<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>

#define sp <<" "<<
class Solution {
public:
    int racecar(int target) {
        map<pair<long,long>,int> d;

        queue<array<long,3>> q;
        q.push({0,1,0});

        int ans = 0;
        while(!q.empty()){
            auto [pos,speed,dis] = q.front();
            q.pop();

            if(pos == target){
                return dis;
            }

            // cout << pos sp speed sp dis sp endl;
            d[{pos,speed}] = dis;

            // when there is an A
            if(pos + speed >= 0 and pos + speed <= 4*target and d.count({pos + speed, 2*speed}) == 0){
                d[{pos + speed, 2*speed}] = dis + 1;
                q.push({pos + speed,2*speed,dis+1});
            }

            // when there is an R
            if(speed > 0){
                speed = -1;
            }
            else{
                speed = 1;
            }
            if(d.count({pos,speed}) == 0){
                d[{pos,speed}] = dis + 1;
                q.push({pos,speed,dis + 1});
            }
        }

        return -1;
    }
};

/*
4
100
*/
133091