Find the Minimum Cost Array Permutation
<p>You are given an array <code>nums</code> which is a <span data-keyword="permutation">permutation</span> of <code>[0, 1, 2, ..., n - 1]</code>. The <strong>score</strong> of any permutation of <code>[0, 1, 2, ..., n - 1]</code> named <code>perm</code> is defined as:</p>

<p><code>score(perm) = |perm[0] - nums[perm[1]]| + |perm[1] - nums[perm[2]]| + ... + |perm[n - 1] - nums[perm[0]]|</code></p>

<p>Return the permutation <code>perm</code> which has the <strong>minimum</strong> possible score. If <em>multiple</em> permutations exist with this score, return the one that is <span data-keyword="lexicographically-smaller-array">lexicographically smallest</span> among them.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,0,2]</span></p>

<p><strong>Output:</strong> <span class="example-io">[0,1,2]</span></p>

<p><strong>Explanation:</strong></p>

<p><strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3100-3199/3149.Find%20the%20Minimum%20Cost%20Array%20Permutation/images/example0gif.gif" style="width: 235px; height: 235px;" /></strong></p>

<p>The lexicographically smallest permutation with minimum cost is <code>[0,1,2]</code>. The cost of this permutation is <code>|0 - 0| + |1 - 2| + |2 - 1| = 2</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [0,2,1]</span></p>

<p><strong>Output:</strong> <span class="example-io">[0,2,1]</span></p>

<p><strong>Explanation:</strong></p>

<p><strong><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3100-3199/3149.Find%20the%20Minimum%20Cost%20Array%20Permutation/images/example1gif.gif" style="width: 235px; height: 235px;" /></strong></p>

<p>The lexicographically smallest permutation with minimum cost is <code>[0,2,1]</code>. The cost of this permutation is <code>|0 - 1| + |2 - 2| + |1 - 0| = 2</code>.</p>
</div>

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

<ul>
	<li><code>2 &lt;= n == nums.length &lt;= 14</code></li>
	<li><code>nums</code> is a permutation of <code>[0, 1, 2, ..., n - 1]</code>.</li>
</ul>
Bit Manipulation; Array; Dynamic Programming; Bitmask
class Solution {
public:
    vector<int> findPermutation(vector<int>& nums) {
        int n = nums.size();
        vector<int> ans;
        int f[1 << n][n];
        memset(f, -1, sizeof(f));
        function<int(int, int)> dfs = [&](int mask, int pre) {
            if (mask == (1 << n) - 1) {
                return abs(pre - nums[0]);
            }
            int* res = &f[mask][pre];
            if (*res != -1) {
                return *res;
            }
            *res = INT_MAX;
            for (int cur = 1; cur < n; ++cur) {
                if (mask >> cur & 1 ^ 1) {
                    *res = min(*res, abs(pre - nums[cur]) + dfs(mask | 1 << cur, cur));
                }
            }
            return *res;
        };
        function<void(int, int)> g = [&](int mask, int pre) {
            ans.push_back(pre);
            if (mask == (1 << n) - 1) {
                return;
            }
            int res = dfs(mask, pre);
            for (int cur = 1; cur < n; ++cur) {
                if (mask >> cur & 1 ^ 1) {
                    if (abs(pre - nums[cur]) + dfs(mask | 1 << cur, cur) == res) {
                        g(mask | 1 << cur, cur);
                        break;
                    }
                }
            }
        };
        g(1, 0);
        return ans;
    }
};