Syntax error Program to apply Russian Peasant Multiplication in Python

Program to apply Russian Peasant Multiplication in Python

Suppose we are given four integer numbers p, q, r, and k. We will use a method called the Russian Peasant Multiplication method and determine the value of (p + q.i)^r = r + s.i. We have to return the value of r mod k and s mod k.

So, if the input is like p = 3, q = 0, r = 8, k = 10000, then the output will be (6561, 0) 3^8 = 6561, as q = 0 value of r mod k = 6561.

To solve this, we will follow these steps −

  • if r is same as 0, then
    • return 1
  • therwise when r is same as 1, then
    • return a pair containing (p mod k, q mod k)
  • therwise when r mod 2 is same as 0, then
    • return solve((p*p - q*q) mod k, 2*p*q mod k, r/2, k)
  • therwise,
    • a pair (pr, qr) = solve(p, q, r-1, k)
    • return a pair containing ((p * pr - q * qr) mod k, (p * qr + q * pr) mod k)

Example

Let us see the following implementation to get better understanding −

def solve(p, q, r, k):
   if r == 0:
      return 1
   elif r == 1:
      return (p % k, q % k)
   elif r % 2 == 0:
      return solve((p*p - q*q) % k, 2*p*q % k, r/2, k)
   else:
      (pr, qr) = solve(p, q, r-1, k)
      return ((p * pr - q * qr) % k, (p * qr + q * pr) % k)

print(solve(3, 0, 8, 10000))

Input

3, 0, 8, 10000

Output

(6561, 0)
Updated on: 2021-10-23T07:52:50+05:30

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