Python map function | Count total set bits in all numbers from 1 to n

Given a positive integer n, count the total number of set bits in binary representation of all numbers from 1 to n. Examples:

Input: n = 3
Output:  4
Binary representations are 1, 2 and 3
1, 10 and 11 respectively. Total set
bits are 1 + 1 + 2 = 4.

Input: n = 6
Output: 9

Input: n = 7
Output: 12

Input: n = 8
Output: 13

We have existing solution for this problem please refer Count total set bits in all numbers from 1 to n link. We can solve this problem in python using map() function. Approach is very simple,

1. Write a function which first converts number into binary using bin(num) function and returns count of set bits in it.
2. Map user defined function on list of numbers from 1 to n and we will get list of individual count of set bits in each number.
3. Sum up count of all set bits.

# Function to Count total set bits in all numbers
# from 1 to n

# user defined function
def countSetBit(num):

     # convert decimal value into binary and
     # count all 1's in it
     binary = bin(num)

     return len([ch for ch in binary if ch=='1'])

# function which count set bits in each number
def countSetBitAll(input):
    
    # map count function on each number
    print (sum(map(countSetBit,input)))

# Driver program
if __name__ == "__main__":
    n = 8
    input=[]
    for i in range(1,n+1):
         input.append(i)
    countSetBitAll(input)

Output:

13

Time Complexity : O(log n)

Auxiliary Space: O(log n)

Another Approach:

The approach can be made more efficient using a lambda function, and the count() method in order to count the set bits in the binary form, as outlined below:

# Function to Count total set bits in all numbers
# from 1 to n


#Get the sum of all set bits
#in the range [1, n]
def countSetBitAll(n):
    # map count function on each number
    print(sum(map(lambda x: bin(x).count("1"), range(1, n + 1))))


# Driver program
n = 8

#Function Call
countSetBitAll(n)


#This code is contributed by phasing17

13

Time Complexity : O(1 )

Auxiliary Space : O(1)