<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) {
        int dp[30000][30];
        memset(dp, -1, sizeof(dp));
        // for(int i=0;i<30000;i++){
        //     for(int j=0;j<30;++j){
        //         cout<<dp[i][j]<<" ";
        //     }
        //     cout<<endl;
        // }
        queue<pair<int,int>> q;
        dp[0][0] = 0;
        q.push({0, 0});
        while (1) {
            int pos,speed;
            speed = q.front().second;
            pos = q.front().first;
            // cout<<pos<<" "<<speed<<endl;

            if(pos==target) return dp[pos][speed];
            q.pop();
            if (speed < 15) {
                // cout<<(1<<speed)<<endl;
                // cout<<" "<<pos<<" "<<speed<<endl;;
                int nw = pos + (1 << speed);
                // cout<<nw<<"abc"<<endl;
                if (nw < 3e4 && speed < 14 && dp[nw][speed + 1] == -1) {
                    dp[nw][speed + 1] = dp[pos][speed] + 1;
                    // cout<<1<<endl;
                    q.push({nw,speed+1});
                }
                if (dp[pos][15]==-1){
                    dp[pos][15]=dp[pos][speed]+1;
                    q.push({pos,15});
                }

            } else {
                int nw = pos - (1 << (speed - 15));
                if (nw > 0 && speed < 29 && dp[nw][speed + 1] == -1) {
                    dp[nw][speed + 1] = dp[pos][speed] + 1;
                    q.push({nw,speed+1});
                }
                if (dp[pos][0]==-1){
                    dp[pos][0]=dp[pos][speed]+1;
                    q.push({pos,0});
                }
            }
        }
    }
};
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