Data Structure Algorithm
- 1. Data structure algorithm presented by NIBIYA.G I-MSC(INFORMATION TECHNOLOGY) NADAR SARASWATHI COLLEGE OF ARTS AND SCIENCE VADAPUTHUPATTI, THENI – 625531
- 2. DYNAMIC PROGRAMMING Optimal binary search Tree string editing 0/1 knapsack problem
- 3. OPTIMAL BINARY SEARCH TREE A binary search tree is one of the most important data structures which contain a set of element with the operation of searching, insertion, and deletion.
- 4. An optimal binary search tree is the one for which the average number of comparisons in a search is the smallest possible, if the probability of searching each element is given. Consider four keys A,B,C, and D to be searched for with probabilities 0.1, 0.2, 0.4 and 0.3 respectively.
- 5. The below figure depicts two out of 14 possible binary search trees containing these keys.
- 6. The average number of comparisons in a successful search in the first of these tree 0.1, 1+0.2, 2+0.4, 3+0.3, 4 = 2.9. and for the second one it is 0.1, 2+0.2, 1+0.4, 2+0.3, 3 = 2.1. Neither of these two trees is, in fact, optimal.
- 7. The total number of binary search trees with n keys is equal to the nth catalan number. Let a1,………, aa be distinct keys ordered from smallest to the largest and let p1,…….pa be the probabilities of searching for them.
- 8. Let C( I , j ) be the smallest average number of comparisons made in a successful search in a binary search tree T1j. Suppose the root contains key ak, the left subtree Tik-1 contains keys ai,…….ak-1 optimally arranged, and the right sutree tjk+1 contain keys ak+1….aj also optimally arranged
- 10. The recurrence relation Here C(i,i-1) = 0 for 1
- 14. Figure 5.12 two possible binary search tree
- 15. Figure 5.13 binary search tree of figure 5.12 with external nodes added
- 16. Optimal binary search tree(*)
- 17. Optimal binary search tree(*)
- 18. Figure 5.16 computation of c(0,4), w(0,4), and r(0,4)
- 20. string editing
- 21. string editing
- 27. 0/1 knapsack problem (recursive formula sub-program)
- 29. Example -1
- 30. Example -2
- 31. Example -3
- 32. Example -4
- 33. Example -5
- 34. Example -6
- 35. Example -7
- 36. Example -8
- 37. Example -9
- 38. Example -10
- 39. Example -11
- 40. Example -12
- 41. Example -13
- 42. Example -14
- 43. Example -15
- 44. Example -16
- 45. Example -17
- 46. Example -18