1. Data Structures and Analysis (COMP 410)
David Stotts
Computer Science Department
UNC Chapel Hill

2. Representing Trees as Arrays

3. Array Rep for any BT Not heap structure (complete binary tree)4 18 11 9 3 7 16 21 12
Not heap structure (complete binary tree)
just a random binary tree 7 21 4 18 3 11 12 16 9

4. Now get bigger… Add one node, double space needed in array4 18 11 9 3 7 16 21 12
Add one node,
double space needed in array 5 7 21 4 18 3 11 12 16 9 5

5. 4 18 11 9 3 7 16 21 12 5
And bigger… 7 21 4 18 3 11 12 16 9 5 8 8

6. Array space used Some languages (without objects) would use huge space
Array element is a static collection of data, each element might need 1000’s bytes
array[10000] of struct { int, real, char[48] }

7. array
int
real
chars
int
real
chars 1
. . .

8. Array space used
In Java (and languages with objects, pointers) can improve this
Array element is an object, then each space in the array is a 8-byte address
Each object is a collection of data, might be large, but we only need a object for each occupied array location
class Element { int, real, char[48] }
array[10000] of Element
array[0] = new Element { 3, 4.5, “now is the time”}
array[4] = new Element { 1, 6.3, “for all good code”}

9. . . . 3 4.5 “now is the time” 2 6.3 “for all good code” array 1 2 3 43
4.5
“now is the time” 1 2 3 4 5 6 7 2
6.3
“for all good code”
. . .

10. Static layout,
big space for each array element, used or not
dynamic layout, each array element 64-bits,
then big space for only elements used

11. Other problems… Add a node 8 3 and 16 have now changed levels
When we add/move new nodes in a tree in the middle layers, we force rearrangement of values stored in the array
Ex: 4 18 11 9 3 7 16 21 12 8 4 18 11 9 3 7 16 21 12
Add a node 8
between the 21 and 3
3 and 16 have now changed levels

12. Inner insert encoding the original tree4 18 11 9 3 7 16 21 12
encoding the original tree 7 21 4 18 3 11 12 16 9

13. Inner insert Add a node 8 between the 21 and 34 18 11 9 3 7 16 21 12 8
Add a node 8 between the 21 and 3 7 21 4 18 11 12 9 3 16 8

14. Summary
Array representation can be fast if the tree is built and then not changed (much)
Changes in a tree require a lot of array element movement
Array rep can be space inefficient if tree is not fairly full
Array rep can be very space inefficient if array elements are static memory blocks rather than dynamically allocated objects

15. Beyond this is just templates
END
Beyond this is just templates