Find Concatenation of Consecutive Binary Numbers in Python

Suppose we have a number n, we have to find the decimal value of the binary string by concatenating the binary representations of 1 to n one by one in order, if the answer is too large then return answer modulo 10^9 + 7.

So, if the input is like n = 4, then the output will be 220 because, by concatenating binary representation from 1 to 4 will be "1" + "10" + "11" + "100" = 110111000, this is binary representation of 220.

To solve this, we will follow these steps −

• ans := 1
• m := 10^9+7
• for i in range 2 to n, do
  • ans := shift ans (bit length of i) number of times
  • ans := (ans+i) mod m
• return ans

Example

Let us see the following implementation to get better understanding −

def solve(n):
   ans = 1
   m = (10**9+7)
   for i in range(2,n+1):
      ans = ans<<i.bit_length()
      ans = (ans+i) % m
   return ans

n = 4
print(solve(n))

Input

4

Output

220