06 - Trees

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I used this set of slides for the lecture on Trees I gave at the University of Zurich for the 1st year students following the course of Formale Grundlagen der Informatik.

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edge
node

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leaf
root

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parent
child

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height = 1
depth = level = 2
degree = 1

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height = 1
depth = level = 1
degree = 3

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ordered tree
leftmost rightmost

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isomorphic trees

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left right
left leftright right

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not a binary tree binary tree
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complete binary tree

breadth-ﬁrst traversal
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breadth-ﬁrst traversal
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breadth-ﬁrst traversal
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breadth-ﬁrst traversal
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breadth-ﬁrst traversal
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breadth-ﬁrst traversal
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breadth-ﬁrst traversal
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preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

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preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

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2
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preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

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1
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

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1
preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

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preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

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preorder(node)
visit(node).
preorder(node.left).
preorder(node.right).

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inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

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inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

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2
1
inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

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inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

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inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

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inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

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inorder(node)
inorder(node.left).
visit(node).
inorder(node.right).

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postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

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1
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

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postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

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1 2
postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

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postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

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postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

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postorder (node)
postorder(node.left).
postorder(node.right).
visit(node).

!"#$%&'(")$*
!
"#$#%&'!&$()*+,%&)$!&-!.,--#/!)$!(*)+!0#$#*,%&)$!%)!
Example (group 15)

Binary search tree
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Inﬁx notation
a
+
b
-
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*
d
Postﬁx notation
Preﬁx notation

Inﬁx notation
a
+
b
-
c
*
d
Postﬁx notation
Preﬁx notation -+ab*cd

Inﬁx notation
a
+
b
-
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*
d
a+b-c*d
Postﬁx notation
Preﬁx notation -+ab*cd

Inﬁx notation
a
+
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*
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a+b-c*d
Postﬁx notation ab+cd*-
Preﬁx notation -+ab*cd

Tudor Gîrba
www.tudorgirba.com
creativecommons.org/licenses/by/3.0/

Research shows that we think like we speak. The first step in Visual Design Thinking, then, is learning visual language. Come learn Glyph™, a language that balances verbal and visual elements to improve the way you learn, remember, create, and communicate. After this 2.5 hour workshop, you will be bursting through that “I can’t draw” trap and stepping into your new role as a standout visual problem solver. Come join Stanford’s Alli McKee for a workshop that will build your creative confidence and amplify your communication. With extensive experience in both business (Bain & Company + Stanford GSB) and design (IDEO.org + Stanford d.school), Alli has come from Silicon Valley to bring you the best of both worlds to deliver a unique experience that is challenging, fun, and fulfilling. Interested in teaching this workshop: http://visualdesignthinking.co/join-us/

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"IDEO의 디자인 Thinking" (Design Thinking from IDEO) "왜 IDEO는 혁신적인가?" 혁신의 상징, 거대기업들이 끊임없이 배우고자 하는 창의적 사고. 그 중심에는 'Design Thinking'이 있습니다. IDEO의 사례들과 디자인Thinking의 프로세스를 알아보세요! 창의적인 1%의 비밀노트, Beecanvas 페이스북페이지에서 만나보세요! - http://facebook.com/beecanvas 슬라이드쉐어에서도 만나보실 수 있습니다. - https://www.slideshare.net/BeeCanvas 모든 아이디어 발상 테크닉들을 페이지에서 만나보세요! 사진 출처 : https://flic.kr/p/jKqgHD - Stilte na de brainstorm Impact Hub Amsterdam 원작자 플리커 : https://www.flickr.com/photos/mvonederland/ - MVO Nederland 참고 : http://en.wikipedia.org/wiki/Design_thinking, OPENIDEO

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We cannot continue to let systems loose in the wild without any concern for how we will deal with them at a later time. Two decades ago, Richard Gabriel coined the idea of software habitability. Indeed, given that engineers spend a significant part of their active life inside software systems, it is desirable for that system to be suitable for humans to live there. We go further and introduce the concept of software environmentalism based on a simple principle: Engineers have the right to build upon assessable systems and have the responsibility of producing assessable systems.

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