Program to find bitwise AND of range of numbers in given range in Python

Suppose we have two values start and end, we have to find the bitwise AND of all numbers in the range [start, end] (both inclusive).

So, if the input is like start = 8 end = 12, then the output will be 8 is 1000 in binary and 12 is 1100 in binary, so 1000 AND 1001 AND 1010 AND 1011 AND 1100 is 1000 which is 8.

To solve this, we will follow these steps −

• n := end - start + 1
• x := 0
• for b in range 31 to 0, decrease by 1, do
  • if 2^b < n, then
    • come out from loop
  • if 2^b AND start AND end is non-zero, then
    • x := x + (2^b)
• return x

Example

Let us see the following implementation to get better understanding −

def solve(start, end):
   n = end - start + 1
   x = 0
   for b in range(31, -1, -1):
      if (1 << b) < n:
         break
      if (1 << b) & start & end:
         x += 1 << b
   return x

start = 8
end = 12
print(solve(start, end))

Input

8, 12

Output

8

Arnab Chakraborty

Updated on: 16-Oct-2021

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