<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 getshift(int step) {
        if (step % 2 == 0) {
            step /= 2;
            return 1 << step;
        }
        --step;
        step /= 2;
        return -(1 << step);
    }

    int racecar(int target) {
        vector<vector<int> > dp(4 * target + 4, vector<int> (30, 1e9));
        int mx = 4 * target + 4;
        dp[2 * target][0] = 0;
        vector<pair<int, int> > q;
        q.push_back({2 * target, 0});
        int head = 0, tail = 1;
        while (head < tail) {
            int coord = q[head].first, step = q[head].second;
            int shift = getshift(step);
            if (coord + shift < mx && coord + shift >= 0 && step + 2 < 30 && dp[coord + shift][step + 2] > dp[coord][step] + 1) {
                dp[coord + shift][step + 2] = dp[coord][step] + 1;
                q.push_back({coord + shift, step + 2});
                ++tail;
            }
            if (shift > 0) {
                if (dp[coord][1] > dp[coord][step] + 1) {
                    dp[coord][1] = dp[coord][step] + 1;
                    q.push_back({coord, 1});
                    ++tail;
                }
            } else {    
                if (dp[coord][0] > dp[coord][step] + 1) {
                    dp[coord][0] = dp[coord][step] + 1;
                    q.push_back({coord, 0});
                    ++tail;
                }
            }
            ++head;
        }
        int answer = 1e9;
        for (int i = 0; i < 30; ++i) {
            answer = min(answer, dp[3 * target][i]);
        }
        return answer;
    }
};
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