Updated complementary exercises for CLRS 20110609

Chapter 2 General:

-Watch the MIT video if it is only about Ch2. (done)

-Write up the summary of the video. 

-Read all the solution sets after I finished the videos. 

-work out cost analysis similar to P.26 on selection sort, linear search and merge sort (tedious).

-Think how to draw the recursion tree for the insertion sort algorithm. 

-Work out all proofs for the following algorithms

  -insertion sort

  -selection sort

  -bubble sort

  -binary insertion sort

  -merge sort

  -linear search

  -binary search

-Implement 2.3.7, P2.1, Horner's rule in P2.3 and inversion calculation in P2.4.  2.3.7 has two solutions, one is trivial, one is based on merge.  Think them through.

Chapter 3 General

-TAOCP? Knuth must have talk about Big Oh at a certain point.  (done)

-There is no difference between CLRS and TAOCP (done)

-Read the Wikipedia's entries in the big Oh notation, iterative logarithm and all Math related subject. (done)

-Finish all exercises of Sedgewick Chapter 2.

-Finish all exercises below Level 25 of TAOCP Section 1.1 and 1.2 

-Read CMath Chapter 2, 3 and 9.  Finished all easy exercises.

-Alternative definitions of the asymptotic notion.
-What is the difference between the definitions of Sedgewick with CLRS?

Insertion sort:

-C, perl, python (done)

-sentinel version of straight insertion sort (done)

-binary search (done, now a separate item)

-binary insertion sort (done, now a separate item)

-recursive version of insertion sort (done)
-start to write a performance driver
-shell sort, how does the decrement business works?
   -Pratt's increments.
   -Sedgewick's increments.
-library sort
-tree sort(from wikipedia, what is it?)
-insertion sort improvement, all suggested by Exercises from TAOCP. 

-insertion sort with linked list
-How does the idea of insert leads to merge sort?

-C++,java, lisp, ASM, TAOCP Pseudo, TAOCP MIX, TAOCP MMIX.
-performance, worst case, average case
-different ways to avoid -INT_MAX as the sentinel. (state of art?)
-non-adaptive version of insertion sort.
-TAOCP Exercises in 5.2.1
-Sedgewick 6.3 Exercises

Selection sort:
-C, perl, python (done)
-C++,java, lisp, ASM
-stable version of selection sort.
-bidirectional version of selection sort.
-comparison with insertion sort.
-comparison with bubble sort
-recursive version of insertion sort
-cycle sort
-heap sort variants
     -tournament sort
     -smoothsort.
-TAOCP Exercise in 5.2.3
-Sedgewick 6.2
-Sedgewick 6.2 Exercise

Binary Insertion sort:

-C (done)

-perl, python, C++, java, lisp, ASM

Bubble sort:

-C (done)

-shaker sort

-perl, python, java, lisp, ASM

-TAOCP 5.2.2

Merge sort:
-C, perl(done)
-python, C++,java, lisp, ASM
-timsort
-performance, worst case, average case
-Improvements from Sedgewick.
-Non-recursive version or Bottom up version
-in place mergesort.
-no extra memory implementation (state of art?)

-variations of merge sort. 

-implement merge sort with k list and a k-list merging. 2.4.1.
-TAOCP Exercise in 5.4
-Sedgewick 8 (read - done)
-Sedgewick 8 Exercises.
-Shene's 5-9 Exercises. 

-where can I find problems which apply merging? 

  -Implement CLRS 2.3-7 using merging

  -like to calculate number of inversions.

Linear search:

-C, MIXAL (done)
-perl, python, C++,java, lisp, ASM

-TAOCP 6.1 and exercises.  Remember, it's not as trivial as you may think. 

Binary search: 

-C (done)
-perl, python, C++,java, lisp, ASM

-At least 100 problems which applies binary search.

   -TopCoder's exercises on binary search. 

   -Implement CLRS 2.3-7.

   -Shene Chapter 4. 

-After reading Gries, make sure you prove your own binary search is correct. 

-TAOCP 6.2 and exercises. 

-Chapter 4 and 5 of Programming Pearl exercises. 

-Sedgewick 12.4

-Fibonacci search

-Range search

-Variations of binary search. 

-Thinking: variations of binary search.  They produce different lo, up bounds. Interesting. 

-Thinking: can we combine the idea of distribution in binary search?

-Thinking: what happens if binary search is applied to a sequence with N inversions?

Inversions:
-Try to understand TAOCP 5.1 as much as I can. 
-Try to do exercises in TAOCP 5.1.