<p>Given a string <code>s</code>, return whether <code>s</code> is a <strong>valid number</strong>.<br />
<br />
For example, all the following are valid numbers: <code>&quot;2&quot;, &quot;0089&quot;, &quot;-0.1&quot;, &quot;+3.14&quot;, &quot;4.&quot;, &quot;-.9&quot;, &quot;2e10&quot;, &quot;-90E3&quot;, &quot;3e+7&quot;, &quot;+6e-1&quot;, &quot;53.5e93&quot;, &quot;-123.456e789&quot;</code>, while the following are not valid numbers: <code>&quot;abc&quot;, &quot;1a&quot;, &quot;1e&quot;, &quot;e3&quot;, &quot;99e2.5&quot;, &quot;--6&quot;, &quot;-+3&quot;, &quot;95a54e53&quot;</code>.</p>

<p>Formally, a&nbsp;<strong>valid number</strong> is defined using one of the following definitions:</p>

<ol>
	<li>An <strong>integer number</strong> followed by an <strong>optional exponent</strong>.</li>
	<li>A <strong>decimal number</strong> followed by an <strong>optional exponent</strong>.</li>
</ol>

<p>An <strong>integer number</strong> is defined with an <strong>optional sign</strong> <code>&#39;-&#39;</code> or <code>&#39;+&#39;</code> followed by <strong>digits</strong>.</p>

<p>A <strong>decimal number</strong> is defined with an <strong>optional sign</strong> <code>&#39;-&#39;</code> or <code>&#39;+&#39;</code> followed by one of the following definitions:</p>

<ol>
	<li><strong>Digits</strong> followed by a <strong>dot</strong> <code>&#39;.&#39;</code>.</li>
	<li><strong>Digits</strong> followed by a <strong>dot</strong> <code>&#39;.&#39;</code> followed by <strong>digits</strong>.</li>
	<li>A <strong>dot</strong> <code>&#39;.&#39;</code> followed by <strong>digits</strong>.</li>
</ol>

<p>An <strong>exponent</strong> is defined with an <strong>exponent notation</strong> <code>&#39;e&#39;</code> or <code>&#39;E&#39;</code> followed by an <strong>integer number</strong>.</p>

<p>The <strong>digits</strong> are defined as one or more digits.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;0&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">true</span></p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;e&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">false</span></p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;.&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">false</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 20</code></li>
	<li><code>s</code> consists of only English letters (both uppercase and lowercase), digits (<code>0-9</code>), plus <code>&#39;+&#39;</code>, minus <code>&#39;-&#39;</code>, or dot <code>&#39;.&#39;</code>.</li>
</ul>

class Solution {
     bool exp(string_view s, int i) {
        if (s.length() == i + 1)
            return false;

        if (s[i] == '+' or s[i] == '-')
            i++;

        if (s.length() == i + 1)
            return false;

        for (; i + 1 < s.length(); i++) {
            if (s[i] < '0' or s[i] > '9')
                return false;
        }
        return true;
    }

     bool dec(string_view s, int start, bool num) {
        for (int i = start; i + 1 < s.length(); i++) {
            if (s[i] == 'e' or s[i] == 'E') {
                if (num and i == start)
                    return false;
                return exp(s, i + 1);
            }
            if (s[i] < '0' or s[i] > '9')
                return false;
        }
        return true;
    }

public:
     bool isNumber(string_view s) {
        if (s.length() == 2)
            return false;

        int start = 1;
        if (s[1] == '+' or s[1] == '-')
            start++;

        if (s.length() == start + 1)
            return false;

        for (int i = start; i + 1 < s.length(); i++) {
            if (s[i] == 'e' or s[i] == 'E') {
                if (i == start)
                    return false;
                return exp(s, i + 1);
            }
            if (s[i] == '.') {
                if (s.length() == start + 2)
                    return false;
                return dec(s, i + 1, i == start);
            }
            if (s[i] < '0' or s[i] > '9')
                return false;
        }
        return true;
    }
};

int init = [] {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    ofstream out("user.out");
    cout.rdbuf(out.rdbuf());

    Solution s;
    for (string line; getline(cin, line); cout << endl)
    {
        if(s.isNumber(line))
            cout << "true";
        else
            cout << "false";
    }
    exit(0);
    return 0;
}();
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