Exercises 1-5 for recursion tracing

README.md

@@ -1,16 +1,22 @@
 # Recursion Problems
 
 ## Definitions
-Define the following: 
+Define the following:
 
 - Recursion
+Recursion : See recursion
 - Recursive Case
+A problem that can be divided into smaller problems
 - Base Case
+A problem that can be solved immediately
 - Activation Chain/Stack
+This is what Crystal used bubbles to show us, how the methods are using one another
 - Activation Record/Call
+ The methods that are called as we follow what is happening in a recursive call
 - Infinite Recursion/Stack Overflow/Stack too deep
+Never ending recursion, too much memory/resources being used up to solve this never ending recursion
 - Tail Recursion
-
+the return value of any given recursive step is the same as the return value of the next recursive call
 ## Tracing through a recursive method
 
 ### Trace #1
@@ -25,9 +31,24 @@ end
 ```
 
 - What is mystery1(5)?
+= 5 + mystery 4 =  15
+m(4) = 4 + m(3) = 10
+m(3) = 3 + m(2) = 6
+m(2) = 2 + m(1) = 3
+m(1) = 1
 - What is mystery1(10)?
+  m(10)  = 10 + mystery 9=  55
+m(9) = 9  + m(8) = 45
+m(8) = 8 + m(7) = 36
+m(7) =7 + m(6) = 28
+m(6) = 6 + m(5) = 21
+m(5) = 5 + mystery 4 =  15
+m(4) = 4 + m(3) = 10
+m(3) = 3 + m(2) = 6
+m(2) = 2 + m(1) = 3
+m(1) = 1
 - What is mystery1(0)?
-
+infinite recursion, stack too deep (never reaches end)
 ### Trace #2
 ```
 def mystery2(n)
@@ -40,8 +61,16 @@ end
 ```
 
 - What is mystery2(123)?
+mystery2(123) = (3) + mystery2(12) = 5
+m2(12) = 1 + m2(1) = 2
+m2(1) = 1
 - What is mystery2(9005)?
+mystery2(9005) = 5 + m2(900) = 14
+m2(900) = 0 + m2(90) = 9
+m2(90) = 0+ m2(9) = 9
+m2(9) =9
 - What is mystery2(-123)?
+mystery2(-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 +90,22 @@ end
 ```
 
 - What is mystery3(1)?
+m3(1) = m3(0) = 100
+m3(0) = 100
 - What is mystery3(13)?
+m3(13) = m3(12) =100
+m3(12) = m(6) =100
+m(6) = m(3) =100
+m(3) = m(2) =100
+m(2) = m(1) =100
+m(1) = m(0) = 100
+m(0) = 100
 - What is mystery3(-6)?
+m(-6) = m(-3) = 200
+m(-3) = m(-4)= 200
+m(-4) = m(-2) =200
+m(-2) = m(-1) = 200
+m(-1) = 200
 
 ### Trace #4
 ```
@@ -76,8 +119,16 @@ end
 ```
 
 - What is mystery4(10,2)?
+m(10,2) = 10 * m(10, 1) =100
+m(10,1) = 10 * m(10, 0) = 10
+m(10,0) =1
 - What is mystery4(4,3)?
+m(4,3) = 4 * m(4, 2) = 64
+m(4,2) = 4 * m(4,1) = 16
+m(4,1) = 4 * m(4,0) = 4
+m(4,0) = 1
 - What is mystery4(5,0)?
+m(5,0) = 1
 
 ### Trace #5
 ```
@@ -91,11 +142,16 @@ end
 ```
 
 - What is mystery5("hi")?
+m(hi) = * + m(h) = "**"
+m(h) = * + “”= “*"
+m(“”) = “"
 - What is mystery5("")?
+m(“”) = (“”)
 - What is mystery5("Hi, there!")?
+m(hi, there!)  “**********"
 - _Added Fun: How could we make only alphabetic characters to be changed to stars?_
 
-### Trace #6
+### Trace #6 #Will come back to this one =)
 ```
 def mystery6(s)
   if s == nil || s.length == 0