Josephus Problem Using Bit Magic - Python Datastructures Algorithm

Hi,Today program implements the Josephus Problem using Bit Magic in Python. The Josephus Problem is a famous mathematical problem that involves selecting a person from a group of 'n' people arranged in a circle and executing them in a certain order. The program uses bitwise operations to find the survivor in the circle. The user is prompted to enter the number of people and the program calculates and prints the survivor's position. The program utilizes the bitwise left shift and bitwise or operations to perform the calculation efficiently.

def josephus(n):
    # Determine the position of the most significant bit
    msb = 0
    while (1 << msb) <= n:
        msb += 1
    msb -= 1

    # Determine the value of the survivor
    return (n ^ (1 << msb)) << 1 | 1


# Example usage
n = 7
print("The survivor position for n={} is: {}".format(n, josephus(n)))

we first determine the position of the most significant bit in n using a simple loop. We then use this information to calculate the position of the survivor using bit operations.

The ^ operator is used to perform a bitwise XOR operation between n and 2^msb, where msb is the position of the most significant bit. This results in a value that has all bits the same as n, except for the bit at position msb, which is flipped. We then shift this value to the left by one bit and set the least significant bit to 1 using the | operator. This gives us the position of the survivor.

For example, if n is 7 (binary 0b111), the most significant bit is at position 2. We perform the following calculation:

7 ^ 4 = 3 (binary 0b011)
(3 << 1) | 1 = 7

So the survivor is at position 7. Thanks.