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10.3 Tree Transversal

10.3 Tree Transversal. Pre/post fix notation and order. See handout. . a . b c . d e f g h i j k . Preorder transversal- root first, then left to right . a . b c . d e f g

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10.3 Tree Transversal

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  1. 10.3 Tree Transversal

  2. Pre/post fix notation and order • See handout . a . b c . d e f g h i j k

  3. Preorder transversal- root first, then left to right a . b c . d e f g h i j k

  4. Inorder transversal- left tree, then root, then rest of trees- left to right a b c d e f g h i j k

  5. Postorder transversal- left to right, then root last a . b c . d e f g h i j k

  6. Infix, prefix, and postfix • See handout • Infix order is ambiguous – so parentheses are required • Prefix and postfix are not– so parentheses are unnecessary • Prefix- “Polish notation” • Read from R to L • Operations are on the L • Postfix • Read from L to R • Operations are on the R

  7. Example– transverse in 3 ways, and evaluate each notation +  * 3 2 5 2 • Preorder- prefix • Inorder-infix • Postorder-postfix

  8. Example- prefix • Evaluate a prefix expression + - * 2 3 5 /  2 3 4

  9. Ex- postfix 7 2 3 * - 4  9 3 / +

  10. Example– transverse in 3 ways, and evaluate each notation +  * 5 2 3 4 • Preorder- prefix • Inorder-infix • Postorder-postfix -  *

  11. Find the value of each prefix expression (R to L,operations on the L) • - * 2 / 8 4 3 •  - * 3 3 * 4 2 5

  12. Find the value of each prefix expression (R to L,operations on the L) • + -  3 2  2 3 / 6 – 4 2 • * + 3 + 3  3 + 3 3 3

  13. Find the value of each postfix expression (L to R, operations on R) • 5 2 1 - - 3 1 4 + + *

  14. Find the value of each postfix expression (L to R, operations on R) • 9 3 / 5 + 7 2 - * • 3 2 * 2  5 3 – 8 4 / * -

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