![Formula:
0 1 2 3 4
1 0 4 8(1)
2 0 2 10(3
)
3 0 6
4 0 3
5 0
C[1,2]=
K=1
C[1,0]+C[2,2]=0+2=2---------
ROOT(1)
K=2
C[1,1]+C[3,2]=4+0=4
+ 6===8
C[2,3]=
I=2
J=3
K=2
C[2,1]+C[3,3]=0+6=6
K=3
C[2,2]+C[4,3]=2+0=2
+8===10](https://image.slidesharecdn.com/lecture-optimalbinarysearchtreeautosaved-200424135015/85/Lecture-optimal-binary-search-tree-13-320.jpg)
![0 1 2 3 4
1 0 4 8(1) 20(3
)
26(3
)
2 0 2 10(3
)
16(3
)
3 0 6 12(3
)
4 0 3
5 0
C[3,4]
k=3
C[3,2]+C[4,4]=0+3=3
i=3,j=4 k=4
C[3,3]+C[5,4]=6+0=6
Frequency=9
=====12ROOT(3)
Minimum cost =2
16
10 21
12 Optimal Binary search
1*6=6
2*4+2*3=14
3*2=6](https://image.slidesharecdn.com/lecture-optimalbinarysearchtreeautosaved-200424135015/85/Lecture-optimal-binary-search-tree-14-320.jpg)
Lecture optimal binary search tree
- 1. Design and Analysis of Algorithm(18CS42) Module 4 Dynamic programming Lecture Presentation Divya K S Dept. of CSE
- 2. OPTIMAL BINARY SEARCH TREE • Basic definitions • Concepts of Optimal Binary Search Tree • Example Problem • Assignment
- 3. BINARY SEARCH TREE • In A Binary Search Tree, The Value Of All The Nodes In The Left Sub-tree Is Less Than The Value Of The Root. • Similarly, Value Of All The Nodes In The Right Sub-tree Is Greater Than Or Equal To The Value Of The Root. • This Rule Will Be Recursively Applied To All The Left And Right Sub-trees Of The Root.
- 4. EXAMPLE
- 5. KEYS 1, 2,3
- 6. BST 3BST 2 BST 4 BST 1 BST 5
- 11. Cost: 13
- 12. • Using dynamic programming find the optimal binary search tree for the given data. Keys 10 12 16 21 Frequency 4 2 6 3 0 1 2 3 4 1 0 4 2 0 2 3 0 6 4 0 3 5 0 1 2 3 4 Keys 10 12 16 21 Frequency 4 2 6 3 Solution: Solution matrix
- 13. Formula: 0 1 2 3 4 1 0 4 8(1) 2 0 2 10(3 ) 3 0 6 4 0 3 5 0 C[1,2]= K=1 C[1,0]+C[2,2]=0+2=2--------- ROOT(1) K=2 C[1,1]+C[3,2]=4+0=4 + 6===8 C[2,3]= I=2 J=3 K=2 C[2,1]+C[3,3]=0+6=6 K=3 C[2,2]+C[4,3]=2+0=2 +8===10
- 14. 0 1 2 3 4 1 0 4 8(1) 20(3 ) 26(3 ) 2 0 2 10(3 ) 16(3 ) 3 0 6 12(3 ) 4 0 3 5 0 C[3,4] k=3 C[3,2]+C[4,4]=0+3=3 i=3,j=4 k=4 C[3,3]+C[5,4]=6+0=6 Frequency=9 =====12ROOT(3) Minimum cost =2 16 10 21 12 Optimal Binary search 1*6=6 2*4+2*3=14 3*2=6
- 15. ALGORITHM OPTIMAL BINARY SEARCH TREE
- 16. ASSIGNMENT