<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>

#define MAXL 18
#define MAXV (numeric_limits<int>::max())
#define LOC(idx) ((idx))
#define VALIDI(i) ((i)>=0&&(i)<dp.size())
#define VALIDJ(j) ((j)>=0&&(j)<MAXL)

class Solution {
public:
    int racecar(int target) {
        vector<vector<vector<int>>>dp(1<<((int)ceil(log2(target))+1),vector<vector<int>>(MAXL,vector<int>(2,MAXV)));
        dp[LOC(0)][0][0]=0;
        for(int phase=1;phase<=MAXL;phase++){
            for(int i=0;i<dp.size();i++)for(int j=0;j<MAXL;j++)for(int k=0;k<2;k++)if(dp[i][j][k]!=MAXV){
                // A
                int ni=i+(k?-1:1)*(1<<j);
                int nj=j+1;
                if(VALIDI(ni)&&VALIDJ(nj))dp[ni][nj][k]=min(dp[ni][nj][k],dp[i][j][k]+1);
                // R
                dp[i][0][!k]=min(dp[i][0][!k],dp[i][j][k]+1);
            }
        }
        int sol=numeric_limits<int>::max();
        for(int i=0;i<MAXL;i++)for(int j=0;j<2;j++)sol=min(sol,dp[LOC(target)][i][j]);
        return sol;
    }
};
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