<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>

//This is where we cant use DFS as the dp states would be oscilating between (num,-1) to (num,1) to (num,-1) and so on
//Very imp question.Very well solved
//https://www.youtube.com/watch?v=DBJPWJr5zZ4

#define ll long long
#define pb push_back

class Solution {
public:
    int racecar(int tg) {
        map<pair<ll,ll>,ll>mp;
        mp[{0,1}]=0;

        queue<vector<ll>>q;
        q.push({0,0,1});
        while(!q.empty()){
            ll cnt = q.front()[0];
            ll pos = q.front()[1];
            ll speed = q.front()[2];
            ll speed2 = 0;

            if(speed>0)speed2=1;
            else speed2 = -1;

            if(pos==tg)return cnt;
            q.pop();
            // cout<<pos<<" "<<speed<<" "<<cnt<<endl;
            if(pos>2*tg || pos<-tg)continue;
            if(mp.find({pos+speed,2*speed})==mp.end() || mp[{pos+speed,2*speed}]>cnt+1){
                mp[{pos+speed,2*speed}]=cnt+1;
                q.push({cnt+1,pos+speed,2*speed});
            }
            if(mp.find({pos,-speed2})==mp.end() || mp[{pos,-speed2}]>cnt+1){
                mp[{pos,-speed2}]=cnt+1;
                q.push({cnt+1,pos,-speed2});
            }
        }
        cout<<"may"<<endl;
        return 0;
    }
};
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