<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:
    struct node {
        int position;
        int speed;
        int steps;
        bool operator< (const node& other) const noexcept {
            return this->steps > other.steps;
        }
    };
    std::array<node, 2> getNextNodes(const node& nd, int targetPos) {
        return std::array<node, 2> {node{nd.position + nd.speed, nd.speed*2,  nd.steps+1}, node{nd.position, (nd.speed > 0 ? -1 : 1), nd.steps+1}};
    }
    int racecar(int target) {

        std::set<std::pair<int,int>> visitedStates;
        std::priority_queue<node> q;
        q.push({0,1, 0});
        while(!q.empty()) {
            const auto nd = q.top();
            q.pop();
            if(visitedStates.contains({nd.position, nd.speed}) || abs(nd.position) > (2*target))
                continue;
            visitedStates.insert({nd.position, nd.speed});
            if(nd.position == target)
                return nd.steps;
            for(auto&& nxt : getNextNodes(nd, target)) {
                q.push(nxt);
            }
        }
        return 69420;
    }
};
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