Explain the Topological sorting with the help of an example. Also, explain the algorithm of finding strongly connected components in a directed Graph.
See Answer →Explain the divide and conquer approach of multiplying two large integers. Compute the time complexity of this approach. Also, explain the binary search algorithm and find its time complexity
See Answer →Explain the Merge procedure of the Merge Sort algorithm. Demonstrate the use of recursive Merge sort algorithm for sorting the following data of size 8: [19, 18, 16, 12, 11, 10, 9, 8]. Compute the complexity of Merge Sort algorithm.
See Answer →Assuming that data to be transmitted consists of only characters ‘a’ to ‘g’, design the Huffman code for the following frequencies of character data. Show all the steps of building a huffman tree. Also, show how a coded sequence using Huffman code can be decoded
What is an Optimisation Problem? Explain with the help of an example. When would you use a Greedy Approach to solve optimisation problem? Formulate the Task Scheduling Problem as an optimisation problem and write a greedy algorithm to solve this problem. Also, solve the following fractional Knapsack problem using greedy approach. Show all the steps.
Suppose there is a knapsack of capacity 20 Kg and the following 6 items are to packed in it. The weight and profit of the items are as under:
Select a subset of the items that maximises the profit while keeping the total weight below or equal to the given capacity.
See Answer →What are the uses of recurrence relations? Solve the following recurrence relations using the Master's method
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Write and explain the Bubble sort algorithm. Discuss its best and worst-case time complexity.
See Answer →Write and explain the Left to Right binary exponentiation algorithm. Demonstrate the use of this algorithm to compute the value of 32 (Show the 29 steps of computation). Explain the worst-case complexity of this algorithm.
See Answer →What are asymptotic bounds for analysis of efficiency of algorithms? Why are asymptotic bounds used? What are their shortcomings? Explain the Big O and Big notation with the help of a diagram. Find the Big O-notation and -notation for the function:
Write an algorithm to multiply two square matrices of order n*n. Also explain the time complexity of this algorithm.
See Answer →Differentiate between Cubic-time and Factorial-time algorithms. Give example of one algorithm each for these two running times.
See Answer →Design and develop an efficient algorithm to find the list of prime numbers in the range 501 to 2000. What is the complexity of this algorithm?
See Answer →बिंदु (2,-4,13) पर शांकवज के स्पर्श तल का समीकरण ज्ञात कीजिए। स्पर्श तल को ज्यामितीय रूप से दर्शाइए।
शांकवज को पहचानिए तथा आरेखित कीजिए। समतलों y = 0 और z = 0 द्वारा इसके परिच्छेदों का वर्णन कीजिए।
बिंदुओं (1,-1,6) और (4,3,2) को मिलाने वाले रेखा-खण्ड का रेखा प्रक्षेप ज्ञात कीजिए।
समीकरण को रूपांतरित कीजिए, यदि मूलबिंदु को स्थिर रखा 2 जाए और अक्षों को इस प्रकार घुमाया जाए कि नए अक्षों के दिक-अनुपात 1,-3,0; 3, 1, 0, 0, 0,1 हो।
जांच कीजिए कि निम्नलिखित शांकवों में से कौनसे शांकवज केंद्रीय हैं और कौनसे अकेंद्रीय हैं। यह भी पता कीजिए कि जो केंद्रीय शांकवज हैं उनमें से किनके केंद्र मूलबिंदु पर है।
(i)
(ii)
(iii)
दिखाइए कि शांकवज केंद्रीय है। अतः इसका केंद्र निकालिए।
निर्देशांक अक्षों की दिशाओं को परिवर्तित किए बिना मूलबिंदु को (1,2,0) पर स्थानांतरित करके समीकरण को रूपांतरित कीजिए। यह नया समीकरण क्या निरुपित करता है? इसका स्थूल आरेख बनाइए।