INTERNATIONAL INSTITUTE OF MANAGEMENT, ENGINEERING & TECHNOLOGY, JAIPUR (IIMET) UNIT-1 Q.1 What is the significance of using notations in analysis of algorithm? Explain the various notations in brief? Q.2 How much time does insertion sorting take to sort n distinct Item in the best Care? State yours answer in asymptotic Notation? Q.3 Apply Counting sort an The Following 3, 5, 4, 1, 3, 4, 1, 4 Q4 write short note on: radix sort. Q.5 Explain O, & Q notations and find the constants For following Function F (n) =5n2 +3n-7 Q.6 what is master s the Orem? Explain with suitable example. Q.7 What is the divide and conquer method? Sort the following sequence using merge sort. 5, 2, 4, 7, 1, 3, 2, 6, Q.8 Use slrarren s matrix multiplication algorithm to compute the matrix Product of following matrices. Q.9 Explain the minimum spanning tree knapsack problem. Q.10 (a) what do you understand by space and time complexity of an algorithm. (b) Which notation can be used for policing a (i) (ii) (iii) Lower bound Upper bound Tight bound over an algorithm
UNIT-2 Q.1 X=(A, B, C, B,D, A,B) and Y=(B,D,C,A,B,A)find longest common subsequence (LCS) of the given sequences X and Y, Using dynamic programming approach. Q.2 Find the order of parenthesigation for the optimal chain multiplication. A 1 =30 * 35; A 2 =35 * 15; A 3 = 15 * 5 A 4 =5 * 10; A 5 = 10 * 20: A 4 = 20 * 25 Q.3 Write Short note on backtracking algorithm Q.4 Solve the traveling sales man problem having the following cost matrix using branch and bound technique. Q.5 How is stress s matrix multiplication better than simple matrix multination? Q.6 write short note on: i. Divide and conquer starting? ii. Lower Bound theory? Q.7 Sort the Following Sousing quick Sort Method. (a)15,56,62,2,9,16,21,17,23,3,10 (b)find the average and worst case time completing for quick sort using probe recurrence relation. Q.8 Solve the following recurrence using iteration method. T (n) =7 T (n/2) +cn 2 Q.9 Write short note on: (a)strasaen s matrix Multiplication. (b) Huffman code
Q.10 when the worst care of quick sort will occure, analysis the worst care and average case time complexity of quick sort using recurrence relation. Q.11 Explain binary search tree taking suitable example. Unit-3 Q.1 Describe fractional knapsack problem and algorithm for gelding optimal solution. Give an example to show that if we apply this algorithm to solve get optimal solution. Q.2 Write short note on: optimal merge pattern (Huffman code)? Q.3 Write prim s algorithm for finding minimum spanning tree for a graph. Q.4 What is a minimum spanning tree? Write an algorithm to build a minimum spanning tree for a given graph. Q.5 give the krurkal;s and prim s algorithm of minimum spanning tree. Q.6 find minimum spanning tree of the following graph using prim s algorithm. Q.7 Explain naïve method with some suitable example. Also give the algorithm for the same. Q.8 using Knuth- marrie-part algorithm find whether the pattern P=(10100111) Is in text T=(1001010100111) or not. Q.9 explain quadratic arraignment problem. Q.10 solves the following arraignment problem using branch and bound method for which cost matrix is given bellow. 1 2 3 4_ A 11 12 18 40 B 14 15 13 22 C 11 17 19 23 D 17 14 20 28
UNIT-4 Q.1 Explaining the following terms. (i)residual network (ii)augmenting Path (iii) Cuts of flow network Q.2 Find the order of parentherigation for the optimal chain multiplication. A 1 =10 * 5 A 3 =50 * 1 A 2 = 5 * 50 A 4 =1 * 20 Q.3 What is dynamic programming? What is principle of optimality? Explain knapsack problem using dynamic programming. Q.4 Write short note on knapsack and O/1 knapsack problem. Q.5 Write an algorithm for finding LCS. Q.6 writes principle of optimality? Explain knapsack problem using dynamic programming. Q.7 Describe matrix chain multiplication problem. Write algorithm for getting optimal parantherigation of matrix. Chain multiplications compute the complexity of this algorithm. Q.8 write ford Fulkerson algorithm and explain it. Q.9 Explain Monte Carlo algorithm? Q.10 Define flow network and solve the following network for maximum flow.
Unit-V Q.1 Define the terms P, NP, NP-complete, give suitable example of each? Q.2 proves that clique problem is NP-complete? Q.3 What is cook s theorem? Explain it? Q.4 Explain vertex cover and set cover problem prove that vertex cover is NP-complete? Q.5 Write short note on: Traveling sales man problem? Q.6 Pattern=COLAKOLA Find the good suffix function for the about pattern? Q.7 Write short note on: 1. Quadratic and biquadrate assignment problem 2. Bad character heuristic 3. Lower bound theory Q.8 gives the max-flow min cut theorem? Q.9 states the assignment problem and solves the following assignment problem using branch and bound for which cost matrix is given below