<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 isNumber(string s) {
        // @akshay
        return isint2(s) || isdecimal(s) || isexp(s);
    }

    bool isint(string s){
        bool sign = false;
        if(s.size() > 0){
            if(!(isdigit(s[0]) || s[0] == '-' || s[0] == '+'))  return false;
        }
        for(int i = 1; i<s.size(); i++){
            if(!isdigit(s[i])) 
                return false;
            
        }
        return true;
    }

    bool isint2(string s){
        bool sign = false;
        if(s.size() > 0){
            if((s[0] == '-' || s[0] == '+') && s.size() == 1)
                return false;
            
            if(!(isdigit(s[0]) || s[0] == '-' || s[0] == '+'))  return false;
        }
        for(int i = 1; i<s.size(); i++){
            if(!isdigit(s[i])) 
                return false;
            
        }
        return true;
    }

    bool isnum(string s){
        for(int i = 0; i<s.size(); i++)
            if(!isdigit(s[i])) return false;
        return true;
    }

    bool isdecimal(string s){
        string temp = "";
        string temp0 = "";
        bool decimal = false;

        for(int i = 0; i<s.size(); i++){
            if(s[i] != '.'){
                temp+=s[i];
            }
            else{
                if(decimal) return false;
                decimal = true;
                if(!isint(temp)) return false;
                temp0 = temp;
                temp = "";
            }
        }

        if(!isnum(temp)) return false;
        if(temp0.size()== 0 && temp.size() == 0)return false;
        if(temp.size() == 0 && !isint2(temp0)) return false;
        return true;
    }


    bool isexp(string s){
        string temp = "";
        string temp0 = "";
        bool expo = false;

        for(int i = 0; i<s.size(); i++){
            if(s[i] != 'e' && s[i] != 'E'){
                temp+=s[i];
            }
            else{
                if(expo) return false;
                expo = true;
                if(!isdecimal(temp) && !isint2(temp)) return false;
                temp0 = temp;
                temp = "";
            }
        }

        if(!isint2(temp)) return false;
        if(temp0.size()== 0 || temp.size() == 0)return false;
        return true;
    }
};
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