CS241: Spring 2017 -- Recursion, merge sort, quick sort

1. Recursion
   1. base case -- when the recursion stops (always start by writing this!)
   2. recursion -- where you suspend your disbelief
   3. fib(n)
   4. Implementing a queue using a single stack
      1. initialization is just instantiate the stack (it, of course, starts out empty!)
      2. isEmpty is trivial
      3. either enqueue or dequeue is simple -- the other more complicated
      4. say dequeue is return pop(); -- then we must arrange that each enqueue puts the new element at the bottom of the stack
      5. example: enqueue(1); enqueue(2); enqueue(3); then while (!isEmpty()) soutv dequeue(), should print 1, 2, 3
2. Quick sort pseudocode

   	quickSort(List aList) {
   		if (size>1) {
   			select a pivot and split aList into head and tail (where everything in head is < pivot...) with the pivot in between
                           quickSort(head)
                           quickSort(tail)
   		}
   	}
           

3. quicksorting 3, 2, 1, 6, 7, 8, 5, 4 (in place)
4. Merge sort pseudocode

   	mergeSort(List aList) {
   		if (size>1) {
   			split aList roughly in half creating head and tail
                           mergeSort(head)
                           mergeSort(tail)
   			merge head and tail
   		}
   	}
           

5. mergesorting 3, 2, 1, 6, 7, 8, 5, 4 (in place)
6. From pseudocode to code; details! It's all about the details!? No. First it's about the representation; after you choose that, it's about the details.
   1. starting -- also known as initializing
   2. stopping
   3. in between
7. Proactive debugging
   1. souts on enter and exit to recursive routines; like this:

          void foo(int[] list, int startI, int endI) {
              System.out.print("Top of foo: ");
              System.out.print(" startI = " + startI);
              System.out.print(" endI = " + endI);
              System.out.println(list.toString(startI, endI));
              
              ...foo code...
              
              System.out.print("bottom of foo: ");
              System.out.print(" startI = " + startI);
              System.out.print(" endI = " + endI);
              System.out.println(list.toString(startI, endI));       
          }
                      

   2. list:toString(firstI, lastI)