<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<pair<int,int>,int>>q;
        q.push({{0,1},0});
        map<pair<int,int>,bool>vis;
        vis[{0,1}] = true;        
        while(q.size()) {
            
            int sz = q.size();
            
                int cur = q.front().first.first;
                int speed = q.front().first.second;
                int level = q.front().second;
                q.pop();
                int nxtLevel = level+1;
            
                if( (cur + speed <= 2*target) and (cur + speed >= 0)) {
                    
                    int nxt = cur + speed;
                    int nxtSpeed = speed * 2;
                    
                    if(nxt == target) {
                        return nxtLevel;
                    }
                    
                    if(!vis[{nxt,nxtSpeed}]) {
                        q.push({{nxt, nxtSpeed},nxtLevel});                    
                        vis[{nxt,nxtSpeed}] = true;
                    }                    
                }


                // reverse;
                int nxt = cur;
                int nxtSpeed;
                if(speed > 0) {
                    nxtSpeed = -1;
                } else {
                    nxtSpeed = 1;
                }

                if(!vis[{nxt,nxtSpeed}]) {
                    q.push({{nxt, nxtSpeed},nxtLevel});              
                    vis[{nxt,nxtSpeed}] = true;
                }
                                                        
        }
        
        return -1;
        
    }
};
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