feat: add count_bits algorithm with doctests

bit_manipulation/count_bits.py

@@ -0,0 +1,32 @@
+def count_bits(n: int) -> int:
+    """
+    Count the number of set bits (1s) in the binary representation of a
+    non-negative integer.
+
+    Examples:
+    >>> count_bits(0)
+    0
+    >>> count_bits(1)
+    1
+    >>> count_bits(5)  # 101
+    2
+    >>> count_bits(15)  # 1111
+    4
+    >>> count_bits(16)  # 10000
+    1
+    """
+    if n < 0:
+        raise ValueError("Input must be non-negative")
+
+    count = 0
+    while n > 0:
+        count += n & 1
+        n >>= 1
+
+    return count
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()