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    Predicting the outcome of recursive calls
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#     Predicting the outcome of recursive calls
Predicting the outcome helps solidify your understanding of recursion. On this page, you are given recursive function definitions, and you will predict what is printed with various invocations.


## Example 1. `flow`
```py
def flow(num):
  if num > 0:
      print('before', num)
      flow (num - 2)
      print('after', num)
  else:
      print('base case')
```
## Your task: 
Predict what the `flow` function prints with these invocations (write it down):

```py
flow(4)
```

You can see the solution for `flow(4)` by <span style='text-decoration:underline; font-weight:bold; cursor:pointer' onClick='javascript:document.getElementById("solution").style = "display:block"'>clicking here</span>.

<div style='display:none;' markdown=1 id='solution'>
Expected results:
```xml
before 4
before 2
base case
after 2
after 4
```
</div>

```py
flow(7)
```

You can see the solution for `flow(7)` by <span style='text-decoration:underline; font-weight:bold; cursor:pointer' onClick='javascript:document.getElementById("solution2").style = "display:block"'>clicking here</span>.

<div style='display:none;' markdown=1 id='solution2'>
Expected results:
```xml
before 7
before 5
before 3
before 1
base case
after 1
after 3
after 5
after 7
```
</div>

<hr>

## Example 2. `chop`
Note that `chop` has two recursive calls.

```py
def chop(word):
  if len(word) > 0:
      print(word)
      chop(w[1:])  # 1st recursive call
      print('---')
      chop(w[1:] ) # 2nd recursive call
      print('*')
```

## Your task: 
Predict what the chop function prints with this invocation:

```py
chop('mat')
```

Click [here for a diagram of the solution](chopSolution) using function call frames.



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