1

MIS 3500 * Exercise: B+Tree with degree of 3 - Soluation

< 6104 <=

<3678<=

<1164<=...<2314<= <4164<=…<5931<=

1038 1164 2314 3678 4164 5931

<8442<=…<8777<=

<7368<=…<7547<=

6104 7368 7547 8442 8556 8777 9114

<8556<= <9114<=

a. Root=6104

Solution with operators < <= (as in class notes).

< 5931<=

<3678<=

<1164<=...<2314<=

<4164<=

1038 1164 2314 3678 4164

<8442<=…<8777<=

<6104<=…<7368<=

5931 6104 7368 7547 8442 8556 8777 9114

<8442<=…<8556<= <9114<=

b. Root=5931

6104

2314 -- 3678

1038 -- 1164 3678

1038 1164 2314 3678 4164 5931 6104

8442 -- 8556

7368 – 7547 8556 9114

7368 7547 8442 8556

<

<<=

<=

<=<=

<=

<=

<= <=<=<<

<=

<

< < =

< <=

<

< 5931

<

<

8777

<

9114 <open>

Solution like (b) but a different root value. It leaves a space for a new value to be inserted at the top point of the leaf set (9114).

A B+-tree can be expanded at the leaf level. Since the key values are stored in increasing order (reading left-to-right),sequential search within a leaf is possible. For example, the leaf level bound by 1038 can store values smaller than 1038; the middle set ranges from 1039 to 1164; and the subsequent set stores from 1165 to 2314.

< <=

2

d.

5931

2314

1038 -- 1164 3678 -- 4164

1038 1164 2314 3678 4164 5931

7547 – 8556

6104 – 7368 8442 8777

6104 7368 7547 8442 8556 8777 9114

<

<<=

<=

<=<=

<=

<=

< <=<=<

<

<

<

< <=

< <= < <= < <= <

Solutions with operators <= < . c.