<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:

    // string help(int pos, int speed, int target){
    //     // if(pos == target) return "";
        

    //     // // A
    //     // help(pos+speed, speed*2, target);

    //     // // R
    //     // if(speed > 0)
    //     //     help(pos, -1, target);
    //     // else
    //     //     help(pos, 1, target);



    // } 
    int racecar(int target) {
        queue <pair<pair<int, long long>, int>> q; // {{pos, speed}, commands}
        q.push({{0, 1}, 0});
        set <pair<int, long long>> vis; 
        vis.insert({0, 1});
        while(!q.empty()){
            auto it = q.front();
            int pos = it.first.first;
            long long speed = it.first.second;
            int commands = it.second;
            q.pop();

            // R
            if(speed > 0){
                if(vis.find({pos, -1}) == vis.end()){
                    vis.insert({pos, -1});
                    q.push({{pos, -1}, commands + 1});
                }
            }
            else{
                if(vis.find({pos, 1}) == vis.end()){
                    vis.insert({pos, 1});
                    q.push({{pos, 1}, commands + 1});
                }
            }

            // A
            if(pos + speed < 2*target && vis.find({pos + speed, speed * 2}) == vis.end()){
                vis.insert({pos + speed, speed * 2});
                q.push({{pos + speed, speed * 2}, commands + 1});
                if(pos + speed == target) return commands + 1;
            }

            

        }

        return -1;


    }
};
264303