<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) {
        // BFS queue: {position, speed, moves}
        queue<vector<int>> lastMove;
        // Use a set to keep track of visited states to avoid revisiting them
        unordered_set<string> visited;
        
        lastMove.push({0, 1, 0}); // Initial state: position=0, speed=1, moves=0
        visited.insert("0,1"); // Mark initial state as visited

        while (!lastMove.empty()) {
            auto current = lastMove.front();
            lastMove.pop();

            int position = current[0];
            int speed = current[1];
            int moves = current[2];

            // Check if we have reached the target
            if (position == target) {
                return moves;
            }

            // Generate the next state after accelerating
            int newPosition = position + speed;
            int newSpeed = speed * 2;
            string newState = to_string(newPosition) + "," + to_string(newSpeed);
            if (visited.find(newState) == visited.end() && newPosition > 0 && newPosition < 2 * target) {
                lastMove.push({newPosition, newSpeed, moves + 1});
                visited.insert(newState);
            }

            // Generate the next state after reversing
            newSpeed = speed > 0 ? -1 : 1;
            newState = to_string(position) + "," + to_string(newSpeed);
            if (visited.find(newState) == visited.end()) {
                lastMove.push({position, newSpeed, moves + 1});
                visited.insert(newState);
            }
        }

        return -1; // If the loop ends without reaching the target, return -1
    }
};

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