This is similar to another question but it has an invariant method. I can't figure this out. Please help! Thank you!

This second python programming assignment, PA2, is about loop invariants. You will write a function eExp(left,right) that computes exponentials left ** right in a similar fashion as the egyptian_multiplication function computes products, as discussed in lecture 8: loop invariants.

eExp.txt contains some skeleton code. Download it and rename it eExp.py. Study egyptian multiplication in the lecture slides. The program logic in egyptian_multiplication, and thus the loop invariant is based on the fact that

 a * b = if odd(a): b + (a//2)*(b*2) else: (a//2)*(b*2) 

and that p stepwise gathers the product.

For your exponentiation code, the program logic, and thus the loop invariant, is based on the fact that

 n ** k = if odd(k): n * (n*n)**(k//2) else (n*n)**(k//2) 

and that e stepwise gathers the exponential.

Your job is to complete the code **INCLUDING** the correct assert statements to check the loop invariant, loop test and their combination, as indicated in the skeleton code. Leave the print statements in place. Be sure to use the invariant function, as we will call this directly with different values to check that it is correct. A correct implementation of eExp:

 python3 eExp.py 2 11 

produces

 program: eExp.py 2 11 n: 2 k: 11 e: 1 n: 4 k: 5 e: 2 n: 16 k: 2 e: 8 n: 256 k: 1 e: 8 k: 0 e: 2048 2 ** 11 = 2048

import sys def invariant(n, k, e, left, right): return True def eExp(left, right): # precondition: left>0 AND right>0 if left <= 0 or right <= 0 : raise "eExp: invalid inputs!" n=left; k=right; e=1 #e: the exponent assert invariant(n, k, e, left, right) # fill in the proper loop invariant while (False) : # the loop test assert True and invariant(n, k, e, left, right) # fill in the proper loop test and loop invariant print(" n:",n,"k:",k,"e:",e) # body assert invariant(n, k, e, left, right) # fill in the proper loop invariant print("k:",k,"e:",e) assert True and invariant(n, k, e, left, right) # fill in proper not(loop test) and loop invariant return e if __name__ == "__main__": print("program:", sys.argv[0], sys.argv[1], sys.argv[2]) n = int(sys.argv[1]) k = int(sys.argv[2]) e = eExp(n,k) print(n,"**",k,"=",e)