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Write a function that takes the binary representation of an unsigned integer and returns the number of '1' bits it has (also known as the Hamming weight).Note: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.In Java, the compiler represents the signed integers using 2's complement notation. Therefore, in Example 3, the input represents the signed integer. -3. Example 1:Input: n = 00000000000000000000000000001011Output: 3Explanation: The input binary string 00000000000000000000000000001011 has a total of three '1' bits.Example 2:Input: n = 00000000000000000000000010000000Output: 1Explanation: The input binary string 00000000000000000000000010000000 has a total of one '1' bit.Example 3:Input: n = 11111111111111111111111111111101Output: 31Explanation: The input binary string 11111111111111111111111111111101 has a total of thirty one '1' bits. Constraints:The input must be a binary string of length 32. Follow up: If this function is called many times, how would you optimize it?

Question

Write a function that takes the binary representation of an unsigned integer and returns the number of '1' bits it has (also known as the Hamming weight).Note: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.In Java, the compiler represents the signed integers using 2's complement notation. Therefore, in Example 3, the input represents the signed integer. -3. Example 1:Input: n = 00000000000000000000000000001011Output: 3Explanation: The input binary string 00000000000000000000000000001011 has a total of three '1' bits.Example 2:Input: n = 00000000000000000000000010000000Output: 1Explanation: The input binary string 00000000000000000000000010000000 has a total of one '1' bit.Example 3:Input: n = 11111111111111111111111111111101Output: 31Explanation: The input binary string 11111111111111111111111111111101 has a total of thirty one '1' bits. Constraints:The input must be a binary string of length 32. Follow up: If this function is called many times, how would you optimize it?

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Solution

Sure, here is a Python function that solves the problem:

def hammingWeight(n):
    return bin(n).count('1')

This function works by converting the integer n to a binary string using the bin function, and then counting the number of '1' characters in the string with the count method.

If this function is called many times, you could optimize it by using a lookup table to store the Hamming weight of all 16-bit integers, and then use this table to compute the Hamming weight of a 32-bit integer. This would reduce the time complexity from O(n) to O(1). Here is how you could implement this:

class Solution:
    def __init__(self):
        self.table = [0] * 65536
        for i in range(65536):
            self.table[i] = (i & 1) + self.table[i >> 1]

    def hammingWeight(self, n):
        return self.table[n & 65535] + self.table[(n >> 16) & 65535]

In this optimized solution, the __init__ method initializes the lookup table, and the hammingWeight method uses the table to compute the Hamming weight of a 32-bit integer. The & operator is used to get the last 16 bits of the integer, and the >> operator is used to shift the integer 16 bits to the right.

This problem has been solved

Similar Questions

Reverse bits of a given 32 bits unsigned integer.Note:Note that in some languages, such as Java, there is no unsigned integer type. In this case, both input and output will be given as a signed integer type. They should not affect your implementation, as the integer's internal binary representation is the same, whether it is signed or unsigned.In Java, the compiler represents the signed integers using 2's complement notation. Therefore, in Example 2 above, the input represents the signed integer -3 and the output represents the signed integer -1073741825. Example 1:Input: n = 00000010100101000001111010011100Output: 964176192 (00111001011110000010100101000000)Explanation: The input binary string 00000010100101000001111010011100 represents the unsigned integer 43261596, so return 964176192 which its binary representation is 00111001011110000010100101000000.Example 2:Input: n = 11111111111111111111111111111101Output: 3221225471 (10111111111111111111111111111111)Explanation: The input binary string 11111111111111111111111111111101 represents the unsigned integer 4294967293, so return 3221225471 which its binary representation is 10111111111111111111111111111111. Constraints:The input must be a binary string of length 32

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