Number of 1 Bits

Clarify the problem:

• The problem requires counting the number of 1 bits (binary ones) in an unsigned integer.
• We need to implement a function that takes an unsigned integer as input and returns the count of 1 bits.

Analyze the problem:

• Input: An unsigned integer.
• Output: The count of 1 bits.
• Constraints: The input is an unsigned 32-bit integer.

Design an algorithm:

• We can count the number of 1 bits by performing bitwise operations on the input number.
• Initialize a variable count as 0 to store the count of 1 bits.
• Iterate from 0 to 31 (since the input is a 32-bit integer):
  • Check if the current bit is 1 by performing a bitwise AND operation between the input number and a bitmask (1 shifted to the current position).
  • If the result is not zero, increment the count by 1.
• Return the final count.

Explain your approach:

• We will implement a function called hammingWeight that takes an unsigned integer as input.
• Initialize a variable count as 0.
• Iterate from 0 to 31 and perform bitwise operations to check the bits.
• If a bit is 1, increment the count.
• Return the final count.

Write clean and readable code:

python

def hammingWeight(n):
    count = 0
    for i in range(32):
        if n & (1 << i):
            count += 1
    return count

Test your code:

python

# Test case 1
# Input: 11 (binary: 1011)
# The number of 1 bits is 3.
assert hammingWeight(11) == 3

# Test case 2
# Input: 128 (binary: 10000000)
# The number of 1 bits is 1.
assert hammingWeight(128) == 1

# Test case 3
# Input: 0
# The number of 1 bits is 0.
assert hammingWeight(0) == 0

Optimize if necessary:

• The provided solution has a time complexity of O(1) since we iterate through 32 bits, which is a constant number.
• The space complexity is O(1) since we use a constant amount of extra space.

Handle error cases:

• The given code assumes that the input n is a valid unsigned 32-bit integer. If the input is not within this range, the behavior is undefined.

Discuss complexity analysis:

• The time complexity of the solution is O(1) since we iterate through 32 bits, which is a constant number.
• The space complexity is O(1) since we use a constant amount of extra space to store the count of 1 bits.