I want to know the maximum no of levels in a binary tree of which the total leaf nodes are n . Nothing has been said about type of binary tree ,just it is a binary tree
Binary tree: a rooted tree where each node has 0, 1, or 2 children.
Full binary tree: a binary tree where each node has 0 or 2 children.
Perfect binary tree: a full binary tree where each leaf has the same depth.
The level of a tree is the depth plus 1. The depth of a binary tree with n leaves can be from to infinite. The depth of a full binary tree can be from to . The lower bound in these two cases is when it is a perfect binary tree.
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I am looking at LeetCode problem 110. Balanced Binary Tree:
Given a binary tree, determine if it is height-balanced.
For this problem, a height-balanced binary tree is defined as:
a binary tree in which the left and right subtrees of every node differ in height by no more than 1.
I have this input:
[2,1,3,0,null,null,4,null,null,null,5]
For this input, the expected output is false. Why is this not a height balanced binary search tree? I did look up the definition of what height balanced means, but maybe I am unclear of the direction in which to look at this tree to determine whether it is height balanced or not.
The tree represented by this array is:
2
/ \
1 3
/ \
0 4
\
5
The definition of what balanced means in this LeetCode exercise is:
a binary tree in which the left and right subtrees of every node differ in height by no more than 1.
This is not true for the tree rooted at 3. Its left and right subtrees differ in height by 2.
I am a beginner in the field of data structures, I am studying binary trees and in my textbook there's a tree which is not a binary tree but I am not able to make out why the tree is not a binary tree because every node in the tree has atmost two children.
According to Wikipedia definition of binary tree is "In computer science, a binary tree is a treedata structure in which each node has at most two children, which are referred to as the left child and the right child."
The tree in the picture seems to satisfy the condition as mentioned in the definition of binary tree.
I want an explanation for why the tree is not a binary tree?
This is not even a tree, let alone binary tree. Node I has two parents which violates the tree property.
I got the answer, This not even a tree because a tree is connected acyclic graph also a binary tree is a finite set of elements that is either empty or is partitioned into three disjoint subsets. The first subset contains a single element called the root of the tree. The other two subsets are themselves binary trees called the left and right subtrees of the original tree.
Here the word disjoint answers the problem.
It's not a binary tree because of node I
This can be ABEI or ACFI
This would mean the node can be represented by 2 binary numbers which is incorrect
Each node has either 0 or 1 parents. 0 in the case of the root node. 1 otherwise. I has 2 parents E and F
What is the Formula to Find the minimum number of vertices required to make a binary tree (not a complete binary tree) of height 5 ?
A binary tree's height cannot be bigger than the number of nodes or vertices in the tree. So yes, the minimum number of vertices required for a binary tree of height 5 will be 5. Also, there must be n-1 edges between them. You can imagine a single series of connected nodes, and that is basically what you get.
Alternately, a full binary tree is a binary tree in which each internal vertex has exactly two children.This means a binary tree with n internal vertices has 2n + 1 vertices, 2n edges, and n + 1 leaves.
the minimum number of vertices in a binary tree of height n (with no further constraints) is always n.
proof:
if there were less than n nodes, the tree wouldn't be a valid binary tree (I guess I don't need to further explain this point)
if there were more than n nodes, it means at least one of the nodes has a brother (pigeonhole principle), which could be taken off the tree and it would result in a valid, smaller binary tree, so we know that this tree is not minimal, which opposes our assumption of a minimal tree.
-> a binary tree T is minimal -> T has n nodes
Can we sort 7 numbers in 10 comparisons?
Depth of a binary tree with n node is? log(n)+1 or something else
If every node in a binary tree has either 0 or 2 children then the height of the tree is log(n): is it true or false?
Inserting an element into a binary search tree of size n takes time proportional to ------?
A binary tree not balanced can have all children at the right (for example), so the maximum height of a tree with n nodes is n
Same as 2.
If the tree is not balanced the insertion is proportional to the number of nodes that you need to traverse to find the correct position. Potentially n nodes.
What is the name of the binary tree (or the family of the binary
trees), that is balanced, and has the minimum number of nodes
possible for its height?
Well this is special kind of tree not the AVL tree.
if the binary tree is balanced then, it height is a function of its nodes (n). height = log2n. so a balanced tree don't have a range of heights.
The minimum number of nodes a completely balanced binary tree can have for height d is 2^(d-1)+1. As far as i know this type doesn't have a name.
The maximal number of nodes is 2^d. This is called a complete tree. All layers are completely full and each node has either 2 or zero childern(implied).
Red-black tree?
Any one from http://en.wikipedia.org/wiki/Self-balancing_binary_search_tree#Implementations?
The name of the binary tree (or the family of the binary trees), that has the minimum number of nodes possible for its height is a linked list :D