def test(i,j):
if(i==0):
    return j
else:
    return test(i-1,i j)

print(test(4,7))

I understand that i=4 and 4 is not equal to zero, therefore the second condition is executed but how does "test(i-1,i j) work? Do you substitute i and j? eg. (3-1,3 7)? Can someone please clarify this for me as I am highly confused.

CodePudding user response：

this is called a recursive function, you might notice that the function calls itself. Usually those functions have base conditions, which will stop the recursion, in your case, it's when i reaches zero. But be careful: if you start with a negative value for i, you won't reach the base condition, since i is getting decreased by one in each call: e.g.: let's say i=-1 and j=10 => test(-1,10)

test(-1,10): i is not equal to zero, therefore else block is applied:
test(i-1, i j) -> test(-1-1, -1 10) -> test(-2, -9)

test(-2, -9): i is not equal to zero, therefore else block is applied:
test(i-1, i j) -> test(-2-1, -2 9) -> test(-3, -7)

test(-3, -7)
... as you can see, i get's decremented in each call and ONLY stops when i is equal to zero.

This also explained the logic of the recursive function:

test(4,7) -> return test(3,11) 
          -> return test(2,14)
          -> return test(1,16)
          -> return test(0, 17)
          -> return 17 (base condition is reached, i==0)

Now, the recursion goes backwards and the 17 is returned to the first call.

CodePudding user response：

As suggested by @AdroMine, you can modify your function to print the values of i and j before each recursive call to test():

def test(i, j):
    print(f'i = {i} j = {j}')
    if (i == 0):
        return j
    else:
        return test(i-1, i j)

Calling test(4, 7) would result in:

i = 4 j = 7
i = 3 j = 11
i = 2 j = 14
i = 1 j = 16
i = 0 j = 17

This function calculates the sum of j and i, i-1, i-2, ..., 1.

how does "test(i-1,i j) work?

At every call:

• The value of i is decremented by 1, then passed as a first argument.
• The value of j i is calculated, then passed as a second argument (returned when i is equal to 0).

In other words:

• The first parameter i serves the purpose of the loop counter.
• The second parameter j serves the purpose of holding the sum.

To better clear things, you can write an iterative version of test():

def test2(a, b):
    j = b
    for i in range (a, 0, -1):
        j  = i
    
    return j