<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){
        if(l > r)return false;
        if(l == r && (s[l] == '+' || s[l] == '-'))return false;
        return true;
    }

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

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

    bool isNumber(string s) {
        int n=s.length();
        map<char,int> M;
        for(int i=0;i<n;i++){
            M[s[i]]++;
            if(s[i] >= '0' && s[i] <= '9')continue;
            if(s[i] == 'e' || s[i] =='E' || s[i] == '-' || s[i] == '+' || s[i] == '.')continue;
            return false;
        }

        if(M['e'] > 1 || M['E'] > 1 || M['.'] > 2 || M['-'] > 2 || M['+'] > 2)return false;
        if(M['+'] + M['-'] > 2 || M['e'] + M['E'] > 1)return false;

        if(M['e'] == 1 || M['E'] == 1){
            int ind=-1;
            for(int i=0;i<n;i++){
                if(s[i] == 'e' || s[i] == 'E')ind=i;
            }
            if(isValid1(s,0,ind-1) && isValid2(s,ind+1,n-1))return true;
            return false;
        }
        else return isValid1(s,0,n-1);
    }
};
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