<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) {

        vector<vector<long>> prev = {{0, 1}};
        unordered_set<string> visited = {hash(0, 1)};
        int res = 1;
        while (!prev.empty()) {
            vector<vector<long>> curr;
            for (auto& p : prev) {
                // A
                long pos = p[0] + p[1];
                long spd = p[1] * 2;
                if (pos == target) {
                    return res;
                }

                string h = hash(pos, spd);
                if (visited.count(h) == 0) {
                    curr.push_back({pos, spd});
                    visited.insert(h);
                }

                // R
                if ((p[0] + p[1] < target && p[1] < 0) ||
                    (p[0] + p[1] > target && p[1] > 0)) {
                    pos = p[0];
                    spd = p[1] > 0 ? -1 : 1;
                    h = hash(pos, spd);
                    if (visited.count(h) == 0) {
                        curr.push_back({pos, spd});
                        visited.insert(h);
                    }
                }
            }
            prev = curr;
            res += 1;
        }
        return 0;
    }

    string hash(long p, long s) { return to_string(p) + "," + to_string(s); }
};
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