<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>

#include <iostream>
#include <queue>
#include <set>

class Solution {
public:
    int racecar(int target) {
        struct State {
            int position;
            int speed;
        };

        std::queue<State> q;
        std::set<std::pair<int, int>> visited;

        q.push({0, 1});
        visited.insert({0, 1});

        int steps = 0;

        while (!q.empty()) {
            int size = q.size();
            while (size--) {
                State current = q.front();
                q.pop();

                int position = current.position;
                int speed = current.speed;

                if (position == target) {
                    return steps;
                }

                // Accelerate instruction
                int new_position = position + speed;
                int new_speed = speed * 2;
                if (abs(new_position) <= 2 * target && abs(new_speed) <= 2 * target) {
                    if (visited.find({new_position, new_speed}) == visited.end()) {
                        visited.insert({new_position, new_speed});
                        q.push({new_position, new_speed});
                    }
                }

                // Reverse instruction
                new_speed = speed > 0 ? -1 : 1;
                if (visited.find({position, new_speed}) == visited.end()) {
                    visited.insert({position, new_speed});
                    q.push({position, new_speed});
                }
            }
            steps++;
        }

        return -1; // Should not reach here
    }
};

118906