<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:
    typedef pair<long long, long long> pi;
    int racecar(int tgt) {
        unordered_map<int, unordered_set<int>> vis;

        queue<pair<int, pi>> q; // dist, pos, speed
        q.push({0, {0, 1}});
        vis[0].insert(0);

        while(q.size()) {
            auto [d, ps] = q.front();
            auto [pos, speed] = ps;
            q.pop();
            
            // if(pos==tgt) return d;
            if(vis.count(pos) && vis[pos].count(speed)) continue;
            vis[pos].insert(speed);

            // 1. 'A'
            long long npos = pos + speed;
            if(0<=npos && npos<=1e5 && abs(speed*2)<=1e4) {
                if(npos==tgt) return d+1;
                q.push({d+1, {npos, speed*2}});
            }

            // 2. 'R'
            q.push({d+1, {pos, (speed>0)? -1 : 1}});
        }
        return -1;
    }
};
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