<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:
    using ipair = pair<long long, long long>;
    int racecar(int target) {
        auto hash = [](const ipair &p) {
            return (p.first + 10000) * 20001 + p.second;
        };
        unordered_set<ipair, decltype(hash)> visited;
        queue<ipair> candidates;
        candidates.push({0, 1});
        int steps = 0;

        while (!candidates.empty()) {
            int n = candidates.size();
            for (int i = 0; i < n; ++i) {
                auto [pos, speed] = candidates.front();
                candidates.pop();
                if (pos == target) {
                    return steps;
                }

                ipair operationA = make_pair(pos + speed, speed * 2);
                if (abs(operationA.first) <= 20000 && !visited.count(operationA)) {
                    visited.insert(operationA);
                    candidates.push(operationA);
                }

                ipair operationB = make_pair(pos, speed > 0 ? -1 : 1);
                if (abs(operationB.first) <= 20000 &&!visited.count(operationB)) {
                    visited.insert(operationB);
                    candidates.push(operationB);
                }
            }
            ++steps;
        }

        return 0;
    }
};
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