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Jou-Jou's Answers to Recursion Tracing #11

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164 changes: 140 additions & 24 deletions README.md
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Original file line number Diff line number Diff line change
@@ -1,14 +1,14 @@
# Recursion Problems

## Definitions
Define the following:

- Recursion
- Recursive Case
- Base Case
- Activation Chain/Stack
- Activation Record/Call
- Infinite Recursion/Stack Overflow/Stack too deep
Define the following:

- Recursion: a method that calls itself in the method
- Recursive Case: where in the method it's called, which will bring us closer to the base case
- Base Case: the stopping case to end recursion. The input is produced without recurring
- Activation Chain/Stack: All of the calls to the recursive method
- Activation Record/Call: Every time the recursive method is run
- Infinite Recursion/Stack Overflow/Stack too deep: The recursion never stops; base case is never reached
- Tail Recursion

## Tracing through a recursive method
Expand All @@ -24,10 +24,28 @@ def mystery1(n)
end
```

- What is mystery1(5)?
- What is mystery1(10)?
- What is mystery1(0)?
- What is mystery1(5)? 15
m1(5) = 5 + m1(4)
m1(4) = 4 + m1(3)
m1(3) = 3 + m1(2)
m1(2) = 2 + m1(1)
m1(1) = 1
1 => 3 (2+1) => 6 (3+3) => 10 (4 + 6) => 15 (5+10)
- What is mystery1(10)? 55
m1(10) = 10 + m1(9)
m1(9) = 9 + m1(8)
m1(8) = 8 + m1(7)
m1(7) = 7 + m1(6)
m1(6) = 6 + m1(5)
m1(5) = 5 + m1(4)
m1(4) = 4 + m1(3)
m1(3) = 3 + m1(2)
m1(2) = 2 + m1(1)
m1(1) = 1
1 => 3 (2+1) => 6 (3+3) => 10 (4 + 6) => 15 (5+10) => 21 (6+15) => 28 (7+21) => 36 (8+28) => 45 (9+36) => 55 (10+45)
- What is mystery1(0)? Stack too deep

Sum of all numbers up to and including n
### Trace #2
```
def mystery2(n)
Expand All @@ -39,10 +57,23 @@ def mystery2(n)
end
```

- What is mystery2(123)?
- What is mystery2(9005)?
- What is mystery2(123)? 6
m2(123) = 3 + m2(12)
m2(12) = 2 + m2(1)
m2(1) = 1
1 => 3 (2+1) => 6 (3+3)
- What is mystery2(9005)? 14
m2(9005) = 5 + m2(900)
m2(900) = 0 + m2(90)
m2(90) = 0 + m2(9)
m2(9) = 9
9 => 9 (0+9) => 9 (0+9) => 14 (5+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?_
Maybe we can specify the absolute value of n?

Sum of the digits in n

### Trace #3
```
Expand All @@ -60,10 +91,28 @@ def mystery3(n)
end
```

- What is mystery3(1)?
- What is mystery3(13)?
- What is mystery3(-6)?
- What is mystery3(1)? 100
m3(1) = m3(0)
m3(0) = 100
100 => 100
- What is mystery3(13)? 100
m3(13) = m3(12)
m3(12) = m3(6)
m3(6) = m3(3)
m3(3) = m3(2)
m3(2) = m3(1)
m3(1) = m3(0)
m3(0) = 100
100 => 100 => 100 => 100 => 100 => 100 => 100 => 100
- What is mystery3(-6)? 200
m3(-6) = m3(-3)
m3(-3) = m3(-4)
m3(-4) = m3(-2)
m3(-2) = m3(-1)
m3(-1) = 200
200 => 200 => 200 => 200 => 200 => 200

returns 100 if n is positive, 200 if n is negative
### Trace #4
```
def mystery4(b,e)
Expand All @@ -75,9 +124,21 @@ def mystery4(b,e)
end
```

- What is mystery4(10,2)?
- What is mystery4(4,3)?
- What is mystery4(10,2)? 100
m4(10,2) = 10 * m4(10,1)
m4(10,1) = 10 * m4(10,0)
m4(0) = 1
1 => 10 (10*1) => 100 (10*10)
- What is mystery4(4,3)? 64
m4(4,3) = 4 * m4(4,2)
m4(4,2) = 4 * m4(4,1)
m4(4,1) = 4 * m4(4,0)
m4(4,0) = 1
1 => 4 (4*1) => 16 (4*4) => 64 (4*16)
- What is mystery4(5,0)?
m4(5,0) = 1

b to the power of e

### Trace #5
```
Expand All @@ -90,11 +151,29 @@ def mystery5(s)
end
```

- What is mystery5("hi")?
- What is mystery5("")?
- What is mystery5("Hi, there!")?
- 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("") = ""
"" => "*" ("*" + "") => "**" ("*" + "*") => "***" ("*" + "**") => "****" ("*" + "***"), etc.
- _Added Fun: How could we make only alphabetic characters to be changed to stars?_

Replace characters with * (AKA censoring word)
### Trace #6
```
def mystery6(s)
Expand All @@ -110,7 +189,44 @@ def mystery6(s)
end
```

- What is mystery6("goodnight moon")?
- What is mystery6("Ada Developers Academy")?
- What is mystery6("Hi, there!")?
- What is mystery6("goodnight moon")? " moon goodnight"
m6("goodnight moon") = m6("moon") + " " + "goodnight"
iteration table: iteration | space
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
m6("moon") = "" + " " + "moon"
iteration table: iteration | space
1 1
2 2
3 3
4 4
- What is mystery6("Ada Developers Academy")? " Academy Developers Ada"
m6("Ada Developers Academy") = m6("Developers Academy") + " " + "Ada"
iteration table: iteration | space
1 1
2 2
3 3
m6("Developers Academy") = m6("Academy") + " " + "Developers"
iteration table: iteration | space
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
m6("Academy") = m6("") + " " + "Academy"
- What is mystery6("Hi, there!")? " there! Hi,"
m6("Hi, there!") = m6("there!") + " " + "Hi,"
m6("there!") = m6("") + " " + "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")?_