<p>You are given an integer array <code>cards</code> of length <code>4</code>. You have four cards, each containing a number in the range <code>[1, 9]</code>. You should arrange the numbers on these cards in a mathematical expression using the operators <code>[&#39;+&#39;, &#39;-&#39;, &#39;*&#39;, &#39;/&#39;]</code> and the parentheses <code>&#39;(&#39;</code> and <code>&#39;)&#39;</code> to get the value 24.</p>

<p>You are restricted with the following rules:</p>

<ul>
	<li>The division operator <code>&#39;/&#39;</code> represents real division, not integer division.

	<ul>
		<li>For example, <code>4 / (1 - 2 / 3) = 4 / (1 / 3) = 12</code>.</li>
	</ul>
	</li>
	<li>Every operation done is between two numbers. In particular, we cannot use <code>&#39;-&#39;</code> as a unary operator.
	<ul>
		<li>For example, if <code>cards = [1, 1, 1, 1]</code>, the expression <code>&quot;-1 - 1 - 1 - 1&quot;</code> is <strong>not allowed</strong>.</li>
	</ul>
	</li>
	<li>You cannot concatenate numbers together
	<ul>
		<li>For example, if <code>cards = [1, 2, 1, 2]</code>, the expression <code>&quot;12 + 12&quot;</code> is not valid.</li>
	</ul>
	</li>
</ul>

<p>Return <code>true</code> if you can get such expression that evaluates to <code>24</code>, and <code>false</code> otherwise.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> cards = [4,1,8,7]
<strong>Output:</strong> true
<strong>Explanation:</strong> (8-4) * (7-1) = 24
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> cards = [1,2,1,2]
<strong>Output:</strong> false
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>cards.length == 4</code></li>
	<li><code>1 &lt;= cards[i] &lt;= 9</code></li>
</ul>

class Solution {
public:
    void solve(vector<double> cards, int &ans){
        if(ans) return;
        if(cards.size()==1){
            if(23.9 <=cards[0] && cards[0]<= 24.1){
                ans=true;
            }
            return;
        }
        if(cards.size()==2){
            solve({cards[0]+cards[1]},ans);
            if(ans) return;
            solve({cards[0]-cards[1]},ans);
            if(ans) return;
            solve({cards[0]*cards[1]},ans);
            if(ans) return;
            solve({cards[0]/cards[1]},ans);
            return;
        }
        if(cards.size()==3){
            solve({cards[0]+cards[1],cards[2]},ans);
            if(ans) return;
            solve({cards[0]-cards[1],cards[2]},ans);
            if(ans) return;
            solve({cards[0]*cards[1],cards[2]},ans);
            if(ans) return;
            solve({cards[0]/cards[1],cards[2]},ans);
            if(ans) return;
            solve({cards[0],cards[1]+cards[2]},ans);
            if(ans) return;
            solve({cards[0],cards[1]-cards[2]},ans);
            if(ans) return;
            solve({cards[0],cards[1]*cards[2]},ans);
            if(ans) return;
            solve({cards[0],cards[1]/cards[2]},ans);
            return;
        }
        if(cards.size()==4){
            solve({cards[0]+cards[1],cards[2],cards[3]},ans);
            if(ans) return;
            solve({cards[0]-cards[1],cards[2],cards[3]},ans);
            if(ans) return;
            solve({cards[0]*cards[1],cards[2],cards[3]},ans);
            if(ans) return;
            solve({cards[0]/cards[1],cards[2],cards[3]},ans);
            if(ans) return;
            solve({cards[0],cards[1]+cards[2],cards[3]},ans);
            if(ans) return;
            solve({cards[0],cards[1]-cards[2],cards[3]},ans);
            if(ans) return;
            solve({cards[0],cards[1]*cards[2],cards[3]},ans);
            if(ans) return;
            solve({cards[0],cards[1]/cards[2],cards[3]},ans);
            if(ans) return;
            solve({cards[0],cards[1],cards[2]+cards[3]},ans);
            if(ans) return;
            solve({cards[0],cards[1],cards[2]-cards[3]},ans);
            if(ans) return;
            solve({cards[0],cards[1],cards[2]*cards[3]},ans);
            if(ans) return;
            solve({cards[0],cards[1],cards[2]/cards[3]},ans);
            return;
        }
    }
    bool judgePoint24(vector<int>& cards) {
        vector<double> card;
        for(auto e:cards) card.push_back(e);
        int ans = false;
        solve({card[0],card[1],card[2],card[3]},ans);
        if(ans) return true;
        solve({card[0],card[1],card[3],card[2]},ans); 
        if(ans) return true;
        solve({card[0],card[2],card[1],card[3]},ans); 
        if(ans) return true;
        solve({card[0],card[2],card[3],card[1]},ans); 
        if(ans) return true;
        solve({card[0],card[3],card[1],card[2]},ans); 
        if(ans) return true;
        solve({card[0],card[3],card[2],card[1]},ans); 
        if(ans) return true;
        solve({card[1],card[0],card[2],card[3]},ans); 
        if(ans) return true;
        solve({card[1],card[0],card[3],card[2]},ans); 
        if(ans) return true;
        solve({card[1],card[2],card[0],card[3]},ans);
        if(ans) return true; 
        solve({card[1],card[2],card[3],card[0]},ans); 
        if(ans) return true;
        solve({card[1],card[3],card[0],card[2]},ans); 
        if(ans) return true;
        solve({card[1],card[3],card[2],card[0]},ans); 
        if(ans) return true;
        solve({card[2],card[0],card[1],card[3]},ans); 
        if(ans) return true;
        solve({card[2],card[0],card[3],card[1]},ans); 
        if(ans) return true;
        solve({card[2],card[1],card[0],card[3]},ans); 
        if(ans) return true;
        solve({card[2],card[1],card[3],card[0]},ans); 
        if(ans) return true;
        solve({card[2],card[3],card[0],card[1]},ans); 
        if(ans) return true;
        solve({card[2],card[3],card[1],card[0]},ans); 
        if(ans) return true;
        solve({card[3],card[0],card[1],card[2]},ans); 
        if(ans) return true;
        solve({card[3],card[0],card[2],card[1]},ans); 
        if(ans) return true;
        solve({card[3],card[1],card[2],card[0]},ans);
        if(ans) return true;
        solve({card[3],card[1],card[0],card[2]},ans); 
        if(ans) return true;
        solve({card[3],card[2],card[0],card[1]},ans); 
        if(ans) return true;
        solve({card[3],card[2],card[1],card[0]},ans); 
        return ans;
    }
};
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