<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) {
        queue<tuple<int, int, int>> q;
    // Use a set to keep track of visited states (position, speed)
    unordered_set<string> visited;

    // Initialize with the starting state (position=0, speed=1, steps=0)
    q.push({0, 1, 0});
    visited.insert("0,1");

    while (!q.empty()) {
        int position, speed, steps;
        tie(position, speed, steps) = q.front();
        q.pop();

        // If the target is reached
        if (position == target) {
            return steps;
        }

        // Option 1: Accelerate
        int new_position = position + speed;
        int new_speed = speed * 2;
        string state1 = to_string(new_position) + "," + to_string(new_speed);

        if (visited.find(state1) == visited.end() && abs(new_position) <= 2 * target) {
            visited.insert(state1);
            q.push({new_position, new_speed, steps + 1});
        }

        // Option 2: Reverse
        new_position = position;
        new_speed = speed > 0 ? -1 : 1;
        string state2 = to_string(new_position) + "," + to_string(new_speed);

        if (visited.find(state2) == visited.end()) {
            visited.insert(state2);
            q.push({new_position, new_speed, steps + 1});
        }
    }
    return -1; // In case no solution is found, although this shouldn't happen
    }
};
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