# 191-number-of-1-bits


Try it on <a href='https://leetcode.com/problems/191-number-of-1-bits'>leetcode</a>

## Description
<div class="description">
<div><p>Write a function that takes an unsigned integer and returns the number of '1' bits it has (also known as the <a href="http://en.wikipedia.org/wiki/Hamming_weight" target="_blank">Hamming weight</a>).</p>

<p><strong>Note:</strong></p>

<ul>
	<li>Note that in some languages, such as Java, there is no unsigned integer type. In this case, the input will be given as a signed integer type. It should not affect your implementation, as the integer's internal binary representation is the same, whether it is signed or unsigned.</li>
	<li>In Java, the compiler represents the signed integers using <a href="https://en.wikipedia.org/wiki/Two%27s_complement" target="_blank">2's complement notation</a>. Therefore, in <strong>Example 3</strong>, the input represents the signed integer. <code>-3</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>

<pre><strong>Input:</strong> n = 00000000000000000000000000001011
<strong>Output:</strong> 3
<strong>Explanation:</strong> The input binary string <strong>00000000000000000000000000001011</strong> has a total of three '1' bits.
</pre>

<p><strong>Example 2:</strong></p>

<pre><strong>Input:</strong> n = 00000000000000000000000010000000
<strong>Output:</strong> 1
<strong>Explanation:</strong> The input binary string <strong>00000000000000000000000010000000</strong> has a total of one '1' bit.
</pre>

<p><strong>Example 3:</strong></p>

<pre><strong>Input:</strong> n = 11111111111111111111111111111101
<strong>Output:</strong> 31
<strong>Explanation:</strong> The input binary string <strong>11111111111111111111111111111101</strong> has a total of thirty one '1' bits.
</pre>

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

<ul>
	<li>The input must be a <strong>binary string</strong> of length <code>32</code>.</li>
</ul>

<p>&nbsp;</p>
<strong>Follow up:</strong> If this function is called many times, how would you optimize it?</div>
</div>

## Solution(Python)
```Python
class Solution:
    def hammingWeight(self, n: int) -> int:
        return self.bitmanipulation(n)

    # Time Complexity: O(2^logn)
    # Space Complexity: O(logn)
    def bruteforce(self, n):
        n = bin(n)

        def recur(n):
            if not n:
                return 0
            return recur(n[1:]) + 1 if n[0] == "1" else recur(n[1:])

        return recur(n)

    # Time Complexity: O(log(n))
    # Space Complexity: O(logn)
    def naive(self, n):
        return bin(n).count("1")

    # Time Complexity: O(log(n))
    # Space Complexity: O(1)
    def bitmanipulation(self, n):
        cnt = 0
        while n:
            n &= n - 1
            cnt += 1
        return cnt

```