Theresa's 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 method that calls itself
+- Recursive Case: Part of the method where the recursion happens
+- Base Case: Stoping case, where the recursion stops rather than going onto infinitely.
+- Activation Chain/Stack: The whole chain of events that happen in a recursive method.
+- Activation Record/Call: The separate pieces of the Activation Chain (each individual 'recursion bubble')
+- Infinite Recursion/Stack Overflow/Stack too deep: When there is no stopping point in the recursion, can never hit the base case.
+- Tail Recursion: When the recursive call is the very last thing in the method.
 
 ## Tracing through a recursive method
 
@@ -25,8 +25,24 @@ end
 ```
 
 - What is mystery1(5)?
+m1(5) = 5 + m1(4) = **15**
+m1(4) = 4 + m1(3) = 10
+m1(3) = 3 + m1(2) = 6
+m1(2) = 2 + m1(1) = 3
+m1(1) = 1
 - What is mystery1(10)?
+m1(10) = 10 + m1(9) = **55**
+m1(9) = 9 + m1(8) = 45
+m1(8) = 8 + m1(7) = 36
+m1(7) = 7 + m1(6) = 28
+m1(6) = 6 + m1(5) = 21
+m1(5) = 5 + m1(4) = 15
+m1(4) = 4 + m1(3) = 10
+m1(3) = 3 + m1(2) = 6
+m1(2) = 2 + m1(1) = 3
+m1(1) = 1
 - What is mystery1(0)?
+**"Stacked too deep" / infinite recursion**
 
 ### Trace #2
 ```
@@ -40,8 +56,16 @@ end
 ```
 
 - What is mystery2(123)?
+m2(123) = 3 + m2(12) = **6**
+m2(12) = 2 + m2(1) = 3
+m2(1) = 1
 - What is mystery2(9005)?
+m2(9005) = 5 + m2(900) = **14**
+m2(900) = 0 + m2(90) = 9
+m2(90) = 0 + m2(9) = 9
+m2(9) = 9
 - What is mystery2(-123)?
+m2(-123) = **-123**
 - _Added Fun: How could we make `mystery2(-123)` work the way we might expect it to work instead of the way it does?_
 
 ### Trace #3
@@ -61,8 +85,22 @@ end
 ```
 
 - What is mystery3(1)?
+m3(1) = m3(0) = **100**
+m3(0) = 100
 - What is mystery3(13)?
+m3(13) = m3(12) = **100**
+m3(14) = m3(6) = 100
+m3(6) = m3(3) = 100
+m3(3) = m3(2) = 100
+m3(2) = m3(1) = 100
+m3(1) = m3(0) = 100
+m3(0) = 100
 - What is mystery3(-6)?
+m3(-6) = m3(-3) = **200**
+m3(-3) = m3(-4) = 200
+m3(-4) = m3(-2) = 200
+m3(-2) = m3(-1) = 200
+m3(-1) = 200
 
 ### Trace #4
 ```
@@ -76,8 +114,16 @@ end
 ```
 
 - What is mystery4(10,2)?
+m4(10,2) = 10 * m4(10,1) = **100**
+m4(10,1) = 10 * m4(10,0) = 10
+m4(10,0) = 1
 - What is mystery4(4,3)?
+m4(4,3) = 4 * m4(4,2) = **64**
+m4(4,2) = 4 * m4(4,1) = 16
+m4(4,1) = 4 * m4(4,0) = 4
+m4(4,0) = 1
 - What is mystery4(5,0)?
+m4(5,0) = **1**
 
 ### Trace #5
 ```
@@ -91,8 +137,25 @@ end
 ```
 
 - What is mystery5("hi")?
+m5("hi") = * + m5("i") = __**__
+m5("i") = * + m5("") = *
+m5("") = ""
 - What is mystery5("")?
+m5("") = __""__
 - What is mystery5("Hi, there!")?
+m5("Hi, there!") = * + m5("i, there!") = __**********__
+m5("i, there!") = * + m5(", there!") = *********
+m5(", there!") = * + m5(" there!") = ********
+m5(" there!") = * + m5("there!") = *******
+m5("there!") = * + m5("here!") = ******
+m5("here!") = * + m5("ere!") = *****
+m5("ere!") = * + m5("re!") = ****
+m5("re!") = * + m5("e!") = ***
+m5("e!") = * + m5("!") = **
+m5("!") = * + m5("") = *
+m5("") = ""
+
+
 - _Added Fun: How could we make only alphabetic characters to be changed to stars?_
 
 ### Trace #6
@@ -111,6 +174,18 @@ end
 ```
 
 - What is mystery6("goodnight moon")?
+m6("goodnight moon") = m6("moon") + " " + "goodnight" = **" moon goodnight"**
+m6("moon") = m6("") + " " + "moon" = " moon"
+m6("") = ("")
+
 - What is mystery6("Ada Developers Academy")?
+m6("Ada Developers Academy") = m6("Developers Academy") + " " + "Ada" = **" Ada Developers Academy"**
+m6("Developers Academy") = m6("Academy") + " " + "Developers" = " Developers Academy"
+m6("Academy") = m6("") + " " + "Academy" = " Academy"
+m6("") = ""
+
 - What is mystery6("Hi, there!")?
+m6("Hi, there!") = m6("there!") + " " + "Hi," = **" there! Hi,"**
+m6("there!") = m6("") + " " + "there!" =  " there!"
+m6("") = ""
 - _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")?_