<p>Your car starts at position <code>0</code> and speed <code>+1</code> on an infinite number line. Your car can go into negative positions. Your car drives automatically according to a sequence of instructions <code>&#39;A&#39;</code> (accelerate) and <code>&#39;R&#39;</code> (reverse):</p>

<ul>
	<li>When you get an instruction <code>&#39;A&#39;</code>, your car does the following:

	<ul>
		<li><code>position += speed</code></li>
		<li><code>speed *= 2</code></li>
	</ul>
	</li>
	<li>When you get an instruction <code>&#39;R&#39;</code>, your car does the following:
	<ul>
		<li>If your speed is positive then <code>speed = -1</code></li>
		<li>otherwise <code>speed = 1</code></li>
	</ul>
	Your position stays the same.</li>
</ul>

<p>For example, after commands <code>&quot;AAR&quot;</code>, your car goes to positions <code>0 --&gt; 1 --&gt; 3 --&gt; 3</code>, and your speed goes to <code>1 --&gt; 2 --&gt; 4 --&gt; -1</code>.</p>

<p>Given a target position <code>target</code>, return <em>the length of the shortest sequence of instructions to get there</em>.</p>

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

<pre>
<strong>Input:</strong> target = 3
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
The shortest instruction sequence is &quot;AA&quot;.
Your position goes from 0 --&gt; 1 --&gt; 3.
</pre>

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

<pre>
<strong>Input:</strong> target = 6
<strong>Output:</strong> 5
<strong>Explanation:</strong> 
The shortest instruction sequence is &quot;AAARA&quot;.
Your position goes from 0 --&gt; 1 --&gt; 3 --&gt; 7 --&gt; 7 --&gt; 6.
</pre>

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

<ul>
	<li><code>1 &lt;= target &lt;= 10<sup>4</sup></code></li>
</ul>

class carAttributes {
private:
    int pos, speed;
public:
    carAttributes(int pos, int speed) {
        this->pos = pos;
        this->speed = speed;
    }

    void setPos(int pos) {
        this->pos = pos;
    }
    void setSpeed(int speed) {
        this->speed = speed;
    }
    int getPos() {
        return pos;
    }
    int getSpeed() {
        return speed;
    }
};
class Solution {
public:
    int racecar(int target) {
        int minInstructions=0;
        queue<carAttributes*> bfsQueue;
        bfsQueue.push(new carAttributes(0, 1));
        unordered_set<string> vis;

        string key = to_string(0)+"_"+to_string(1);
        vis.insert(key);

        while(!bfsQueue.empty()) {
            int sz = bfsQueue.size();
            while(sz--) {
                carAttributes* front = bfsQueue.front();
                bfsQueue.pop();

                int cPos = front->getPos();
                int cSpeed = front->getSpeed();

                if(cPos == target)
                    return minInstructions;
                
                // A case
                int nPos = cPos + cSpeed;
                int nSpeed = cSpeed*2;
                string key = to_string(nPos)+"_"+to_string(nSpeed);

                if(vis.find(key)==vis.end() && abs(target - nPos) < target) {
                    vis.insert(key);
                    bfsQueue.push(new carAttributes(nPos, nSpeed));
                }

                // R case
                nPos = cPos;
                nSpeed = cSpeed < 0 ? 1 : -1;
                key = to_string(nPos)+"_"+to_string(nSpeed);

                if(vis.find(key)==vis.end() && abs(target - nPos) < target) {
                    vis.insert(key);
                    bfsQueue.push(new carAttributes(nPos, nSpeed));
                }
            }
            minInstructions++;
        }
        return -1;
    }
};
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