sai's recursion tracing

README.md

@@ -1,14 +1,20 @@
 # Recursion Problems
 
 ## Definitions
-Define the following: 
+Define the following:
 
 - Recursion
+  --see recursion; when a method calls itself
 - Recursive Case
+  --the case where the recursion will be called
 - Base Case
+  --the case that stops the recursion
 - Activation Chain/Stack
+  --the process of stepping through the recursion
 - Activation Record/Call
+  --an individual step in the activation chain
 - Infinite Recursion/Stack Overflow/Stack too deep
+  --never reaching the base case--the error that gets raised
 - Tail Recursion
 
 ## Tracing through a recursive method
@@ -24,9 +30,27 @@ def mystery1(n)
 end
 ```
 
-- What is mystery1(5)?
+- What is mystery1(5)?  
+>   mystery1(5) = 15  
+    m(5) = 5 + m1(4) --> 15  
+    m(4) = 4 + m1(3) --> 10  
+    m(3) = 3 + m1(2) --> 6  
+    m(2) = 2 + m1(1) --> 3  
+    m1(1) = 1
 - What is mystery1(10)?
+> mystery1(10)= 55  
+  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)?
+> m1(0) --> returns stack too deep error because base case of n == 1 is never met
 
 ### Trace #2
 ```
@@ -40,9 +64,21 @@ end
 ```
 
 - What is mystery2(123)?
+>mystery2(123) = 6  
+  m2(123) = 3 + m2(12) --> 6  
+  m(12) = 2 + m2(1) --> 3  
+  m(1) = 1
 - What is mystery2(9005)?
+>mystery2(9005) = 14  
+  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)?
+>mystery2(-123) = -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?_
+>make the first part of the conditional check if a negative number is greater than -10 and a pos. number is less than ten. i think division would need to return positive values (i.e. -123/10 should return 12 not -12), or be converted to a pos value.
 
 ### Trace #3
 ```
@@ -61,8 +97,24 @@ end
 ```
 
 - What is mystery3(1)?
-- What is mystery3(13)?
+>mystery3(1) = 100  
+  m3(1) = m3(0) --> 100  
+  m3(0) = 100
+- What is mystery3(13)?   
+  mystery3(13) = 100    
+  m3(13) = m3(12) --> 100  
+  m3(12) = m3(6) --> 100  
+  m3(6) = m3(3) --> 100  
+  m3(3) = m3(2) --> 100  
+  m3(2) = m3(1) --> 100  
+  m3(1) = 100
 - What is mystery3(-6)?
+>mystery3(-6) = 200  
+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
 ```
@@ -76,7 +128,17 @@ end
 ```
 
 - What is mystery4(10,2)?
+>mystery4(10,2) = 100  
+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)?
+>mystery4(4,3) = 64  
+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)?
 
 ### Trace #5
@@ -91,8 +153,26 @@ end
 ```
 
 - What is mystery5("hi")?
+>mystery5("hi") = string of two asterisks  
+m5("hi") = "*" + m5("i") --> string of two asterisks  
+m5("i") = "*" + m5("") --> "*"  
+m5("") = ""  
+
 - What is mystery5("")?
+>m5("") = ""
 - What is mystery5("Hi, there!")?
+>m5("Hi, there!") = "*" + m5("i, there!") --> string of 10 asterisks  
+m5("i, there!") = "*" + m5(", there!") --> string of 9 asterisks  
+m5(", there!") = "*" + m5(" there!") --> string of 8 asterisks  
+m5(" there!") = "*" + m5("there!") --> string of 7 asterisks   
+m5("there!") = "*" + m5("here!") --> string of 6 asterisks   
+m5("here!") = "*" + m5("ere!") --> string of 5 asterisks   
+m5("ere!") = "*" + m5("re!") --> string of 4 asterisks   
+m5("re!") = "*" + m5("e!") --> string of 3 asterisks   
+m5("e!") = "*" + m5("!") --> string of 2 asterisks   
+m5("!") = "*" + m5("") --> "*"  
+m5("") = ""
+
 - _Added Fun: How could we make only alphabetic characters to be changed to stars?_
 
 ### Trace #6
@@ -111,6 +191,7 @@ 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")?_