Timeline for Prove $T$ is a BST iff for every node $x$ of $T$ that is not a leaf, the key of $x$ is larger or equal than the key of the left child of $x$

8 events

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Jun 17, 2017 at 9:46	history	tweeted			twitter.com/StackCompSci/status/876013212264783875
Jun 16, 2017 at 9:23	vote	accept	Yos
Jun 16, 2017 at 9:19	comment	added	fade2black		you write: "...the key of $x$ is larger or equal than the key of the left child of $x$ OR it is less than or equal than the key of the right child". Pay attention to the second 'or' (uppercase 'or). Consider a three node @Yos, binary tree (1)<--left--((3)) --right-->(2), 3 is root, 1 is the left child and 2 is the right child. So your proposition is TRUE: (node 3 is a non-leaf) and ( (3 is larger than or equal to the left child 1) OR (3 is less than or equal to 2 ) . But the tree is not a BST.
Jun 16, 2017 at 9:18	answer	added	Karegar		timeline score: 3
Jun 16, 2017 at 9:06	comment	added	Yos		@fade2black the key of $x$ can be larger OR equal than the key of its left child $y$ why does it have to be AND? Also you're saying no need for further proof in the first direction but what about the second direction?
Jun 16, 2017 at 9:03	comment	added	fade2black		In your proposition: "if for every node $x$ of $T$ that is not a leaf, the key of $x$ is larger or equal than the key of the left child of $x$ OR it is less than or equal than the key of the right child", shouldn't OR be replaced with AND. Even in that case you will already have a definition of a BST, so no need to prove it.
Jun 16, 2017 at 9:00	history	edited	Raphael		edited tags
Jun 16, 2017 at 8:48	history	asked	Yos	CC BY-SA 3.0