Numbers With Repeated Digits
<p>Given an integer <code>n</code>, return <em>the number of positive integers in the range </em><code>[1, n]</code><em> that have <strong>at least one</strong> repeated digit</em>.</p>

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

<pre>
<strong>Input:</strong> n = 20
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only positive number (&lt;= 20) with at least 1 repeated digit is 11.
</pre>

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

<pre>
<strong>Input:</strong> n = 100
<strong>Output:</strong> 10
<strong>Explanation:</strong> The positive numbers (&lt;= 100) with atleast 1 repeated digit are 11, 22, 33, 44, 55, 66, 77, 88, 99, and 100.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 1000
<strong>Output:</strong> 262
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>9</sup></code></li>
</ul>
Math; Dynamic Programming
function numDupDigitsAtMostN(n: number): number {
    const s = n.toString();
    const m = s.length;
    const f = Array.from({ length: m }, () => Array(1 << 10).fill(-1));

    const dfs = (i: number, mask: number, lead: boolean, limit: boolean): number => {
        if (i >= m) {
            return lead ? 0 : 1;
        }
        if (!lead && !limit && f[i][mask] !== -1) {
            return f[i][mask];
        }
        const up = limit ? parseInt(s[i]) : 9;
        let ans = 0;
        for (let j = 0; j <= up; j++) {
            if (lead && j === 0) {
                ans += dfs(i + 1, mask, true, limit && j === up);
            } else if (((mask >> j) & 1) === 0) {
                ans += dfs(i + 1, mask | (1 << j), false, limit && j === up);
            }
        }
        if (!lead && !limit) {
            f[i][mask] = ans;
        }
        return ans;
    };

    return n - dfs(0, 0, true, true);
}
