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GATE CSE
Trees
Data Structures
Previous Years Questions
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Marks 1
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Suppose a binary search tree with 1000 distinct elements is also a complete binary tree. The tree is stored using the ar...
GATE CSE 2022
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What is the worst case time complexity of inserting n2 elements into an AVL-tree with n elements initially?
GATE CSE 2020
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The preorder traversal of a binary search tree is 15, 10, 12, 11, 20, 18, 16, 19. Which one of the following is the post...
GATE CSE 2020
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The postorder traversal of a binary tree is $$8,9,6,7,4,5,2,3,1.$$ The inorder traversal of the same tree is $$8,6,9,4,7...
GATE CSE 2018
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While inserting the elements $$71, 65, 84, 69, 67, 83$$ in an empty binary search tree $$(BST)$$ in the sequence shown, ...
GATE CSE 2015 Set 3
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Consider a binary tree $$T$$ that has $$200$$ leaf nodes. Then, the number of nodes in $$T$$ that have exactly two child...
GATE CSE 2015 Set 3
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A binary tree $$T$$ has $$20$$ leaves. The number of nodes in $$T$$ having two children is _______________.
GATE CSE 2015 Set 2
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Consider a complete binary tree where the left and the right sub-trees of the root are max-heaps. The lower bound for th...
GATE CSE 2015 Set 2
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What are the worst-case complexities of insertion and deletion of a key in a binary search tree?
GATE CSE 2015 Set 1
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Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)? I. 3, 5, 7, 8, 15, 19, 25 ...
GATE CSE 2015 Set 1
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The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a ...
GATE CSE 2015 Set 1
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Consider a rooted n node binary tree represented using pointers. The best upper bound on the time required to determine ...
GATE CSE 2014 Set 1
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Consider the following rooted tree with the vertex labelled P as the root The order in which the nodes are visited duri...
GATE CSE 2014 Set 3
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A max-heap is a heap where the value of each parent is greater than or equal to the value of its children. Which of the ...
GATE CSE 2011
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Which of the following is TRUE?
GATE CSE 2008
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The maximum number of binary trees that can be formed with three unlabeled nodes is:
GATE CSE 2007
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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 bi...
GATE CSE 2007
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In a binary tree, the number of internal nodes of degree 1 is 5, and the number of internal nodes of degree 2 is 10. The...
GATE CSE 2006
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A scheme for storing binary trees in an array X is as follows. Indexing of X starts at 1 instead of 0. the root is store...
GATE CSE 2006
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The numbers 1, 2, ........, n are inserted in a binary search tree in some order. In the resulting tree, the right subtr...
GATE CSE 2005
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The following numbers are inserted into an empty binary search tree in the given order: 10, 1, 3, 5, 15, 12, 16. What is...
GATE CSE 2004
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Level order traversal of a rooted tree can be done by starting from the root and performing
GATE CSE 2004
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Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. ...
GATE CSE 2003
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Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stres...
GATE CSE 2000
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Which of the following statements is false?
GATE CSE 1998
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In the balanced binary tree in Fig. given below, how many nodes will become unbalanced when a node is inserted as a chil...
GATE CSE 1996
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Which of the following sequences denotes the post order traversal sequence of the tree of previous question?
GATE CSE 1996
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A binary tree T has n leaf nodes. The number of nodes of degree 2 in T is:
GATE CSE 1995
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If the no of leaves in a tree is not a power of 2,then the tree is not a binary tree.
GATE CSE 1987
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It is possible to construct a binary tree uniquely whose pre-order and post-order traversals are given.
GATE CSE 1987
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Marks 2
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Consider the following statements. S1 : The sequence of procedure calls corresponds to a preorder traversal of the acti...
GATE CSE 2021 Set 1
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A binary search tree T contains n distinct elements. What is the time complexity of picking an element in T that is smal...
GATE CSE 2021 Set 1
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Consider the array representation of a binary min-heap containing 1023 elements. The minimum number of comparisons requi...
GATE CSE 2020
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In a balanced binary search tree with n elements, what is the worst case time complexity of reporting all elements in ra...
GATE CSE 2020
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Let T be a full binary tree with 8 leaves. (A full binary tree has every level full). Suppose two leaves a and b of T ar...
GATE CSE 2019
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The number of ways in which the numbers $$1, 2, 3, 4, 5, 6, 7$$ can be inserted in an empty binary search tree, such tha...
GATE CSE 2016 Set 2
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Consider the following $$New-order$$ strategy for traversing a binary tree: $$\,\,\,\,\,\,\, \bullet \,\,\,\,\,$$ Visit...
GATE CSE 2016 Set 2
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Suppose we have a balanced binary search tree T holding n numbers. We are given two numbers L and H and wish to sum up a...
GATE CSE 2014 Set 3
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Consider the pseudocode given below. The function Dosomething () takes as argument a pointer to the root of an arbitrary...
GATE CSE 2014 Set 3
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Consider the expression tree shown. Each leaf represents a numerical value, which can either be 0 or 1. Over all possibl...
GATE CSE 2014 Set 2
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Consider the C function given below. Assume that the array listA contains n (> 0) elements, sored in ascending order....
GATE CSE 2014 Set 3
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The height of a tree is defined as the number of edges on the longest path in the tree. The function shown in the pseudo...
GATE CSE 2012
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We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate th...
GATE CSE 2011
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What is the maximum height of any AVL-tree with 7 nodes? Assume that the height of a tree with a single node is 0.
GATE CSE 2009
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You are given the postorder traversal, P, of a binary search tree on the n elements 1, 2,..........., n. You have to det...
GATE CSE 2008
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How many distinct BSTs can be constructed with 3 distinct keys?
GATE CSE 2008
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A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys. I. 81, 537, 1...
GATE CSE 2008
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A Binary Search Tree (BST) stores values in the range 37 to 573. Consider the following sequence of keys. I. 81, 537, ...
GATE CSE 2008
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The following three are known to be the preorder, inorder and postorder sequences of a binary tree. But it is not known ...
GATE CSE 2008
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A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes ...
GATE CSE 2007
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When searching for the key value 60 in a binary search tree, nodes containing the key values 10, 20, 40, 50, 70 80, 90 a...
GATE CSE 2007
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Consider the following C program segment where CellNode represents a node in a binary tree: struct CellNode { st...
GATE CSE 2007
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The inorder and preorder traversal of a binary tree are d b e a f c g and a b d e c f g, respectively. The postorder tra...
GATE CSE 2007
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An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array ...
GATE CSE 2006
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An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array ...
GATE CSE 2006
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An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array ...
GATE CSE 2006
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Which of the following sequences of array elements forms a heap?
GATE CSE 2006
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Suppose that we have numbers between 1 and 100 in a binary search tree and want to search for the number 55. Which of th...
GATE CSE 2006
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A Priority-Queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is gi...
GATE CSE 2005
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A binary search tree contains the numbers 1, 2, 3, 4, 5, 6, 7, 8. When the tree is traversed in pre-order and the values...
GATE CSE 2005
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How many distinct binary search trees can be created out of 4 distinct keys?
GATE CSE 2005
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In a binary tree, for every node the difference between the number of nodes in the left and right subtrees is at most 2....
GATE CSE 2005
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In a complete k-ary tree, every internal node has exactly k children. The number of leaves in such a tree with n interna...
GATE CSE 2005
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Postorder traversal of a given binary search tree T produces the following sequence of keys 10, 9, 23, 22, 27, 25, 15, ...
GATE CSE 2005
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A program takes as input a balanced binary search tree with n leaf nodes and computes the value of a function g(x) for e...
GATE CSE 2004
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Consider the label sequences obtained by the following pairs of traversals on a labeled binary tree. Which of these pair...
GATE CSE 2004
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Consider the following C program segment struct CellNode{ struct CellNode *leftChild; int element; struc...
GATE CSE 2004
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The number of leaf nodes in a rooted tree of n nodes, with each node having 0 or 3 children is:
GATE CSE 2002
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Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal. Respecti...
GATE CSE 2000
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A complete n-ary tree is one in which every node has O or n sons. If x is the number of internal nodes of a complete n-a...
GATE CSE 1998
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A binary search tree contains the value 1, 2, 3, 4, 5, 6, 7, 8. The tree is traversed in pre-order and the values are pr...
GATE CSE 1997
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A binary search tree is used to locate the number 43. Which of the following probe sequences are not possible?
GATE CSE 1996
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A binary search tree is generated by inserting in order the following integers: 50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60...
GATE CSE 1996
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If the binary tree in figure is traversed in inorder, then the order in which the nodes will be visited is ______ ...
GATE CSE 1991
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