<p>Given the binary representation of an integer as a string <code>s</code>, return <em>the number of steps to reduce it to </em><code>1</code><em> under the following rules</em>:</p>

<ul>
	<li>
	<p>If the current number is even, you have to divide it by <code>2</code>.</p>
	</li>
	<li>
	<p>If the current number is odd, you have to add <code>1</code> to it.</p>
	</li>
</ul>

<p>It is guaranteed that you can always reach one for all test cases.</p>

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

<pre>
<strong>Input:</strong> s = &quot;1101&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> &quot;1101&quot; corressponds to number 13 in their decimal representation.
Step 1) 13 is odd, add 1 and obtain 14.&nbsp;
Step 2) 14 is even, divide by 2 and obtain 7.
Step 3) 7 is odd, add 1 and obtain 8.
Step 4) 8 is even, divide by 2 and obtain 4.&nbsp; 
Step 5) 4 is even, divide by 2 and obtain 2.&nbsp;
Step 6) 2 is even, divide by 2 and obtain 1.&nbsp; 
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;10&quot;
<strong>Output:</strong> 1
<strong>Explanation:</strong> &quot;10&quot; corresponds to number 2 in their decimal representation.
Step 1) 2 is even, divide by 2 and obtain 1.&nbsp; 
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;1&quot;
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>1 &lt;= s.length&nbsp;&lt;= 500</code></li>
	<li><code>s</code> consists of characters &#39;0&#39; or &#39;1&#39;</li>
	<li><code>s[0] == &#39;1&#39;</code></li>
</ul>

class Solution {
public:
    int numSteps(string s) {
        int ans = 0;
        // 1101 -> 1110 -> 111 -> 1000 -> 100 -> 10 -> 1 -> TC O(n^2)
        while(s != "1") {
            ans++;
            if (s[s.size() - 1] == '1') {
                int j = s.size() - 2;
                while(j >= 0 && s[j] == '1') {
                    j--;
                }
                if (j < 0) {
                    string temp = "";
                    for (int i = 0; i < s.size() - 1; i++)
                        temp += "0";;
                    s = "1" + temp;
                    ans++;
                } else {
                    s[s.size() - 1] = '0';
                    s[j] = '1';
                }
            } else
                s = s.substr(0, s.size() - 1);
        }
        return ans;
    }
};
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