<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 GlobalBestCost = INT_MAX;
    void bestRoute(int costToGetHere, int target){
        // Don't bother investigating solutions that are over the global best:
        if (costToGetHere > GlobalBestCost){
            return;
        }
        int distance = 1;
        costToGetHere++;
        while(distance < target){
            // This is equivalent to updatign position an speed:
            distance = (distance << 1) + 1;
            costToGetHere++;
        }
        
        // We have reached our destination:
        if (distance == target){
            GlobalBestCost = min(GlobalBestCost, costToGetHere);
            return;
        }

        // We overshot, reverse and then recurse the remaining distance, adding the reverse cost:
        bestRoute(costToGetHere + 1, distance - target);

        // We will undershoot(undo last acceleration), reverse, walk some steps, reverse and then recurse:
        // Undo last acceleration:
        distance = distance >> 1;
        costToGetHere--;
        // Try every possible number of steps in reverse that makes sense
        int reverse_steps = 0;
        int distance_reverse = 0;
        while(distance_reverse < target){
            bestRoute(costToGetHere + 2 + reverse_steps, target - distance + distance_reverse);
            reverse_steps++;
            distance_reverse = (distance_reverse << 1) + 1;
        }
    }

    int racecar(int target) {
        bestRoute(0, target);
        return GlobalBestCost;
    }
};
8973