<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 {
 unordered_map<long long int, unordered_set<long long int>> s;
public:
    int racecar(long long int target) {
        long long int bfs = 0;
        queue<pair<long long int, long long int>> q;
        q.push({1, 0});
        while(!q.empty()) {
            long long int size = q.size();
            while(size--) {
                long long int speed = q.front().first;
                long long int pos = q.front().second;
                q.pop();
                if(pos < 0 || (s.find(pos) != s.end() && s[pos].find(speed) != s[pos].end()))
                    continue;
                if(target == pos) {
                    return bfs;
                }
                s[pos].insert(speed);
                if(speed > 0) {
                    q.push({speed*2, pos + speed});
                    q.push({-1, pos});
                } else {
                    q.push({speed*2, pos + speed});
                    q.push({1, pos});
                }
            }
            ++bfs;
        }
        return -1;
    }

    
};
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