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

Last Updated : 16 Jun, 2022

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,

Write a function which first converts number into binary using bin(num) function and returns count of set bits in it.
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.
Sum up count of all set bits.

Python3

# 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:

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:

Python3

# 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

Output

Time Complexity : O(1 )

Auxiliary Space : O(1)

S

Shashank Mishra

Improve

Count total set bits in all numbers from 1 to n | Set 2

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