Queues - Tamiko Terada - recursion-tracing

README.md

@@ -1,15 +1,15 @@
 # Recursion Problems
 
 ## Definitions
-Define the following: 
+Define the following:
 
-- Recursion
-- Recursive Case
-- Base Case
-- Activation Chain/Stack
-- Activation Record/Call
-- Infinite Recursion/Stack Overflow/Stack too deep
-- Tail Recursion
+- Recursion: a function in that iterates on itself
+- Recursive Case: an input (in a recursion) that returns something that calls itself
+- Base Case: an input (in a recursion) that produces an output that is not recursive--needs at least one to not be an infinite loop
+- Activation Chain/Stack: the entire run of the function--from first recursive case to base case
+- Activation Record/Call: each iteration of the function
+- Infinite Recursion/Stack Overflow/Stack too deep: base case cannot be reached by the input so there's an infinite loop
+- Tail Recursion: the final output is reflected in the output of each activation record
 
 ## Tracing through a recursive method
 
@@ -25,8 +25,34 @@ end
 ```
 
 - What is mystery1(5)?
+```
+n=5 | 5 + m(4)
+n=4 | 4 + m(3)
+n=3 | 3 + m(2)
+n=2 | 2 + m(2)
+n=1 | 1
+5+(4+(3+(2+(1))))
+returns 15
+```
 - What is mystery1(10)?
+```
+n=10 | 10 + m(9)
+n=9 | 9 + m(8)
+n=8 | 8 + m(7)
+n=7 | 7 + m(6)
+n=6 | 6 + m(5)
+n=5 | returns 15 (from above)
+10+(9+(8+(7+(6+(15)))))
+returns 55
+```
 - What is mystery1(0)?
+```
+n= 0 | 0 + m(0)
+n=-1 | -1 + m(-1)
+n=-2 | -2 + m(-2)
+...
+infinite recursion
+```
 
 ### Trace #2
 ```
@@ -40,9 +66,28 @@ end
 ```
 
 - What is mystery2(123)?
+```
+n=123 | 3 + m(12)
+n=12 | 2 + m(1)
+n=1 | 1
+3+(2+(1))
+returns 6
+```
 - What is mystery2(9005)?
+```
+n=9005 | 5 + m(900)
+n=900 | 0 + m(90)
+n=90 | 0 + m(9)
+n=9 | 9
+5+(0+(0+(9)))
+returns 14
+```
 - What is mystery2(-123)?
-- _Added Fun: How could we make `mystery2(-123)` work the way we might expect it to work instead of the way it does?_
+```
+n= -123
+returns -123
+```
+- _Added Fun: How could we make `mystery2(-123)` work the way we might expect it to work instead of the way it does?_ ANSWER: change base case conditional to absolute value < 10 OR % by 1000 < 10
 
 ### Trace #3
 ```
@@ -61,8 +106,25 @@ end
 ```
 
 - What is mystery3(1)?
+```
+n=1 | m(0)
+n=0 | 100
+returns 100
+```
 - What is mystery3(13)?
+```
+n=13 | m(12)
+n=12 | m(6)
+n=6 | m(3)
+n=3 | m(2)
+n=2 | m(1)
+n=1 | m(0)
+n=0 | 100
+returns 100
+```
 - What is mystery3(-6)?
+```
+```
 
 ### Trace #4
 ```
@@ -76,8 +138,14 @@ end
 ```
 
 - What is mystery4(10,2)?
+```
+```
 - What is mystery4(4,3)?
+```
+```
 - What is mystery4(5,0)?
+```
+```
 
 ### Trace #5
 ```
@@ -91,8 +159,14 @@ end
 ```
 
 - What is mystery5("hi")?
+```
+```
 - What is mystery5("")?
+```
+```
 - What is mystery5("Hi, there!")?
+```
+```
 - _Added Fun: How could we make only alphabetic characters to be changed to stars?_
 
 ### Trace #6
@@ -111,6 +185,12 @@ end
 ```
 
 - What is mystery6("goodnight moon")?
+```
+```
 - What is mystery6("Ada Developers Academy")?
+```
+```
 - What is mystery6("Hi, there!")?
+```
+```
 - _Added Fun: How could we make the reversal happen by letter, instead of by word (i.e. Make it so that mystery6("goodnight moon") returned "noom thgindoog")?_