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Jackie - Ampers #2

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86 changes: 43 additions & 43 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/Function Call Stack
- Activation Record/Function Call
- Infinite Recursion/Stack Overflow/Stack too deep
- Tail Recursion
Define the following:
- Recursion - Recursion occurs when a method calls itself. A recursive algorithm always has a base case and a recursive case.
- Recursive Case - Each recursive call gets you closer to a problem scope for which an answer is known.
- Base Case - A base case is the point at which the recursive calls stop. The returned value can then be returned back to the previous calls.
- Activation Chain/Function Call Stack - Each function call is added to the call stack which takes space in the stack memory.
- Activation Record/Function Call - An activation record is each individual function call that was made.
- Infinite Recursion/Stack Overflow/Stack too deep - This happens when a base case is not defined. The recursive algorithm keeps on making recursive calls which are added to the stack memory which eventually overflows.
- Tail Recursion - A algorithm with tail recursion returns the value immediately and does not need to do any additional computation.

## Tracing through a recursive method. Time & Space complexity.
### Trace #1
Expand All @@ -22,11 +22,11 @@ def mystery1(n)
end
```

- What is mystery1(5)?
- What is mystery1(10)?
- What is mystery1(0)?
- What is the time complexity of mystery1(n)?
- What is the space complexity of mystery1(n)?
- What is mystery1(5)? --> 15
- What is mystery1(10)? --> 55
- What is mystery1(0)? --> stack overflow - infinity loop
- What is the time complexity of mystery1(n)? O(n)
- What is the space complexity of mystery1(n)? O(n)

### Trace #2
```ruby
Expand All @@ -39,11 +39,11 @@ def mystery2(n)
end
```

- What is mystery2(123)?
- What is mystery2(9005)?
- What is mystery2(-123)?
- What is the time complexity of mystery2(n)?
- What is the space complexity of mystery2(n)?
- What is mystery2(123)? --> 6
- What is mystery2(9005)? --> 14
- What is mystery2(-123)? --> -123
- What is the time complexity of mystery2(n)? O(n)
- What is the space complexity of mystery2(n)? O(n)
- _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
Expand All @@ -62,11 +62,11 @@ def mystery3(n)
end
```

- What is mystery3(1)?
- What is mystery3(13)?
- What is mystery3(-6)?
- What is the time complexity of mystery3(n)?
- What is the space complexity of mystery3(n)?
- What is mystery3(1)? --> 100
- What is mystery3(13)? --> 100
- What is mystery3(-6)? --> 200
- What is the time complexity of mystery3(n)? O(abs(n)/2)
- What is the space complexity of mystery3(n)? O(abs(n)/2)

### Trace #4
```ruby
Expand All @@ -79,11 +79,11 @@ def mystery4(b, e)
end
```

- What is mystery4(10, 2)?
- What is mystery4(4, 3)?
- What is mystery4(5, 0)?
- What is the time complexity of mystery4(b, e)?
- What is the space complexity of mystery4(b, e)?
- What is mystery4(10, 2)? --> 100
- What is mystery4(4, 3)? --> 64
- What is mystery4(5, 0)? --> 1
- What is the time complexity of mystery4(b, e)? O(e)
- What is the space complexity of mystery4(b, e)? O(e)

### Trace #5
```ruby
Expand All @@ -96,11 +96,11 @@ def mystery5(s)
end
```

- What is mystery5("hi")?
- What is mystery5("")?
- What is mystery5("Hi, there!")?
- What is the time complexity of mystery5(s)?
- What is the space complexity of mystery5(s)?
- What is mystery5("hi")? --> "**"
- What is mystery5("")? --> ""
- What is mystery5("Hi, there!")? "**********"
- What is the time complexity of mystery5(s)? --> O(n)
- What is the space complexity of mystery5(s)? --> O(n)
- _Added Fun: How could we make only alphabetic characters to be changed to stars?_

### Trace #6
Expand All @@ -118,11 +118,11 @@ def mystery6(s)
end
```

- What is mystery6("goodnight moon")?
- What is mystery6("Ada Developers Academy")?
- What is mystery6("Hi, there!")?
- What is the time complexity of mystery6(s)?
- What is the space complexity of mystery6(s)?
- What is mystery6("goodnight moon")? --> "moon goodnight"
- What is mystery6("Ada Developers Academy")? --> "Academy Developers Ada"
- What is mystery6("Hi, there!")? --> "there! Hi,"
- What is the time complexity of mystery6(s)? O(n)
- What is the space complexity of mystery6(s)? O(n)
- _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")?_

### Trace #7
Expand All @@ -138,8 +138,8 @@ def mystery7(word)
end
```

- What is mystery7("cupcake")?
- What is mystery7("detected")?
- What is mystery7("eye")?
- What is the time complexity of mystery7(word)?
- What is the space complexity of mystery7(word)?
- What is mystery7("cupcake")? --> false
- What is mystery7("detected")? --> false
- What is mystery7("eye")? --> true
- What is the time complexity of mystery7(word)? O(n/2)
- What is the space complexity of mystery7(word)? O(n/2)
2 changes: 2 additions & 0 deletions mystery-methods.rb
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Original file line number Diff line number Diff line change
Expand Up @@ -15,6 +15,8 @@ def mystery2(n)
end
end

puts mystery2(-123)

def mystery3(n)
if n == 0
return 100
Expand Down