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Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is _________.
Correct answer is '31'. Can you explain this answer?
Verified Answer
Breadth First Search (BFS) is started on a binary tree beginning from ...
No of nodes at level 0(root) of tree =>1
No of nodes at level 1 of tree =>2
No of nodes at level 2 of tree =>4
No of nodes at level 3 of tree =>8
No of nodes at level 4 of tree =>16
Last node in level 4th is the node we are looking for => 1+2+4+8+16 => 31
No of nodes at level 1 of tree =>2
No of nodes at level 2 of tree =>4
No of nodes at level 3 of tree =>8
No of nodes at level 4 of tree =>16
Last node in level 4th is the node we are looking for => 1+2+4+8+16 => 31
Most Upvoted Answer
Breadth First Search (BFS) is started on a binary tree beginning from ...
Understanding BFS in a Binary Tree
Breadth First Search (BFS) explores nodes level by level, starting from the root. In a binary tree, each node can have up to two children, which leads to an exponential growth in the number of nodes at each level.
Tree Structure
- Level 0 (Root): 1 node
- Level 1: 2 nodes
- Level 2: 4 nodes
- Level 3: 8 nodes
- Level 4: 16 nodes
By the fourth level, the total number of nodes is the sum of all nodes up to that level.
Calculating Total Nodes
- Total nodes from Level 0 to Level 4:
- Level 0: 1
- Level 1: 2
- Level 2: 4
- Level 3: 8
- Level 4: 16
This totals to: 1 + 2 + 4 + 8 + 16 = 31
Position of Vertex t
- Since vertex t is at distance four from the root, it resides on Level 4.
- In BFS, all nodes at Level 4 will be explored after all nodes at Levels 0, 1, 2, and 3.
- The maximum number of nodes explored before reaching Level 4 is 15 (from Levels 0 to 3).
Maximum Possible Value of n
- Adding the nodes from Level 4 (16 nodes) to the previous total (15 nodes):
- 15 (from Levels 0-3) + 16 (from Level 4) = 31
Thus, the maximum possible value of n, where t is the n-th vertex in the BFS traversal, is 31.
Breadth First Search (BFS) explores nodes level by level, starting from the root. In a binary tree, each node can have up to two children, which leads to an exponential growth in the number of nodes at each level.
Tree Structure
- Level 0 (Root): 1 node
- Level 1: 2 nodes
- Level 2: 4 nodes
- Level 3: 8 nodes
- Level 4: 16 nodes
By the fourth level, the total number of nodes is the sum of all nodes up to that level.
Calculating Total Nodes
- Total nodes from Level 0 to Level 4:
- Level 0: 1
- Level 1: 2
- Level 2: 4
- Level 3: 8
- Level 4: 16
This totals to: 1 + 2 + 4 + 8 + 16 = 31
Position of Vertex t
- Since vertex t is at distance four from the root, it resides on Level 4.
- In BFS, all nodes at Level 4 will be explored after all nodes at Levels 0, 1, 2, and 3.
- The maximum number of nodes explored before reaching Level 4 is 15 (from Levels 0 to 3).
Maximum Possible Value of n
- Adding the nodes from Level 4 (16 nodes) to the previous total (15 nodes):
- 15 (from Levels 0-3) + 16 (from Level 4) = 31
Thus, the maximum possible value of n, where t is the n-th vertex in the BFS traversal, is 31.
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Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance fourfrom the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is _________.Correct answer is '31'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance fourfrom the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is _________.Correct answer is '31'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance fourfrom the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is _________.Correct answer is '31'. Can you explain this answer?.
Solutions for Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance fourfrom the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is _________.Correct answer is '31'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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