T r e e t r a v e r s a l s ( W e i s s 4 . 6 - - PowerPoint PPT Presentation

SLIDE 1

T r e e t r a v e r s a l s ( W e i s s 4 . 6 )

SLIDE 2

T r e e t r a v e r s a l

T r a v e r s i n g a t r e e m e a n s v i s i t i n g a l l i t s n

• d

e s i n s

• m

e

• r

d e r Tii s c a n b e i m p l e m e n t e d b y r e c u r s i

• n

. F

• r

e x a m p l e , p r i n t i n g t h e v a l u e

• f

a l l n

• d

e s i n t h e t r e e :

class Node<E> { E value; Node<E> left, right; } void printAll(Node<E> node) { if (node == null) return; // base case System.out.println(node.value); printAll(node.left); printAll(node.right); }

Tii s k i n d

• f

t r a v e r s a l i s c a l l e d a p r e

• r

d e r t r a v e r s a l b e c a u s e w e v i s i t t h e n

• d

e b e f

• r

e w e r e c u r s e i n t

• i

t s c h i l d r e n .

SLIDE 3

I n

• r

d e r t r a v e r s a l

I n a n i n

• r

d e r t r a v e r s a l w e fj r s t v i s i t t h e n

• d

e ’ s l e f t c h i l d , t h e n t h e n

• d

e i t s e l f , t h e n t h e n

• d

e ’ s r i g h t c h i l d . E x a m p l e : p r i n t i n g

• u

t t h e c

• n

t e n t s

• f

a b i n a r y s e a r c h t r e e i n s

• r

t e d

• r

d e r !

class Node<E> { E value; Node<E> left, right; } void printSorted(Node<E> node) { if (node == null) return; printSorted(node.left); System.out.println(node.value); printSorted(node.right); }

SLIDE 4

S

• r

t i n g a b i n a r y s e a r c h t r e e

I f w e d

• a

n i n

• r

d e r t r a v e r s a l

• f

a B S T , w e v i s i t i t s e l e m e n t s i n s

• r

t e d

• r

d e r !

h

• r

s e h

• r

s e

• w

l

• w

l l e m u r l e m u r g

• r

i l l a g

• r

i l l a p e n g u i n p e n g u i n w

• l

f w

• l

f a p e a p e h a m s t e r h a m s t e r

1 . V i s i t l e f t s u b t r e e 2 . V i s i t r

• t

3 . V i s i t r i g h t s u b t r e e

SLIDE 5

P

• s

t

• r

d e r t r a v e r s a l

I n a p

• s

t

• r

d e r t r a v e r s a l w e v i s i t e a c h n

• d

e ’ s c h i l d r e n b e f

• r

e v i s i t i n g t h e n

• d

e i t s e l f . E x a m p l e : c a l c u l a t i n g t h e h e i g h t

• f

a b i n a r y t r e e :

int height(Node<E> node) { if (node == null) return 0; else { int leftHeight = height(node.left); int rightHeight = height(node.right); return 1 + Math.max(leftHeight, rightHeight); } }

SLIDE 6

S u m m a r y – t r a v e r s a l s

T r e e t r a v e r s a l s c a p t u r e d i fg e r e n t p a t t e r n s

• f

r e c u r s i

• n

f

• r

v i s i t i n g a l l n

• d

e s i n a t r e e

• P

r e

• r

d e r – v i s i t r

• t

, t h e n r e c u r s i v e l y t r a v e r s e c h i l d r e n

• P
• s

t

• r

d e r – r e c u r s i v e l y t r a v e r s e c h i l d r e n , t h e n v i s i t r

• t
• I

n

• r

d e r – r e c u r s i v e l y t r a v e r s e

• n

e c h i l d , t h e n v i s i t r

• t

, t h e n r e c u r s i v e l y t r a v e r s e

• t

h e r c h i l d ( m a k e s s e n s e f

• r

e . g . 2

• 3

t r e e s t

• )

N

• t

h i n g s

• p

h i s t i c a t e d n e e d e d – a s i m p l e r e c u r s i v e f u n c t i

• n

d

• e

s t h e j

• b

L e s s c

• m

m

• n

: l e v e l

• r

d e r t r a v e r s a l – v i s i t n

• d

e s i n

• r

d e r

• f

l e v e l i n t h e t r e e