File of Discrete Structure of I year II semester.
| Question No. | Question |
|---|---|
| Ques 1 | Write a Program to create a SET A and determine the cardinality of SET for an input array of elements (repetition allowed) and perform the following operations on the SET: a) ismember (a, A): checkwhether an element belongs to set or not and return value as true/false. b) powerset(A): list all the elements of power set of A. |
| Ques 2 | Create a class SET andtake two sets as input from user to perform following SET Operations: a) Subset: Check whether one set is a subset of other or not. b) Unionand Intersection of two Sets. c) Complement: Assume Universal Set as per the input elements from the user. d) Set Differenceand Symmetric Difference between two SETS. e) Cartesian Productof Sets. |
| Ques 3 | Create a class RELATION, use Matrix notation to represent a relation. Include functions to check if a relation is reflexive, Symmetric, Anti-symmetric and Transitive. Write a Programto use this class. |
| Ques 4 | Use the functions defined in Ques 3 to find check whether the given relation is: a) Equivalent, or b) Partial Order relation, or c) None |
| Ques 5 | Write a Program to generate the Fibonacci Series using recursion. |
| Ques 6 | Write a Program to implement Tower of Hanoi using recursion. |
| Ques 7 | Write a Program to implement binary search using recursion. |
| Ques 8 | Write a Program to implement Bubble Sort. Find the number of comparisons during each pass and display the intermediate result.Use the observed values to plot a graph to analyse the complexity of algorithm. |
| Ques 9 | Write a Program to implement Insertion Sort. Find the number of comparisons during each pass and display the intermediate result. Use the observedvalues to plot a graphto analyse the complexity of algorithm. |
| Ques 10 | Write a Program that generates all the permutations of a given set of digits, with or without repetition. (For example, if the given set is {1,2}, the permutations are 12 and 21). (One method is given in Liu) |
| Ques 11 | Write a Program to calculate Permutation and Combination for an input value nand r using recursive formula of nCr and nPr. |
| Ques 12 | For any number n, write a program to list all the solutions of the equation x1 + x2 + x3 + ...+ xn= C, where C is a constant (C<=10) and x1, x2,x3,...,xn are non-negative integers using brute force strategy. |
| Ques 13 | Write a Programto accept the truth values of variables x and y, and print the truth table of the following logical operations: a) Conjunction f) Exclusive NOR b) Disjunction g) Negation c) Exclusive OR h) NAND d) Conditional i) NOR e) Bi-conditional |
| Ques 14 | Write a program to accept an input nfrom the user and graphically represent the valuesof T(n) where n varies from 0 to n for the recurrence relations. For e.g. T(n) = T(n-1) + n, T(0) = 1, T(n) = T(n-1) + n^2, T(0) =1, T(n) = 2*T(n)/2 + n, T(1)=1. |
| Ques 15 | Write a Program to store a function (polynomial/exponential), and then evaluate the polynomial. (For example store f(x) = 4n^3+ 2n + 9 in an array and for a given value of n, say n = 5, evaluate (i.e. compute the value of f(5)). |
| Ques 16 | Write a Program to represent Graphs using the Adjacency Matrices and check if it is a complete graph. |
| Ques 17 | Write a Program to accept a directed graph G and compute the in-degree and out-degree of each vertex. |
| Ques 18 | Given a graph G, Write a Program to find the number of paths of length nbetween the source and destination entered by the user. |
| Ques 19 | Given an adjacency matrix of a graph, write a program to check whether a given set of vertices {v1, v2, v3....., vk} forms an Euler path/ Euler Circuit (for circuit assume vk=v1). |
| Ques 20 | Given a full m-ary tree with iinternal vertices, Write a Program to find the number of leaf nodes. |
It also contain some of the random practice questions.