<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:
#define ll long long
#define pll pair<ll,ll>
// #define plll pair<pair<ll,ll>, ll>
#define ff first
#define ss second

const ll MAX = 1e4 + 5;
const ll INF = 1e9 + 5;
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;

    ll cnt=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;
        //cout<<pos<<" "<<speed<<" "<<level<<" "<<ans[pos]<<endl;

        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);
        }
        cnt++;
    }
}

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