<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 {
public:
    bool isValid3(string& s, int l, int r) {
        return !(l > r || (l == r && (s[l] == '+' || s[l] == '-')));
    }

    bool isValid1(string& s, int l, int r) {
        map<char,int> M;
        int dotIndex = -1;
        for(int i = l; i <= r; i++) {
            M[s[i]]++;
            if(s[i] == '.') dotIndex = i;
        }
        if(M['+'] > 1 || M['-'] > 1 || M['.'] > 1 || M['+'] + M['-'] > 1) return false;
        if((M['+'] == 1 && s[l] != '+') || (M['-'] == 1 && s[l] != '-')) return false;
        if(r - l + 1 == M['+'] || r - l + 1 == M['-'] || r - l + 1 == M['.']) return false;
        return (dotIndex == -1) || isValid3(s, l, dotIndex - 1) || isValid3(s, dotIndex + 1, r);
    }

    bool isValid2(string& s, int l, int r) {
        map<char,int> M;
        for(int i = l; i <= r; i++) M[s[i]]++;
        if(M['+'] > 1 || M['-'] > 1 || M['.'] > 0 || M['+'] + M['-'] > 1) return false;
        if((M['+'] == 1 && s[l] != '+') || (M['-'] == 1 && s[l] != '-')) return false;
        return r - l + 1 != M['+'] && r - l + 1 != M['-'];
    }

    bool isNumber(string s) {
        int n = s.length(), eIndex = -1;
        map<char,int> M;
        for(int i = 0; i < n; i++) {
            M[s[i]]++;
            if(isdigit(s[i])) continue;
            if(s[i] == 'e' || s[i] == 'E') eIndex = i;
            else if(s[i] != '+' && s[i] != '-' && s[i] != '.') return false;
        }
        if(M['e'] > 1 || M['E'] > 1 || M['.'] > 2 || M['+'] + M['-'] > 2 || M['e'] + M['E'] > 1) return false;
        return eIndex == -1 ? isValid1(s, 0, n - 1) : isValid1(s, 0, eIndex - 1) && isValid2(s, eIndex + 1, n - 1);
    }
};
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