Binary Trees (and Big “O” notation). CS2303 System Programming Concepts (Slides include materials from The C Programming Language , 2 nd edition, by Kernighan and Ritchie and from C: How to Program , 5 th and 6 th editions, by Deitel and Deitel). Definitions. Linked List
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Binary Trees(and Big “O” notation)
CS2303System Programming Concepts
(Slides include materials from The C Programming Language, 2nd edition, by Kernighan and Ritchie and from C: How to Program, 5th and 6th editions, by Deitel and Deitel)
Binary Trees
Binary Trees
A linked list but with two links per item
struct treeItem {type payload;treeItem *left; treeItem *right;
};
payload
payload
payload
payload
payload
payload
payload
left
left
left
left
left
left
left
right
right
right
right
right
right
right
Binary Trees
struct treeItem {type payload;treeItem *left; treeItem *right;
};
struct treeItem *root;
Binary Trees
See Deitel & Deitel, §12.7K & R, §6.5
Binary Trees
struct treeItem {type payload;treeItem *left; treeItem *right;
};
struct treeItem *root;
payload
payload
payload
payload
payload
payload
payload
left
left
left
left
left
left
left
right
right
right
right
right
right
right
Binary Trees
Binary Trees
Look recursively down sequence of branches until either
Desired node is found; or
Null branch is encountered
Replace with ptr to new item
Decide which branch to follow based on payload
payload
payload
payload
payload
payload
payload
payload
left
left
left
left
left
left
left
right
right
right
right
right
right
right
Binary Trees
typedef struct _treeItem {char *word;// part of payloadint count;// part of payload_treeItem *left, *right;} treeItem;
treeItem *findItem(treeItem *p, char *w) {if (p == NULL)return NULL;// item not foundint c = strcmp(w, p>word);if (c == 0)return p;else if (c < 0)return findItem(p>left, w);elsereturn findItem(p>right, w);
}
Binary Trees
treeItem *addItem(treeItem *p, char *w) {if (p == NULL){p = malloc(sizeof(treeItem));char *c = malloc(strlen(w)+1);p>word = strcpy(c, w); p>count = 1;p>left = p>right = NULL;return p;};int c = strcmp(w, p>word);if (c == 0)p>count++;else if (c < 0)p>left = addItem(p>left, w);elsep>right = addItem(p>right, w);return p;
}
Why do this?
Binary Trees
Question:– how many calls to addItem for a tree with 106 nodes?
Assume balanced
I.e., approx same number of nodes on each subtree
payload
payload
payload
payload
payload
payload
payload
left
left
left
left
left
left
left
right
right
right
right
right
right
right
Binary Trees
Binary Trees
Binary Trees
Questions?
Binary Trees
Binary Trees
“BigO” notation:– means “order of”
Binary Trees
Binary Trees
Binary Trees
x = (a.real*b.imag  b.real*a.imag) / sqrt(a.real*b.real – a.imag*b.imag)
=
x
/
sqrt


*
*
…
.
.
.
.
a
real
b
imag
b
real
a
imag
Binary Trees
Binary Trees
Note: Deitel & Deitel, Ch 12 exercises,
contain a series on building a compiler
Binary Trees
Questions?
Binary Trees
“Big O” notation
New Topic
Binary Trees
I.e., proportional to n, the number of items in the list
Binary Trees
I.e., proportional to log of number of items in the list
Binary Trees
Binary Trees
Binary Trees
Binary Trees
Questions on BigO?
Binary Trees