Assume the level of the root node in a tree is 0. We have a tree with nodes having values as 1,3,7,15,29. Then the maximum value of level number possible is _______.Correct answer is '4'. Can you explain this answer?

Question

Answer

Explanation:

To find the maximum value of the level number in the given tree, we need to analyze the pattern of the values and their corresponding levels.

Given Tree:

```
1 (Level 0)
/ \
3 7 (Level 1)
/ \ / \
15 29 (Level 2)
```

Analysis:

From the given tree, we can observe the following patterns:

- The root node has a value of 1 and is at level 0.
- The left child of the root node has a value of 3 and is at level 1.
- The right child of the root node has a value of 7 and is also at level 1.
- The left child of the left child of the root node has a value of 15 and is at level 2.
- The right child of the left child of the root node has a value of 29 and is also at level 2.

Pattern:

Looking at the values and their corresponding levels, we can observe the following pattern:

- The value at each level is the sum of the values at the previous level multiplied by 2, plus 1.
- For example, the value at level 1 is (1 + 1) * 2 + 1 = 3.
- Similarly, the value at level 2 is (3 + 7) * 2 + 1 = 15.

Finding the Maximum Level:

To find the maximum level number possible, we need to continue this pattern until we reach a level where the value exceeds the maximum value given in the question, which is 29.

- For level 3, the value would be (15 + 29) * 2 + 1 = 91, which exceeds 29.
- Therefore, the maximum level number possible is 2, which is the level of the highest value in the given tree.

Conclusion:

The maximum value of the level number possible in the given tree is 2, not 4 as stated in the question.

Answer

Given,

The values of a node of a tree are:

1,3,7,15,29

As we know,

In worst case, tree might be skewed tree and in that case, there will be 5 levels and root will be at 0. So, the levels can be like this.

1 - Level 0

3 - Level 1

7 - Level 2

15 - Level 3

29 - Level 4

The maximum value of level number possible is 4

Similar Computer Science Engineering (CSE) Doubts

Let G be a complete undirected graph on 4 vertices, having 6 edges with weights being 1, 2, 3, 4, 5, and 6. The maximum possible weight that a minimum weight spanning tree of G can have is __________ Correct answer is '7'. Can you explain this answer?

Consider the expression tree shown. Each leaf represents a numerical value, which can either be 0 or 1. Over all possible choices of the values at the leaves, the maximum possible value of the expression represented by the tree is ___. Correct answer is '6'. Can you explain this answer?

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