Complete Binary Tree MCQ Quiz in मल्याळम - Objective Question with Answer for Complete Binary Tree - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

A full binary tree (sometimes proper binary tree or 2-tree) is a tree in which every node other than the leaves has two children.

Graph with height 5:

The maximum number of nodes present: 63 

Tips and Tricks:

If n is number of nodes and h is minimum height of in a binary search tree, then

2h+1 – 1 = n 

2h+1 – 1 = 63

2h+1 =  64 

∴2h+1 =  2⁶

∴ h = 5

if h is ≥ 5 then 63 nodes are possible and hence option 4 is the correct answer.

In a full binary tree number of nodes is 63 then the height of the tree ≥  5

Consider the following full binary tree of height 3

no. of nodes

(for any height) h 2^h+1-1

The correct answer is option 3.

Concept:

The height of a binary tree is the height of the root node in the whole binary tree. In other words, the height of a binary tree is equal to the largest number of edges from the root to the most distant leaf node

The given height is = 3,

smallest nodes= 4

If the tree is a left skew tree or a right skew tree then nodes will be 4 with height 3.

Largest nodes= 15

If the tree is a full binary tree then nodes will be 15 with a height of 3.

Hence the correct answer is Smallest: 4, Largest: 15.

Answer: Option 4

Explanation: 

This type of "number of nodes in a tree" type Questions can be solved by taking an example

Consider the following example

In this Complete Binary tree, we have height of the tree is 3 and no of leaf nodes is 8.

Hence we can generalize this and can say that number of leaf nodes in a complete binary tree of depth/height m is 2^m.

Concept:

Level is the number of nodes on path from root to the node.

Explanation:

If T is a binary tree with number of levels as L, then number of leaf nodes in the binary tree is at most 2^L-1.

Consider, tree has only one level, then number of nodes = 2^1-1 = 2⁰ = 1

It means tree will have only one node i.e. root

If tree has two levels, then maximum nodes possible at that level = 2^2-1 = 2

i.e. maximum 2 leafs are possible and 3 total nodes are possible with 2 levels.

Similarly, if we take 3 levels, number of nodes that level = 2^3-1 = 4

i.e. maximum leaf nodes possible = 4 and total nodes = 7

Consider an example:

k = 2(internal nodes)

leaves = 2k + 1 = 2 × 3 - 1 = 5

satisfies the case

Tips and Tricks:

If n- ary tree with k internal nodes, then number of leaves:

L = (n – 1) × k + 1

L = (3 – 1) k + 1

The correct order is:  1-q, 2-r, 3-p

Maximum size of an array to store a binary tree with 'n' nodes: 2n-1

Maximum height possible for a binary tree with 'n' nodes: n

Minimum height possible for a binary tree with 'n' nodes: log2n

The correct answer is option 2

CONCEPT:

A Binary tree is a tree that contains nodes that can have zero, one, or two child nodes.

A complete binary tree is a binary tree in which every level is completely filled, except possibly the last, and all nodes are as far left as possible.

Calculation:

Number of nodes at height  0 = 2⁰ = 1

Number of nodes at height  1 = 21 = 2

Number of nodes at height  2 = 22 = 4

Number of nodes at height 3 = 23 = 8

Number of nodes at height 4 = 24 = 16

Number of nodes at height 5 = 25 = 32

So total number of nodes = 1 + 2 +  4 + 8 + 16 + 32 =63

So option 2 is correct

Alternate Method

Graph with height 5:

The maximum number of nodes present: 63 

If n is the number of nodes and h is the minimum height of in a binary search tree, then

n = 2h+1 – 1

n = 25+1 – 1

∴ n = 63 

The correct answer is Non-linear data structure.

Key Points

• Trees and graphs are classified as non-linear data structures.
• Unlike linear data structures (like arrays and linked lists), non-linear data structures do not store data elements in a sequential manner.
• In a tree, data is organized in a hierarchical structure with a root element and sub-elements (children).
• Graphs consist of nodes (vertices) connected by edges, which can represent various relationships between the nodes.
• Non-linear data structures are useful for representing complex relationships and hierarchical data.

Additional Information

• Trees are widely used in databases, file systems, and network routing algorithms.
• Graphs are used in social networks, web page ranking algorithms, and to represent transportation networks.
• Common operations on trees include traversal (in-order, pre-order, post-order) and manipulation (insertion, deletion).
• Graph operations include traversal (depth-first search, breadth-first search), shortest path finding, and network flow analysis.