<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 isInt(string s){
        if(s.size() == 1){
            return (s[0] <= '9' && s[0] >= '0');
        }
        if(!(s[0] == '-' || s[0] == '+' || s[0] <= '9' && s[0] >= '0')){
            return false;
        }
        for(int i = 1; i<s.size(); i++){
            if(s[i]<'0' || s[i] > '9'){
                return false;
            }
        }
        return true;
    }
    bool isNumber(string s) {
        // valid integer number : (-|+)(d)*(""|e)(integer)
        // valid decimal number : (-|+)(d)*.(d)*(integer);
        // regex iptn("(-|+)[1-9]+");
        // regex dptn("(-|+)(d)*.(d)");
        if(s.size() == 1){
            return (s[0] <= '9' && s[0] >= '0');
        }
        bool dot = false;
        bool exp = false;
        if(s[0] == '.'){
            if(s[1] <= '9' && s[1] >='0'){
                dot = true;
            }else{
                return false;
            }
        }else if(!(s[0] == '-' || s[0] == '+' || (s[0] >= '0' && s[0] <= '9'))){
            return false;
        }
        for(int i = 1; i<s.size(); i++){
            if(!exp && (s[i] == 'e'  || s[i] == 'E')&& (s[i-1] != '-' && s[i-1] != '+')){
                cout<<s.substr(i+1);
                exp = true;
                return isInt(s.substr(i+1));
            }
            else if(s[i]<='9' && s[i] >= '0'){
                continue;
            }
            else if(s[i] == '.' && !dot){
                if((s[i-1] >= '0' && s[i-1]<='9')||(i != s.size()-1) && s[i+1] <= '9' && s[i+1] >='0'){
                    dot = true;
                }else{
                    return false;
                }
            }
            else{
                return false;
            }
        }
        return true;
    }
};
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