<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<vector<int>> queue;
        set<vector<int>> visited;
       // 
        queue.push({0, 0, 1});
        while(!queue.empty()){
            vector<int> node = queue.front();
            int moves = node[0];
            int position = node[1];
            int speed = node[2];
            queue.pop();
            if(position == target) return moves;
            if(visited.find({position, speed}) != visited.end()) continue;
            visited.insert({position, speed});

            //for "A"
            if(position + speed <= 10000 && position + speed > 0 && visited.find({position+speed, 2*speed}) == visited.end()){
                //visited.insert({position+speed, 2*speed});
                queue.push({moves + 1, position + speed, 2*speed});
            }
            //for "R"
            int newSpeedR = speed > 0 ? -1 : 1;
            if(visited.find({position, newSpeedR}) == visited.end()){
                //visited.insert({position, newSpeedR});
                queue.push({moves + 1, position, newSpeedR});
            }            
        }
        return 0;
    }
};
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