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Tree Traversal

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Traversal Algorithms

preorder

inorder

postorder

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PreOrder Traversal

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Inorder Traversal

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Postorder Traversal

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output:

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a

for each of {b, c, d}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a

for each of {b, c, d}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b

for each of {e, f}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b

for each of {e, f}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e

for each of {j, k}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e

for each of {j, k}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j

for each of {}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j

for each of {j, k}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k

for each of {n, o, p}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k

for each of {n, o, p}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n

for each of {}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n

for each of {n, o, p}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o

for each of {}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o

for each of {n, o, p}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p

for each of {}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p

for each of {n, o, p}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p

for each of {j, k}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p

for each of {e, f}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p f

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p f

for each of {}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p f

for each of {e, f}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p f

for each of {b, c, d}

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In which order does a preorder traversal visit

the vertices in this ordered rooted tree?

procedurepreorder(T: ordered rooted tree)

r:= root ofT

list rfor each child c ofrfrom left to right

begin

T(c) := subtree with c as its root

preorder(T(c))

end

output: a b e j k n o p f c d g l m h i

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output:

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output:

call

stack

r = a, l = ?

s = {}

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output:

r = a, l = b

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output:

r = a, l = b

s = {}

r = b, l = ?

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output:

r = a, l = b

s = {}

r = b, l = e

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output:

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l = ?

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {}

r = j, l = ?

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e

r = a, l = b

s = {}

r = b, l = e

s = {}

r =e, l =j

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = ?

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = n

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = n

s = {}

call

stack

r = n, l = ?

s = {}

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthenlist r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = n

s = {}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = n

s = {o,p}

call

stack

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthenlist r

else

beginl:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k o

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = n

s = {o,p}

call

stack

r = o, l = ?

s = {}

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k o

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = n

s = {o,p}

call

stack

ll

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k o p

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = n

s = {o,p}

call

stack

r = k, l = ?

s = {}

ll

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k o p

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

r = k, l = n

s = {o,p}

call

stack

ll

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k o p

r = a, l = b

s = {}

r = b, l = e

s = {}

r = e, l =j

s = {k}

call

stack

hi h d d i d l i i

ll

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthenlist r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k o p b

r = a, l = b

s = {}

r = b, l = e

s = {}

call

stack

I hi h d d i d l i i

ll

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k o p b

r = a, l = b

s = {}

r = b, l = e

s = {f}

call

stack

I hi h d d i d l i i

ll

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthenlist r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its root

preorder(T(c))

end

output: j e n k o p b f

r = a, l = b

s = {}

r = b, l = e

s = {f}

r = f, l = e

s = {}

call

stack

I hi h d d i d l i i

ll

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its rootpreorder(T(c))

end

output: j e n k o p b f

r = a, l = b

s = {}

r = b, l = e

s = {f}

call

stack

I hi h d d i d t l i it

call

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its rootpreorder(T(c))

end

output: j e n k o p b f

r = a, l = b

s = {}

call

stack

I hi h d d i d t l i it

call

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its rootpreorder(T(c))

end

output: j e n k o p b f

r = a, l = b

s = {c,d}

call

stack

I hi h d d i d t l i it

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In which order does a inorder traversal visit

the vertices in this ordered rooted tree?

procedureinorder(T: ordered rooted tree)

r:= root ofT

ifr is a leafthen list r

else

begin

l:= first child ofrfrom left to right

T(l) := subtree with l as its root

inorder(T(l))

list r

for each child c ofrexcept for l left to right

T(c) := subtree with c as its rootpreorder(T(c))

end

output: j e n k o p b f a c l g m d h i

In which order does a postorder traversal visit

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In which order does a postorder traversal visit

the vertices in this ordered rooted tree?

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Infix, Prefix, and Postfix Notation

represent complicated expressions using an ordered

rooted tree (typically binary)

Algebraic expressions

preorder Polish notation

inorder

infix notation

postorder reverse Polish notation

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Express in:a. Polish

b. infix

c. reverse Polish

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Evaluating

a prefixexpression

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Evaluate postfix expression 7 2 3 * - 4 ^ 9 e / +

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How do you do trees in Java?