<p>You are given an integer array <code>nums</code>.</p>

<p>You should move each element of <code>nums</code> into one of the two arrays <code>A</code> and <code>B</code> such that <code>A</code> and <code>B</code> are non-empty, and <code>average(A) == average(B)</code>.</p>

<p>Return <code>true</code> if it is possible to achieve that and <code>false</code> otherwise.</p>

<p><strong>Note</strong> that for an array <code>arr</code>, <code>average(arr)</code> is the sum of all the elements of <code>arr</code> over the length of <code>arr</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5,6,7,8]
<strong>Output:</strong> true
<strong>Explanation:</strong> We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have an average of 4.5.
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,1]
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 30</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def splitArraySameAverage(self, nums):
        # knapsack with total/2
        '''
              val0 ....... val_target
        num1
        num2
        num3
        '''

        total = sum(nums)
        n = len(nums)
        
        if n == 1:
            return False
        
        dp = []
        rows = n
        cols = total + 1
        
        for r in range(rows):
            new = [0] * cols
            dp.append(new)
        
        nums.sort(reverse = True)
        for r in range(rows):
            for c in range(cols):
                if nums[r] == c:
                    dp[r][c] += 1

                if r-1 >= 0:
                    dp[r][c] = dp[r-1][c]

                if r-1 >= 0 and c-nums[r] >= 0 and dp[r-1][c-nums[r]] != 0:
                    dp[r][c] = dp[r-1][c-nums[r]] + 1

                if dp[r][c] != 0 and dp[r][c] != n:
                    cur_average = float(c) / float(dp[r][c])
                    other_average = float(total - c) / float(n - dp[r][c])
                    if cur_average == other_average:    # floating point?
                        return True 

        return False
                
        
        
49900