<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 {
private:
    struct PairHash {
        size_t operator()(const pair<int, int> &p) const {
            return p.first + 0x9e3779b9 + (p.second << 6) + (p.second >> 2);
        }
    };
    typedef pair<int, int> pii;
public:
    int racecar(int target) {
        unordered_map<pii, int, PairHash> dist;

        int ans;

        pii s = make_pair(0, 1);
        
        queue<pii> q;
        q.push(s);

        dist[s] = 0;

        while(!q.empty()){
            pii p = q.front();
            q.pop();

            if (abs(p.second) > 2 * target)
                continue;

            if(p.first == target){
                ans = dist[p];
                break;
            }

            pii a = make_pair(p.first + p.second, 2 * p.second);
            pii r = make_pair(p.first, (p.second > 0 ? -1 : 1));

            if(dist.find(a) == dist.end()){
                q.push(a);
                dist[a] = dist[p] + 1;
            }

            if(dist.find(r) == dist.end()){
                q.push(r);
                dist[r] = dist[p] + 1;
            }
        }

        return ans;
    }
};
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