<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>> states;
        unordered_set<string> visited;
        states.push({0, 1});

        int depth = 0;
        while (!states.empty()) {
            int levelSize = states.size();
            for (int i = 0; i < levelSize; i++) {
                pair<int, int> currState = states.front(); states.pop();

                if (currState.first == target) return depth;

                int nextPos = currState.first + currState.second, nextSpeed = currState.second * 2;
        
                if (visited.find(to_string(nextPos) + " " + to_string(nextSpeed)) == visited.end() && nextPos > 0 && nextPos < target * 2)
                    states.push({nextPos, nextSpeed});
                visited.insert(to_string(nextPos) + " " + to_string(nextSpeed));
                nextPos = currState.first, nextSpeed = (currState.second >= 0)? -1 : 1;
                if (visited.find(to_string(nextPos) + " " + to_string(nextSpeed)) == visited.end() && nextPos > 0 && nextPos < target * 2)
                    states.push({nextPos, nextSpeed});
                visited.insert(to_string(nextPos) + " " + to_string(nextSpeed));
            }
            depth++;
        }

        return -1;
    }
};
90536