Number of Digit One
<p>Given an integer <code>n</code>, count <em>the total number of digit </em><code>1</code><em> appearing in all non-negative integers less than or equal to</em> <code>n</code>.</p>

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

<pre>
<strong>Input:</strong> n = 13
<strong>Output:</strong> 6
</pre>

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

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

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

<ul>
	<li><code>0 &lt;= n &lt;= 10<sup>9</sup></code></li>
</ul>
Recursion; Math; Dynamic Programming
function countDigitOne(n: number): number {
    const s = n.toString();
    const m = s.length;
    const f: number[][] = Array.from({ length: m }, () => Array(m).fill(-1));
    const dfs = (i: number, cnt: number, limit: boolean): number => {
        if (i >= m) {
            return cnt;
        }
        if (!limit && f[i][cnt] !== -1) {
            return f[i][cnt];
        }
        const up = limit ? +s[i] : 9;
        let ans = 0;
        for (let j = 0; j <= up; ++j) {
            ans += dfs(i + 1, cnt + (j === 1 ? 1 : 0), limit && j === up);
        }
        if (!limit) {
            f[i][cnt] = ans;
        }
        return ans;
    };
    return dfs(0, 0, true);
}
