CS241: Spring 2017 -- Onward!

1. Administrivia; 5 weeks to go?! We have to go faster!
2. Efficiency; when does it matter? Run time vs. development time (and bugs!!).
3. Representation
   1. The array
   2. start index
   3. end index
   4. Example: head after the first time through 4 3 5 2 7 8 1 2
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. merge(list1, list2)

           Assuming you have created an array of length n outside of any loop, named result
           ...
           while (both list1 and list2 have more elements) {  
   
               if (head of list1 <= head of list2) {
                   add head of list1  to result (and delete it!)
               } else { // bigger
                   add head of list2 to tail of result
               }
           }
           
           if (list1 not empty) {
               add everything from list1 to result
               }
           } else {
               add everything from list2 to result
           }
               

6. Example: mergesorting 3, 2, 1, 6, 7, 8, 5, 4
7. Watch out! There is no way to do it in place (that I can think of) and if you allocate arrays uncarefully, you will get results like I did (below) -- see debug in MergeSort...

               T I M I N G   S O R T S !
                   bubble	merge	better?	quiok
   n=20            t=1	t=0	t=0	t=0
   n=40            t=0	t=0	t=0	t=0
   n=80            t=0	t=0	t=0	t=0
   n=160           t=1	t=0	t=0	t=1
   n=320           t=2	t=1	t=0	t=0
   n=640           t=6	t=1	t=0	t=0
   n=1280          t=2	t=0	t=1	t=0
   n=2560          t=10	t=1	t=1	t=0
   n=5120          t=31	t=4	t=1	t=0
   n=10240         t=128	t=14	t=1	t=0
   n=20480         t=551	t=34	t=2	t=1
   n=40960         t=2242	t=212	t=3	t=4
   n=81920         t=8847	t=705	t=7	t=7
   n=163840	t=35883	t=2189	t=15	t=16
   n=327680	slow	t=13172	t=33	t=35
   n=655360	slow	t=34721	t=71	t=74
   n=1310720	slow	slow	t=154	t=154
   n=2621440	slow	slow	t=320	t=323
   n=5242880	slow	slow	t=655	t=668
   n=10485760	slow	slow	t=1379	t=1433
   n=20971520	slow	slow	t=2905	t=3013
   n=41943040	slow	slow	t=6004	t=6241
   n=83886080	slow	slow	t=12407	t=12562
   n=167772160	slow	slow	t=25164	t=26050
   n=335544320	slow	slow
   Exception in thread "main" java.lang.OutOfMemoryError: Java heap space!

8. Counting sort! O(n)!

   pseudocode
   	tableSort(List aList) {
   		//count em
   		create an array of counters
   		for each element, e {
                       counter[e]++
   		}
   		// spew
   		clear aList
   		for each counter (counter[i]) {
                       emit that many i's (i.e. insert that many into aList)
   		}
   	}