<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 {
public:
    bool splitArraySameAverage(vector<int>& nums) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        int n = nums.size();
        vector<map<int, bool>> dp((n << 5) + n);

        for (int i = 1; i < n; i++) {
            if (sum * i % n == 0 && isContain(sum * i / n, 0, i, nums, dp)) {
                return true;
            }
        }

        return false;
    }

    bool isContain(int target, int idx, int last, vector<int>& nums, vector<map<int, bool>>& dp) {
        if (last == 0)                              return target == 0;
        if (target < 0)                             return false;
        if (idx == nums.size())                     return false;
        if (dp[(idx << 5) + last].count(target))    return dp[(idx << 5) + last][target];

        bool res = false;
        res |= isContain(target - nums[idx], idx + 1, last - 1, nums, dp);
        if (res) return dp[(idx << 5) + last][target] = res;
        res |= isContain(target, idx + 1, last, nums, dp);
        return dp[(idx << 5) + last][target] = res;
    }
};

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