<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 solveBfs(int target){
       queue<pair<int,pair<int,int>> >q;
       q.push({0,{1,0}}); //pos speed cnt
       set<string>vis;
       string key = to_string(0) + "," + to_string(1);
       vis.insert(key);
       while(!q.empty()){
            pair<int,pair<int,int> > front = q.front();
            q.pop();
            int currPos = front.first;
            int currSpd = front.second.first;
            int currSteps = front.second.second;
            if(currPos == target) return currSteps;
            
            // A
            int nextPos = currPos + currSpd;
            int nextSpd = currSpd * 2;
            key = to_string(nextPos) + "," + to_string(nextSpd);
            if(!vis.count(key) && abs(nextPos - target) < target){
                vis.insert(key);
                q.push({nextPos,{nextSpd,currSteps+1}});
            }
            // R
             nextPos = currPos;
             nextSpd = currSpd < 0 ? 1 : -1;
            key = to_string(nextPos) + "," + to_string(nextSpd);
            if(!vis.count(key) && abs(nextPos - target) < target){
                vis.insert(key);
                q.push({nextPos,{nextSpd,currSteps+1}});
            }
       }
       return -1;
    }
    int racecar(int target) {
        return solveBfs(target);
    }
};
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