Stacks - Jackie - Recursion Tracing

jackies-answers.txt

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+# Recursion Problems
+
+## Definitions
+Define the following:
+
+- Recursion - when a method calls itself
+- Recursive Case - the case that includes a version of itself
+- Base Case - stopping case -- the case that has a known answer
+- Activation Chain/Stack -> all the levels of each time a recursive method is called until it hits the base case.
+- Activation Record/Call -> the temporary storage for each level of recursion
+- Infinite Recursion/Stack Overflow/Stack too deep -> when a case goes on forever
+- Tail Recursion -> a recursive method with an end
+
+## Tracing through a recursive method
+
+### Trace #1
+```
+def mystery1(n)
+  if n == 1
+    return n
+  else
+    return n + mystery1(n-1)
+  end
+end
+```
+
+- What is mystery1(5)? --> 15
+- What is mystery1(10)? --> 55
+- What is mystery1(0)? stack level too deep
+
+### Trace #2
+```
+def mystery2(n)
+  if n < 10
+    return n
+  else
+    return (n%10) + mystery2(n/10)
+  end
+end
+```
+
+- What is mystery2(123)? --> 6
+- What is mystery2(9005)? --> 14
+- What is 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
+```
+def mystery3(n)
+  if n == 0
+    return 100
+  elsif n == -1
+    return 200
+  end
+  if n%2 == 0
+    return mystery3(n/2)
+  else
+    return mystery3(n-1)
+  end
+end
+```
+
+- What is mystery3(1)? --> 100
+- What is mystery3(13)? --> 100
+- What is mystery3(-6)? --> 200
+
+### Trace #4
+```
+def mystery4(b,e)
+  if e == 0
+    return 1
+  else
+    return b * mystery4(b,e-1)
+  end
+end
+```
+
+- What is mystery4(10,2)? --> 100
+- What is mystery4(4,3)? --> 64
+- What is mystery4(5,0)? --> 1
+
+### Trace #5
+```
+def mystery5(s)
+  if s.length == 0
+    return ""
+  else
+    return "*" + mystery5(s[1..-1])
+  end
+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
+```
+def mystery6(s)
+  if s == nil || s.length == 0
+    return ""
+  else
+    space = 0
+    until space >= s.length || s[space] == " "
+      space += 1
+    end
+    return mystery6(s[(space+1)..-1]) + " " + s[0...space]
+  end
+end
+```
+
+- What is mystery6("goodnight moon")? --> " moon goodnight"
+- What is mystery6("Ada Developers Academy")? --> " Academy Developers Ada"
+- What is mystery6("Hi, there!")? --> " there! Hi,"
+- _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")?_