如何使用递归而不是在python中使用运算符找到两个整数中的较大者

Question

I want to find the larger of two integers. But I have to use Recursion and without python operators. Code structure is given below.

def gt(a, b):
  '''Returns True if a is an integer greater than b;
     returns False otherwise'''
  # using only incr, decr, zero, and recursion
  return 0


def incr(a):
  '''Returns the next integer after a'''
  return a + 1

def zero(a):
  '''Returns True if a is zero'''
  return a == 0

def decr(a):
  '''Returns the integer before a'''
  return a - 1

Answer 1

version for positive integers

You could decrement both numbers and see whether a or b reaches zero first:

def gt(a, b):
    '''Returns True if a is an integer greater than b;
       returns False otherwise'''
    # using only incr, decr, zero, and recursion
    if zero(b) and not zero(a):
        return True
    if zero(a):
        return False
    return gt(decr(a), decr(b))

examples:

>>> gt(100, 10)
True

>>> gt(10, 10)
False

>>> gt(1, 10)
False

Answer 2

If you are permitted the simplest of loops (using only zero for the breaking condition):

def gt(a, b):
    # 1. get a to zero by going up and down in parallel
    aup = adown = a
    bup = bdown = b
    while True:
        if zero(aup):
            a, b = aup, bup
            break
        if zero(adown):
            a, b = adown, bdown
            break
        aup, adown = incr(aup), decr(adown)
        bup, bdown = incr(bup), decr(bdown)
    if zero(b):
        return False 
    
    # 2. get b to zero
    bup = bdown = b
    while True:
        if zero(bup):
            return True
        if zero(bdown):
            return False
        bup, bdown = incr(bup), decr(bdown)