<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>

static const regex number_regex("[+-]?((\\d+)|((\\d+\\.)|(\\d+\\.\\d+)|(\\.\\d+)))([eE][+-]?\\d+)?");

class Solution {
public:
    bool isNumber(string s) {
    #if 0
        return regex_match(s,number_regex);
    #endif
    #if 1 
        if(s.size()==0) return false;
        
        bool number_found=false;
        bool decimal_found=false;
        bool e_found=false;
        
        for(int i=0;i<s.size();i++)
        {
            char ch=s[i];
            switch(ch)
            {
                case '.':
                    //1. There must not be more than one decimal point 2. 'e' or 'E' must be followed by integer only
                    if(decimal_found || e_found) return false; 
                    decimal_found=true;
                    break;
                
                case 'E':
                case 'e':
                    //3. More than one e not allowed 4. e must have a digit as prefix
                    if(e_found || !number_found) return false;
                    e_found=true;
                    number_found=false; // Reset it to check valid integer after e
                    break;
                case '+':
                case '-':
                    //5. After 0th position + and - can only be just after e
                    if(i>0 && s[i-1]!='e' && s[i-1] != 'E') return false;
                    number_found=false; // Reset it to check valid integer after + -
                    break;
                default:
                    if(!isdigit(ch)) return false;
                    number_found=true;
            }
        }
        return number_found; //6. A valid number always ends with a digit.  
    #endif     
    }
};
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