CSC 375 Homework 8
George Corser
2009 March 25
5.9
Overhead fractions for
full binary tree
implementations:
(a)
75% (data uses 4 bytes, pointers use 12; overhead is 12/16).
(b)
33.3% (data uses 16 bytes, pointers use 8; overhead is 8/24).
(c)
Internal nodes have 20 bytes (12 overhead) and leaf nodes have 12 bytes (4 overhead).
Full binary trees
have n
internal nodes and n+1 leaf nodes, and consume 20n + 12(n+1) bytes, which are 32n+12 total bytes. Overhead is
12n + 4(n+1) bytes, or 16n+4 overhead bytes. To compute the overhead fraction, divide the latter by the former:
12
32n
4
16n
+
+
=
3
8n
1
4n
+
+
. As n approaches infinity, the overhead fraction approaches 50%.
(d)
Internal nodes have 8 bytes (8 overhead) and leaf nodes have 4 bytes (0 overhead).
Full binary trees
have n
internal nodes and n+1 leaf nodes, and consume 8n + 4(n+1) bytes, which are 12n+4 total bytes. Overhead is 8n
+ 0(n+1) bytes, or 8n total overhead bytes. To compute the overhead fraction, divide the latter by the former:
4
12n
8n
+
=
1
3n
2n
+
. As n approaches infinity, the overhead fraction approaches 2/3, or 66.7%.
5.10
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 Winter '09
 Turner
 Data Structures, George Corser

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