<div> 🔴 2025-11-08 #dynamic_programming #bit_manipulation #memoization </div>Given an integer <code>n</code>, you must transform it into <code>0</code> using the following operations any number of times:

<ul>
<li>Change the rightmost (<code>0th</code>) bit in the binary representation of <code>n</code>.</li>
<li>Change the <code>ith</code> bit in the binary representation of <code>n</code> if the <code>(i-1)th</code> bit is set to <code>1</code> and the <code>(i-2)th</code> through <code>0th</code> bits are set to <code>0</code>.</li>
</ul>

Return the minimum number of operations to transform <code>n</code> into <code>0</code>.

&nbsp;
Example 1:

<pre>Input: n = 3
Output: 2
Explanation: The binary representation of 3 is "11".
"11" -&gt; "01" with the 2nd operation since the 0th bit is 1.
"01" -&gt; "00" with the 1st operation.
</pre>

Example 2:

<pre>Input: n = 6
Output: 4
Explanation: The binary representation of 6 is "110".
"110" -&gt; "010" with the 2nd operation since the 1st bit is 1 and 0th through 0th bits are 0.
"010" -&gt; "011" with the 1st operation.
"011" -&gt; "001" with the 2nd operation since the 0th bit is 1.
"001" -&gt; "000" with the 1st operation.
</pre>

&nbsp;
Constraints:

<ul>
<li><code>0 &lt;= n &lt;= 109</code></li>
</ul>

🔴 2025-11-08 
 #dynamic_programming #bit_manipulation #memoization 

Given an integer n, you must transform it into 0 using the following operations any number of times:
Change the rightmost (0th) bit in the binary representation of n.
Change the ith bit in the binary representation of n if the (i-1)th bit is set to 1 and the (i-2)th through 0th bits are set to 0.
Return the minimum number of operations to transform n into 0.
 
Example 1:
Input: n = 3
Output: 2
Explanation: The binary representation of 3 is "11".
"11" -> "01" with the 2nd operation since the 0th bit is 1.
"01" -> "00" with the 1st operation.


Example 2:
Input: n = 6
Output: 4
Explanation: The binary representation of 6 is "110".
"110" -> "010" with the 2nd operation since the 1st bit is 1 and 0th through 0th bits are 0.
"010" -> "011" with the 1st operation.
"011" -> "001" with the 2nd operation since the 0th bit is 1.
"001" -> "000" with the 1st operation.


 
Constraints:
0 <= n <= 109

1611.minimum-one-bit-operations-to-make-integers-zero