<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 pp pair<long long int, pair<long long int, long long int>>

class Solution {
public:
    struct car{
        int dis;
        int speed;
    };

    int racecar(int target) {
        queue<pp> q;
        set<pair<int, int>> vis;
        // vector<vector<long long int>> vis(1000, vector<long long int>(1000, 0));

        q.push({0, {0, 1}});
        //dis, speed

        while(!q.empty()){

            pp p = q.front();
            q.pop();

            if(p.second.first==target)
                return p.first;

            int newdis = p.second.first+p.second.second;
            int news = p.second.second*2;
            if(newdis<=(2*target) && vis.count({newdis, news})<=0){
                q.push({p.first+1, {newdis, news}});
                vis.insert({newdis, news});
            }

            newdis = p.second.first;
            news = p.second.second<0?1:-1;

            if(newdis<=(2*target) && vis.count({newdis, news})<=0){
                q.push({p.first+1, {newdis, news}});
                vis.insert({newdis, news});
            }
        }

        return -1;
        
    }
};
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