<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) {
        int ans = 0;
        queue<pair<int, pair<int, int>>>q;
        q.push({0, {1, 0}});
        unordered_map<int, unordered_set<int>> visited;
        visited[0].insert(1);

        while(!q.empty()) {
            auto [pos, info] = q.front();
            auto [speed, level] = info;
            q.pop();
            int a_speed = 2*speed;
            int a_pos = pos + speed;
            int a_level = level + 1;
            if (a_speed < 100000 && a_speed > -100000 &&visited[a_pos].find(a_speed) == visited[a_pos].end()){
                visited[a_pos].insert(a_speed);
                q.push({a_pos, {a_speed, a_level}});
            }
            if (a_pos == target) {
                ans = a_level;
                break;
            }
            int r_speed = speed > 0 ? -1 : 1;
            int r_level = level + 1;
            if (visited[pos].find(r_speed) == visited[pos].end()){
                visited[pos].insert(r_speed);
                q.push({pos, {r_speed, r_level}});
            }
        }
        return ans;
    }
};
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