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$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline \textbf{Year}&\textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum} \\\hline\textbf{1 Mark Count}&4&2&2&0&2&3&1&1&1&0&1.7&4 \\\hline\textbf{2 Marks Count}&1&0&1&2&0&0&1&3&3&0&1.2&3 \\\hline\textbf{Total Marks}&6&2&4&4&2&3&3&7&7&\bf{2}&\bf{4.2}&\bf{7}\\\hline \end{array}}}$$

# Recent questions in DS

1 vote
1
​​​​​Let $H$ be a binary min-heap consisting of $n$ elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in $H$? $\Theta (1)$ $\Theta (\log n)$ $\Theta (n)$ $\Theta (n \log n)$
2
Consider a complete binary tree with $7$ nodes. Let $A$ denote the set of first $3$ elements obtained by performing Breadth-First Search $\text{(BFS)}$ starting from the root. Let $B$ denote the set of first $3$ elements obtained by performing Depth-First Search $\text{(DFS)}$ starting from the root. The value of $\mid A-B \mid$ is _____________
3
Let $P$ be an array containing $n$ integers. Let $t$ be the lowest upper bound on the number of comparisons of the array elements, required to find the minimum and maximum values in an arbitrary array of $n$ elements. Which one of the following choices is correct? $t>2n-2$ ... $t>n \text{ and } t\leq 3\lceil \frac{n}{2}\rceil$ $t>\lceil \log_2(n)\rceil \text{ and } t\leq n$
4
Consider the following statements. $S_1:\quad$ The sequence of procedure calls corresponds to a preorder traversal of the activation tree. $S_2:\quad$ The sequence of procedure returns corresponds to a postorder traversal of the activation tree. Which one of the following options is correct? $S_1$ is ... $S_2$ is true $S_1$ is true and $S_2$ is true $S_1$ is false and $S_2$ is false
5
A binary search tree $T$ contains $n$ distinct elements. What is the time complexity of picking an element in $T$ that is smaller than the maximum element in $T$? $\Theta(n\log n)$ $\Theta(n)$ $\Theta(\log n)$ $\Theta (1)$
6
Consider the following sequence of operations on an empty stack.$\textsf{push}(54);\textsf{push}(52);\textsf{pop}();\textsf{push}(55);\textsf{push}(62);\textsf{s}=\textsf{pop}();$ ... $\textsf{s+q}$ is ___________.
7
An $articulation$ $point$ in a connected graph is a vertex such that removing the vertex and its incident edges disconnects the graph into two or more connected components. Let $T$ be a $\text{DFS}$ tree obtained by doing $\text{DFS}$ in a connected undirected graph $G$. Which of the following ... and $y$ is a descendent of $u$ in $T$, then all paths from $x$ to $y$ in $G$ must pass through $u$.
8
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 and $L$ be the number of leaves in a complete $n$-ary tree. If $L=41$, and $I=10$, what is the value of $n$? $3$ $4$ $5$ $6$
9
In a binary max heap containing $n$ numbers, the smallest element can be found in ______ $O(n)$ $O(\log _2 n)$ $O(1)$ $O(\log_2 \log_2 n)$
10
Which of the following statements are true? Minimax search is breadth-first; it processes all the nodes at a level before moving to a node in next level. The effectiveness of the alpha-beta pruning is highly dependent on the order in which the states are examined The alpha-beta search algorithms computes the same ... and $(c)$ only $(a)$ and $(d)$ only $(b)$ and $(c)$ only $(c)$ and $(d)$ only
11
Match $\text{List I}$ with $\text{List II}$ Let $R_1=\{(1,1), (2,2), (3,3)\}$ and $R_2=\{(1,1), (1,2), (1,3), (1,4)\}$ ... answer from the options given below: $A-I, B-II, C-IV, D-III$ $A-I, B-IV, C-III, D-II$ $A-I, B-III, C-II, D-IV$ $A-I, B-IV, C-II, D-III$
12
A hash table with $10$ buckets with one slot per bucket is depicted. The symbols, $S1$ to $S7$ are initially emerged using a hashing function with linear probing. Maximum number of comparisons needed in searching an item that is not present is $6$ $5$ $4$ $3$
13
A full binary tree with $n$ non-leaf nodes contains $\log_ 2 n$ nodes $n+1$ nodes $2n$ nodes $2n+1$ nodes
14
We have a binary heap on $n$ elements and wish to insert $n$ more elements (not necessarily one after another) into this heap. Total time required for this is $\Theta (\log n)$ $\Theta (n)$ $\Theta (n \log n)$ $\Theta (n^{2})$
15
You are given the postorder traversal, $P$, of a binary search tree on the $n$ elements $1,2,\dots,n.$ You have to determine the unique binary search tree that has $P$ as its postorder traversal. What is the time complexity of the most efficient algorithm for doing this? $\Theta(\log n)$ $\Theta(n)$ $\Theta(n \log n)$ None of the above, as the tree cannot be uniquely determined.
16
Consider the process of inserting an element into a $Max\ Heap$, where the $Max\ Heap$ is represented by an $array$. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of $comparisons$ performed is $\Theta(\log _{2}n)$ $\Theta(n\log _{2} \log_2 n)$ $\Theta (n)$ $\Theta(n\log _{2}n)$
17
In a circularly linked list organization, insertion of a record involves the modification of no pointer $1$ pointer $2$ pointers $3$ pointers
The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number number of nodes in a binary tree of height $h$ is $2^{h}$ $2^{h-1} – 1$ $2^{h+1} – 1$ $2^{h+1}$