Number of Atoms
<p>Given a string <code>formula</code> representing a chemical formula, return <em>the count of each atom</em>.</p>

<p>The atomic element always starts with an uppercase character, then zero or more lowercase letters, representing the name.</p>

<p>One or more digits representing that element&#39;s count may follow if the count is greater than <code>1</code>. If the count is <code>1</code>, no digits will follow.</p>

<ul>
	<li>For example, <code>&quot;H2O&quot;</code> and <code>&quot;H2O2&quot;</code> are possible, but <code>&quot;H1O2&quot;</code> is impossible.</li>
</ul>

<p>Two formulas are concatenated together to produce another formula.</p>

<ul>
	<li>For example, <code>&quot;H2O2He3Mg4&quot;</code> is also a formula.</li>
</ul>

<p>A formula placed in parentheses, and a count (optionally added) is also a formula.</p>

<ul>
	<li>For example, <code>&quot;(H2O2)&quot;</code> and <code>&quot;(H2O2)3&quot;</code> are formulas.</li>
</ul>

<p>Return the count of all elements as a string in the following form: the first name (in sorted order), followed by its count (if that count is more than <code>1</code>), followed by the second name (in sorted order), followed by its count (if that count is more than <code>1</code>), and so on.</p>

<p>The test cases are generated so that all the values in the output fit in a <strong>32-bit</strong> integer.</p>

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

<pre>
<strong>Input:</strong> formula = &quot;H2O&quot;
<strong>Output:</strong> &quot;H2O&quot;
<strong>Explanation:</strong> The count of elements are {&#39;H&#39;: 2, &#39;O&#39;: 1}.
</pre>

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

<pre>
<strong>Input:</strong> formula = &quot;Mg(OH)2&quot;
<strong>Output:</strong> &quot;H2MgO2&quot;
<strong>Explanation:</strong> The count of elements are {&#39;H&#39;: 2, &#39;Mg&#39;: 1, &#39;O&#39;: 2}.
</pre>

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

<pre>
<strong>Input:</strong> formula = &quot;K4(ON(SO3)2)2&quot;
<strong>Output:</strong> &quot;K4N2O14S4&quot;
<strong>Explanation:</strong> The count of elements are {&#39;K&#39;: 4, &#39;N&#39;: 2, &#39;O&#39;: 14, &#39;S&#39;: 4}.
</pre>

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

<ul>
	<li><code>1 &lt;= formula.length &lt;= 1000</code></li>
	<li><code>formula</code> consists of English letters, digits, <code>&#39;(&#39;</code>, and <code>&#39;)&#39;</code>.</li>
	<li><code>formula</code> is always valid.</li>
</ul>
Stack; Hash Table; String; Sorting
function countOfAtoms(formula: string): string {
    const getCount = (formula: string, factor = 1) => {
        const n = formula.length;
        const cnt: Record<string, number> = {};
        const s: string[] = [];
        let [atom, c] = ['', 0];

        for (let i = 0; i <= n; i++) {
            if (formula[i] === '(') {
                const stk: string[] = ['('];
                let j = i;
                while (stk.length) {
                    j++;
                    if (formula[j] === '(') stk.push('(');
                    else if (formula[j] === ')') stk.pop();
                }

                const molecule = formula.slice(i + 1, j);
                const nextFactor: string[] = [];

                while (isDigit(formula[++j])) {
                    nextFactor.push(formula[j]);
                }

                const nextC = getCount(molecule, +nextFactor.join('') || 1);
                for (const [atom, c] of Object.entries(nextC)) {
                    cnt[atom] = (cnt[atom] ?? 0) + c * factor;
                }

                i = j - 1;
                continue;
            }

            if (s.length && (!formula[i] || isUpper(formula[i]))) {
                [atom, c] = getAtom(s);

                c *= factor;
                cnt[atom] = (cnt[atom] ?? 0) + c;
                s.length = 0;
            }

            s.push(formula[i]);
        }

        return cnt;
    };

    return Object.entries(getCount(formula))
        .sort(([a], [b]) => a.localeCompare(b))
        .map(([a, b]) => (b > 1 ? a + b : a))
        .join('');
}

const regex = {
    atom: /(\D+)(\d+)?/,
    isUpper: /[A-Z]+/,
};
const getAtom = (s: string[]): [string, number] => {
    const [_, atom, c] = regex.atom.exec(s.join(''))!;
    return [atom, c ? +c : 1];
};
const isDigit = (ch: string) => !Number.isNaN(Number.parseInt(ch));
const isUpper = (ch: string) => regex.isUpper.test(ch);
