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Thursday, June 9, 2011

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.

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