from math import log

aval = 17
bval = 34

def reset():
    global a, b
    a = aval
    b = bval

def printVars(message):
    global a, b
    print message
    print a, b
    reset()

reset()

b = a ^ b
a = a ^ b
b = a ^ b

printVars("triple xor method")

a = a + b
b = a - b
a = a - b

printVars("add sub sub method")

b = b - a
a = b + a
b = a - b

printVars("sub add sub method")

a = a * b
b = a / b
a = a / b

printVars("mul div div method")

b = b / a
a = b * a
b = a / b

printVars("div mul div method")

b = b ** a
a = b ** (1.0/a)
b = log(b, a)

printVars("power root log method")

"""
General case:

Let f(a, b) be a binary operator.
Let li(a, b) be a binary operator such that li(f(a, b), b) = a
Let ri(a, b) be a binary operator such that ri(f(a, b), a) = b

Then, the following code can be used to switch the value of two variables a and b:

b = f(b, a)
a = li(b, a)
b = ri(b, a)

Proof:

b = f(b, a)
a = li(f(b, a), a) = b
b = ri(f(b, a), b) = a

Particular examples:

f(a, b) = li(a, b) = ri(a, b) = xor(a, b)

f(a, b) = add(a, b)
li(a, b) = ri(a, b) = sub(a, b)

"""