binpow in fenwick tree

The binpow (binary exponentiation) algorithm in a Fenwick tree is used to efficiently calculate the power of a number modulo a given value. Here are the steps involved in implementing this algorithm:

  1. First, we initialize a variable "result" to 1, which will store the final result of the power calculation.

  2. Next, we start a loop to iterate through all the bits of the exponent. We can do this by using a bitwise operator like the right shift (>>) operation. The loop continues until the exponent becomes zero.

  3. Inside the loop, we check if the least significant bit (LSB) of the exponent is 1. If it is, we multiply "result" by the base number. This is done by using the multiplication operator (*).

  4. After that, we square the base number using the multiplication operator (*). This operation effectively calculates the power of the base number raised to the power of 2.

  5. Finally, we right shift the exponent by 1 to discard the least significant bit. This operation effectively divides the exponent by 2.

  6. The loop continues until the exponent becomes zero, at which point we have calculated the final result.

  7. The time complexity of the binpow algorithm in a Fenwick tree is O(log n), where n is the exponent. This is because we divide the exponent by 2 in each iteration of the loop, effectively reducing the number of iterations logarithmically.

  8. This algorithm is particularly useful when dealing with large exponents, as it avoids the need for repeated multiplication operations.

I hope this explanation helps! Let me know if you have any further questions.