<p>Given a positive integer <code>n</code>,&nbsp;you can apply one of the following&nbsp;operations:</p>

<ol>
	<li>If <code>n</code> is even, replace <code>n</code> with <code>n / 2</code>.</li>
	<li>If <code>n</code> is odd, replace <code>n</code> with either <code>n + 1</code> or <code>n - 1</code>.</li>
</ol>

<p>Return <em>the minimum number of operations needed for</em> <code>n</code> <em>to become</em> <code>1</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 8
<strong>Output:</strong> 3
<strong>Explanation:</strong> 8 -&gt; 4 -&gt; 2 -&gt; 1
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 7
<strong>Output:</strong> 4
<strong>Explanation: </strong>7 -&gt; 8 -&gt; 4 -&gt; 2 -&gt; 1
or 7 -&gt; 6 -&gt; 3 -&gt; 2 -&gt; 1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

typedef pair<long,long> PII;
class Solution {
public:
    int integerReplacement(int n) {
        unordered_map<long,long> used;
        queue<PII> que;
        que.push(PII(n,0));
        
        while(que.size()){
            long num = que.front().first;
            long step = que.front().second;
            que.pop();
            
            if(num == 1){
                return step;
            }
            long newVal;
            if(num %2 == 0){
                newVal = num/2;
                if((used.count(newVal) == 0) || (step+1 < used[newVal])){
                    used[newVal] = step+1;
                    que.push(PII(newVal,step+1));
                }
            }else{
                newVal = num+1;
                if((used.count(newVal) == 0) || (step+1 < used[newVal])){
                    used[newVal] = step+1;
                    que.push(PII(newVal,step+1));
                }
                newVal = num-1;
                if((used.count(newVal) == 0) || (step+1 < used[newVal])){
                    used[newVal] = step+1;
                    que.push(PII(newVal,step+1));
                }
            }
        }
        
        return -1;
            
    }
};
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