<p>Given an integer <code>n</code>, return the count of all numbers with unique digits, <code>x</code>, where <code>0 &lt;= x &lt; 10<sup>n</sup></code>.</p>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 91
<strong>Explanation:</strong> The answer should be the total numbers in the range of 0 &le; x &lt; 100, excluding 11,22,33,44,55,66,77,88,99
</pre>

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

<pre>
<strong>Input:</strong> n = 0
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>0 &lt;= n &lt;= 8</code></li>
</ul>

class Solution {
public:
    int backtrace(vector<bool> &used, int n, int k) {
        if (k < 1) return 1;
        int result = 0;
        for (int i=0; i<used.size(); i++) {
            if (!used[i] && (i!=0 || k != n)) {
                // 可以用作第k位
                used[i] = true;
                result += backtrace(used, n, k-1);
                used[i] = false;
            }
        }

        return result;
    }
    int countNumbersWithUniqueDigits(int n) {
        vector<bool> used(10, false);
        int result = 0;
        for (int i=0; i<=n; i++) {
            result += backtrace(used, i, i);
        }

        return result;
    }
};
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