<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:

    pair<long,long> acc(pair<long,long> attr) {
        long pos = attr.first;
        long speed = attr.second;
        return {pos+speed, speed*2};
    }
    pair<long,long> rev(pair<long,long> attr) {
        long pos = attr.first;
        long speed = attr.second;
        long newSpeed;
        if (speed>0) {
            newSpeed = -1;
        } else{
            newSpeed = 1;
        }
        return {pos, newSpeed};
    }

    int racecar(int target) {

        if (target== 0) {
            return 0;
        }
        int numSteps = 0;
        pair<long,long> attr({0,1});
        set<pair<long,long>> visited;
        

        queue<pair<long,long>> q;
        q.push(attr);
        visited.insert(attr);

        while(!q.empty()) {
            int n = q.size();
            while(n--){
                pair<long,long> top = q.front();
                q.pop();
                if(top.first>20000){
                    continue;
                }

                if (top.first == target){
                    return numSteps;
                }
                else{
                    pair<long,long> accelCar = acc(top);
                    if(!visited.count(accelCar)){
                        q.push(accelCar);
                        visited.insert(accelCar);
                    }

                    pair<long,long> revCar = rev(top);;
                    if(!visited.count(revCar)){
                        q.push(revCar);
                        visited.insert(revCar);
                    }                    
                }              
                
            }
            numSteps++;
        }
 
 
        return numSteps;;
    }
};
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