<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <code>true</code> if it is possible to divide this array into <code>k</code> non-empty subsets whose sums are all equal.</p>

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

<pre>
<strong>Input:</strong> nums = [4,3,2,3,5,2,1], k = 4
<strong>Output:</strong> true
<strong>Explanation:</strong> It is possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4], k = 3
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 16</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
	<li>The frequency of each element is in the range <code>[1, 4]</code>.</li>
</ul>

class Solution {
    bool ans = false;
    int N = 0;
    int target;
    unordered_set<string> memo;
    void backtracking(vector<int>& nums, int visited, int p, int sum) {
        string key = to_string(visited);
        if (memo.count(key) > 0)  return;
        memo.insert(key);
        if (sum == target) {
            if (visited + 1 == (1 << N)) {
                ans = true;
                return;
            }
            sum = 0;
            p = 0;
        }
        for (int i = p ; i < N ; i++) {
            if (((1 << i) & visited) != 0)                continue;
            if (sum + nums[i] > target)    break;
            // printf("nxt = [%d] %d --> %d\n", i, nums[i], sum);
            visited |= (1 << i);
            backtracking(nums, visited, i+1, sum+nums[i]);
            visited &= ~(1 << i);
        }
    }
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        sort(nums.begin(), nums.end());
        N = nums.size();
        int sum = 0;
        for (auto num : nums)   sum += num;
        if (sum % k != 0)           return false;
        target = sum/k;
        if (nums.back() > target)    return false;
        // printf("target = %d\n", target);
        int visited = 0;
        backtracking(nums, visited, 0, 0);
        return ans;
    }
};

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