<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 Solution {
public:
    int racecar(int target) {
        queue<pair<int, int>> q;
        q.push({0, 1});
        unordered_set<string> v;
        v.insert("0_1");
        v.insert("0_-1");
        int steps = 0;
        while(!q.empty())
        {
            int size = q.size();
            while(size--)
            {
                auto p = q.front();
                q.pop();
                int pos = p.first;
                int speed = p.second;
                {
                    int pos1 = pos + speed;
                    if(pos1 == target)
                        return steps + 1;
                    int speed1 = 2 * speed;
                    pair<int, int> p1{pos1, speed1};
                    if(abs(p1.second) < 2 * target && abs(p1.first) < 2 * target)
                        q.push(p1);
                                        
                }
                {
                    int speed2 = speed > 0? -1:1;
                    pair<int, int> p2{pos, speed2};
                    string key2 = to_string(pos) + "_" + to_string(speed2);
                    if(!v.count(key2))
                    {
                        q.push(p2);
                        v.insert(key2);
                    }
                }
            }
            steps++;
        }
        return -1;
    }
};
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