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Recent questions tagged binary-tree

42 votes
5 answers
302
GATE IT 2008 | Question: 76
A binary tree with $n > 1$ nodes has $n_1$, $n_2$ and $n_3$ nodes of degree one, two and three respec­tively. The degree of a node is defined as the number of its neighbours. $n_3$ can be expressed as $n_1 + n_2 - 1$ $n_1 -2$ $[((n_1 + n_2)/2)]$ $n_2 - 1$
A binary tree with $n 1$ nodes has $n_1$, $n_2$ and $n_3$ nodes of degree one, two and three respec­tively. The degree of a node is defined as the number of its neighbo...
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21 votes
3 answers
304
GATE CSE 1996 | Question: 1.15
Which of the following sequences denotes the post order traversal sequence of the below tree? $f\; e\; g\; c\; d\; b\; a$ $g\; c\; b\; d\; a\; f\; e$ $g\; c\; d\; b\; f\; e\; a$ $f\; e\; d\; g\; c\; b \;a$
Which of the following sequences denotes the post order traversal sequence of the below tree?$f\; e\; g\; c\; d\; b\; a$$g\; c\; b\; d\; a\; f\; e$$g\; c\; d\; b\; f\; e\...
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29 votes
3 answers
305
GATE CSE 1996 | Question: 1.14
In the balanced binary tree in the below figure, how many nodes will become unbalanced when a node is inserted as a child of the node “g”? $1$ $3$ $7$ $8$
In the balanced binary tree in the below figure, how many nodes will become unbalanced when a node is inserted as a child of the node “g”?$1$$3$$7$$8$
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25 votes
3 answers
306
GATE CSE 1995 | Question: 6
What is the number of binary trees with $3$ nodes which when traversed in post-order give the sequence $A, B, C ?$ Draw all these binary trees.
What is the number of binary trees with $3$ nodes which when traversed in post-order give the sequence $A, B, C ?$ Draw all these binary trees.
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43 votes
6 answers
307
GATE CSE 1995 | Question: 1.17
A binary tree $T$ has $n$ leaf nodes. The number of nodes of degree $2$ in $T$ is $\log_2 n$ $n-1$ $n$ $2^n$
A binary tree $T$ has $n$ leaf nodes. The number of nodes of degree $2$ in $T$ is$\log_2 n$$n-1$$n$$2^n$
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19 votes
2 answers
309
GATE CSE 1993 | Question: 16
Prove by the principal of mathematical induction that for any binary tree, in which every non-leaf node has $2$-descendants, the number of leaves in the tree is one more than the number of non-leaf nodes.
Prove by the principal of mathematical induction that for any binary tree, in which every non-leaf node has $2$-descendants, the number of leaves in the tree is one more ...
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57 votes
12 answers
311
GATE CSE 2010 | Question: 10
In a binary tree with $n$ nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that have exactly one child? $0$ $1$ $\frac{(n-1)}{2}$ $n-1$
In a binary tree with $n$ nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree ...
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48 votes
9 answers
313
GATE CSE 2011 | Question: 29
We are given a set of $n$ distinct elements and an unlabeled binary tree with $n$ nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree? $0$ $1$ $n!$ $\frac{1} {n+1} .^{2n}C_n$
We are given a set of $n$ distinct elements and an unlabeled binary tree with $n$ nodes. In how many ways can we populate the tree with the given set so that it becomes a...
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90 votes
11 answers
314
GATE CSE 2014 Set 1 | Question: 12
Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly $4$ nodes is $O(n^a\log^bn)$. Then the value of $a+10b$ is __________.
Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine the number of subtrees having exactly $4$ nodes is...
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20 votes
1 answer
315
GATE CSE 1998 | Question: 20
Draw the binary tree with node labels $\text{a, b, c, d, e, f and g}$ for which the inorder and postorder traversals result in the following sequences: Inorder: $\text{a f b c d g e}$ Postorder: $\text{a f c g e d b}$
Draw the binary tree with node labels $\text{a, b, c, d, e, f and g}$ for which the inorder and postorder traversals result in the following sequences:Inorder: $\text{a f...
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29 votes
3 answers
318
GATE CSE 2007 | Question: 13
The maximum number of binary trees that can be formed with three unlabeled nodes is: $1$ $5$ $4$ $3$
The maximum number of binary trees that can be formed with three unlabeled nodes is:$1$$5$$4$$3$
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26 votes
4 answers
319
GATE CSE 2007 | Question: 12
The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is: $2^h -1$ $2^{h-1} -1$ $2^{h+1} -1$ $2^{h+1}$
The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is:$2^h -1$$2^{h-1} -1$$2^...
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20 votes
1 answer
323
GATE CSE 2002 | Question: 6
Draw all binary trees having exactly three nodes labeled $A, B$ and $C$ on which preorder traversal gives the sequence $C, B, A$.
Draw all binary trees having exactly three nodes labeled $A, B$ and $C$ on which preorder traversal gives the sequence $C, B, A$.
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48 votes
4 answers
325
GATE CSE 2000 | Question: 2.16
Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited `in a postorder, inorder and preorder traversal respectively, of a complete binary tree. Which of the following is always true? LASTIN = LASTPOST LASTIN = LASTPRE LASTPRE = LASTPOST None of the above
Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal respectively, of a complete binary tree. Which of the foll...
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33 votes
8 answers
326
GATE CSE 2000 | Question: 1.14
Consider the following nested representation of binary trees: $(X \ Y \ Z)$ indicates $Y$ and $Z$ are the left and right subtrees, respectively, of node $X$. Note that $Y$ and $Z$ may be $NULL$ ... $(1 \ (2 \ 3 \ 4) \ (5 \ 6 \ 7))$ $(1 \ (2 \ 3 \ NULL) \ (4 \ 5))$
Consider the following nested representation of binary trees: $(X \ Y \ Z)$ indicates $Y$ and $Z$ are the left and right subtrees, respectively, of node $X$. Note that $Y...
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25 votes
3 answers
327
GATE CSE 1991 | Question: 14,a
Consider the binary tree in the figure below: What structure is represented by the binary tree?
Consider the binary tree in the figure below:What structure is represented by the binary tree?
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44 votes
2 answers
328
GATE CSE 1991 | Question: 01,viii
The weighted external path length of the binary tree in figure is ______
The weighted external path length of the binary tree in figure is ______
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20 votes
5 answers
329
GATE CSE 1991 | Question: 1,ix
If the binary tree in figure is traversed in inorder, then the order in which the nodes will be visited is ______
If the binary tree in figure is traversed in inorder, then the order in which the nodes will be visited is ______
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