Two Recursive Algorithms

Merge Sort
- A very early, extremely efficient sort is mergesort.
- Basic idea
- ```
split the data into two pieces
sort the bottom half
sort the top half
merge the two pieces.
```
- Where does recursion come into play?
- What is the base case?
- What is the recursive case?
- Can we write this?
- Before we do
  - Mergesort is extremely efficient.
  - It performs as fast as is possible for a comparison sort.
  - It does required double storage space to merge the arrays.
Towers of Hanoi
- There is a legend of a temple
  - With three towers and 62 golden disks.
  - Monks are moving the disks from one tower to another according to a set of rules
    - You may only move one disk at a time.
    - You man never place a larger disk on a smaller disk.
  - When they finish, the world will end.
- Can we develop a recursive algorithm to solve this?
  - Base case? one disk
    - If I want to move a disk from tower a to tower b
    - ```
    move the disk from tower a to tower b.
    		  
```
- Recursive case, more than one disk, a stack.
- ```
move the substack (all but the bottom disk) from tower a to tower c
move the last disk from tower a to tower b
move the stack (previous substack) from tower c to tower b
		  
```
  - Does this algorithm make progress to a solution?