+1):
                row.append(None)
            dp.append(row)
        
        def solve(idx,target):
            if target==0 and idx==n:
                return True
            if idx==n:
                return False
            if dp[idx][target]!=None:
                return dp[idx][target]
            if stones[idx]>target:
                dp[idx][target]=solve(idx+1,target)
            else:
                dp[idx][target]=solve(idx+1,target) or solve(idx+1,target-stones[idx])
            return dp[idx][target]
        
        ans=float("inf")
        for i in range(S+1):
            if solve(0,i)==True:
                ans=min(ans,abs(2*i-S))
        return ans	        
	    
19700