<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 t) {
        // Memoization map
        map<array<int, 3>, int> m;

        // Calculate the maximum overshoot range
        int cur = 0;
        for (int i = 1; cur < t; cur += i, i *= 2);
        cout<<cur<<endl;
        queue<array<int, 3>> q;
        // Start with initial state: position 0, speed 1, direction forward (1)
        q.push({0, 1, 1});
        int ans = -1;

        while (!q.empty()) {
            ++ans;
            for (int i = q.size(); i > 0; --i) {
                auto [pos, speed, dir] = q.front();
                q.pop();

                // If the current position is the target, return the number of moves
                if (pos == t) return ans;

                // Accelerate: move to next position and increase speed
                int newPos = pos + speed;
                int newSpeed = speed * 2;
                if (newPos <= 2 * t && newPos >= t - cur) {
                    array<int, 3> newState = {newPos, newSpeed, dir};
                    if (m.find(newState) == m.end()) {
                        q.push(newState);
                        m[newState] = ans;
                    }
                }

                // Reverse: change direction and reset speed
                newSpeed = dir == 1 ? -1 : 1;
                array<int, 3> reverseState = {pos, newSpeed, -dir};
                if (m.find(reverseState) == m.end()) {
                    q.push(reverseState);
                    m[reverseState] = ans;
                }
            }
        }
        return -1;
    }
};
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