GATE CS question library

The following program fragment is written in a programming language that allows global variables and does not allow nested declarations of functions. global int i=100, j=5; void P(x) { int i=10; print(x+10); i=200; j=20; print (x); } main() {P(i+j);} If the programming language uses static scoping and call by need parameter passing mechanism, the values …

The following resolution rule is used in logic programming. Derive clause $(P \vee Q)$ from clauses $(P\vee R),(Q \vee ¬R)$ Which of the following statements related to this rule is FALSE?

Let $G= (V,E)$ be a directed graph with $n$ vertices. A path from $v_i$ to $v_j$ in $G$ is a sequence of vertices ($v_{i},v_{i+1}, \dots , v_j$) such that $(v_k, v_{k+1}) \in E$ for all $k$ in $i$ through $j-1$. A simple path is a path in which no vertex appears more than once. Let $A$ be an $n \times n$ array initialized as follows: …

The following are the starting and ending times of activities $A, B, C, D, E, F, G$ and $H$ respectively in chronological order: $“a_s \: b_s \: c_s \: a_e \: d_s \: c_e \: e_s \: f_s \: b_e \: d_e \: g_s \: e_e \: f_e \: h_s \: g_e \: h_e”$. Here, $x_s$ denotes the starting time and $x_e$ denotes the ending time of activity X. We need to schedule …

What is the weight of a minimum spanning tree of the following graph?

Let $G =(V,E)$ be an undirected graph with a subgraph $G_1 = (V_1, E_1)$. Weights are assigned to edges of $G$ as follows. $$w(e) = \begin{cases} 0 \text{, if } e \in E_1 \\1 \text{, otherwise} \end{cases}$$ A single-source shortest path algorithm is executed on the weighted graph $(V,E,w)$ with an arbitrary vertex $v_1$ of $V_1$ as the source. …

Consider the following $2-3-4$ tree (i.e., B-tree with a minimum degree of two) in which each data item is a letter. The usual alphabetical ordering of letters is used in constructing the tree. What is the result of inserting $G$ in the above tree?

Let S be a stack of size $n \geq1$. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform $n$ pop operations. Assume that Push and Pop operations take $X$ seconds each, and $Y$ seconds elapse between the end of one such stack operation and the start of the next operation. For $m \geq1$, define the …

A data structure is required for storing a set of integers such that each of the following operations can be done in $O(\log n)$ time, where $n$ is the number of elements in the set. Deletion of the smallest element Insertion of an element if it is not already present in the set Which of the following data structures can be used for this purpose?

In a permutation $a_1 ... a_n$, of n distinct integers, an inversion is a pair $(a_i, a_j)$ such that $i < j$ and $a_i > a_j$. If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of $1. . . n$?

A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by

Consider the syntax directed definition shown below. …

Consider the translation scheme shown below. $S \rightarrow T\;R$ $R \rightarrow + T \{\text{print}(‘+’);\} R\mid \varepsilon$ $T \rightarrow$ num $\{\text{print}$(num.val)$;\}$ Here num is a token that represents an integer and num.val represents the corresponding integer value. For an input string ‘$9 + 5 + 2$’, this translation scheme will …

Consider the grammar shown below. $S \rightarrow C \ C$ $C \rightarrow c \ C \mid d$ This grammar is

Consider the NFA $M$ shown below. Let the language accepted by $M$ be $L$. Let $L_1$ be the language accepted by the NFA $M_1$ obtained by changing the accepting state of $M$ to a non-accepting state and by changing the non-accepting states of $M$ to accepting states. Which of the following statements is true?

A single tape Turing Machine $M$ has two states $q0$ and $q1$, of which $q0$ is the starting state. The tape alphabet of $M$ is $\{0, 1, B\}$ and its input alphabet is $\{0, 1\}$. The symbol $B$ is the blank symbol used to indicate end of an input string. The transition function of $M$ is described in the following table. …

Let $G=\left(\left\{S\right\}, \left\{a,b\right\},R,S\right)$ be a context free grammar where the rule set R is $S \to a S b \mid S S \mid \epsilon$ Which of the following statements is true?

Consider the following deterministic finite state automaton $M$. Let $S$ denote the set of seven bit binary strings in which the first, the fourth, and the last bits are $1$. The number of strings in $S$ that are accepted by $M$ is

Consider the following assembly language program for a hypothetical processor $A, B,$ and $C$ are $8-$bit registers. The meanings of various instructions are shown as comments. …

Consider the ALU shown below. If the operands are in $2’s$ complement representation, which of the following operations can be performed by suitably setting the control lines $K$ and $C_0$ only (+ and – denote addition and subtraction respectively)?