<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 ll long long
#define pll pair<ll,ll>

const ll MAX = 1e4 + 5;

class Solution {
public:
    map<ll,ll> ans;
    map<pll, bool> vis;

    struct tup {
        ll pos, speed, level;
    };

    void precompute(ll target) {
        queue<tup> q;
        vis[{0,1}] = true;
        q.push({0,1,0});
        ans[0]=0;

        while (!q.empty() ) {
            tup cur = q.front();
            q.pop();
            ll pos = cur.pos, speed = cur.speed, level = cur.level;
            if(pos > MAX || pos < - MAX) continue;

            if(ans[pos]) ans[pos]=min(ans[pos], level);
            else ans[pos]=level;
            
            if(pos==target) return;

            pll neighbor = {pos+speed, speed << 1};
            tup nTup = {pos+speed, speed << 1, level+1};
            if (!vis[neighbor]) {
                vis[neighbor] = true;
                q.push(nTup);
            }
            neighbor = {pos, (speed > 0)?-1:1};
            nTup = {pos, (speed > 0)?-1:1, level+1};
            if (!vis[neighbor]) {
                vis[neighbor] = true;
                q.push(nTup);
            }
        }
    }

    int racecar(ll target) {
        precompute(target);
        return ans[target];
    }
};
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