<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) {
        int ans=0;
        int pos=0;
        queue<pair<int,int>> q;
        vector<int> vis(1e5+10,0);
        vector<int> visp(1e5+10,0);
        vector<int> visn(1e5+10,0);
        map<int,map<int,int>> mp;
        q.push({0,1});
        vis[0]=1;
        visp[0]=1;
        mp[1][0]=1;
        while(!q.empty())
        {
            int size=q.size();
            for(int i=0;i<size;i++)
            {
                int curpos=q.front().first, speed=q.front().second;
                q.pop();
                // acc
                int newpos=curpos+speed;

                if(curpos==target) {
                    pos=curpos;
                    break;
                }
                if(newpos>0&&newpos<1e5)
                {
                    if(mp.find(newpos)==mp.end()||mp[newpos].find(speed*2)==mp[newpos].end())
                    {
                        vis[newpos]=1;
                        // if(speed>0)
                        // visp[newpos]=1;
                        // else
                        // visn[newpos]=1;
                        q.push({newpos,2*speed});
                        mp[newpos][2*speed]=1;
                    }
                }
                // r
                if(speed>0)
                {
                    // if(visn[curpos]==0)
                        q.push({curpos,-1});

                }
                else 
                // if(visp[curpos]==0)
                        q.push({curpos,1});

            }
            if(pos==target) break;
            ans++;
        }
        return ans;
    }
};
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