<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:
    bool judgePoint24(vector<int>& cards) {
        vector<double> curr;
        for (auto card : cards) {
            curr.push_back(1.0 * card);
        }

        return backtrack(curr);
    }

private:
    vector<char> signs = {'+', '-', '*', '/'};

    bool backtrack(vector<double> &curr) {
        for (auto c : curr) cout << c << " ";
        cout << "\n";

        if (curr.size() == 1) {
            if (abs(curr[0] - 24) <= 1e-5) {
                return true;
            } else {
                return false;
            }
        }

        for (int i = 0; i < curr.size(); ++i) {
            for (int j = 0; j < curr.size(); ++j) {
                if (i != j) {
                    for (auto sign : signs) {
                        double firstNum = curr[i];
                        double secondNum = curr[j];
                        if (sign == '/' && secondNum == 0) continue;
                        if ((sign == '+' || sign == '*') && j < i) continue; // filter duplicate

                        switch (sign) {
                            case '+':
                                firstNum += secondNum;
                                break;
                            
                            case '-':
                                firstNum -= secondNum;
                                break;

                            case '*':
                                firstNum *= secondNum;
                                break;

                            case '/':
                                firstNum /= secondNum;
                                break;
                        }

                        // build new curr
                        vector<double> newCurr;
                        for (int k = 0; k < curr.size(); ++k) {
                            if (k == i) {
                                newCurr.push_back(firstNum);
                            } else if (k != j) {
                                newCurr.push_back(curr[k]);
                            }
                        }
                        
                        if (backtrack(newCurr)) {
                            return true;
                        }
                    }
                }
            }
        }

        return false;
    }
};
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