Alyce Brady CS 470: Data Structures CS 510: Computer Algorithms Breadth-First Binary Tree Traversal Algorithm.

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Presentation transcript:

Alyce Brady CS 470: Data Structures CS 510: Computer Algorithms Breadth-First Binary Tree Traversal Algorithm

Reminder: Breadth-First Traversal A BC DEFG A B C D E F G

Pseudo-Code for Breadth-First Traversal breadth-first-traversal put root node onto a queue while the queue is not empty dequeue the next node visit the node e.g., print value enqueue the left child node enqueue the right child node

Breadth-First Search A BC DEFG A B C D E F G Queue: Current:

Breadth-First Search A BC DEFG Queue: Current: A

Breadth-First Search A BC DEFG Queue: Current: A A

Breadth-First Search A BC DEFG Queue: Current: A A A

Breadth-First Search A BC DEFG Queue: Current: B A A A

Breadth-First Search A BC DEFG Queue: Current: CBCB A A A

Breadth-First Search A BC DEFG Queue: Current: B A A CBCB

Breadth-First Search A BC DEFG Queue: Current: B C A B

Breadth-First Search A BC DEFG Queue: Current: DCDC B A B

Breadth-First Search A BC DEFG Queue: Current: EDCEDC B A B

Breadth-First Search A BC DEFG Queue: Current: C EDCEDC A B

Breadth-First Search A BC DEFG Queue: Current: C A B C EDED

Breadth-First Search A BC DEFG Queue: Current: C A B C FEDFED

Breadth-First Search A BC DEFG Queue: Current: C A B C GFEDGFED

Breadth-First Search A BC DEFG Queue: Current: D A B C GFEDGFED

A B C D Breadth-First Search A BC DEFG Queue: Current: D GFEGFE

Breadth-First Search A BC DEFG A B C D Queue: Current: E GFEGFE

Breadth-First Search A BC DEFG Queue: Current: E GFGF A B C D E

Breadth-First Search A BC DEFG Queue: Current: F GFGF A B C D E

Breadth-First Search A BC DEFG Queue: Current: F G A B C D E F

Breadth-First Search A BC DEFG Queue: Current: G G A B C D E F

Breadth-First Search A BC DEFG Queue: Current: G A B C D E F G

Breadth-First Search A BC DEFG A B C D E F G

Time and Space Complexity for Breadth-First Search Alg. Time Complexity Time Complexity –Consider each node twiceO(n) when put on queue when put on queue when taken from queue when taken from queue

Space Complexity Space Complexity –Queue to handle unexplored nodes Queue length = width of lowest level(n/2) Queue length = width of lowest level(n/2) O(n) O(n) Time and Space Complexity for Breadth-First Search Alg.