Question

Meet is an operation between zero-one matrices and uses Boolean products (C. Join is an operation between zero-one matrices and uses Boolean products d. Join is an operation between zero-one matrices and uses conjunctions 29. Given set S (-2, -1, 0, 1, 2), R is a relation on S. i. R ( (x, y)| x-y 1} Write R as a set of ordered pairs. (Use roster method to write R as a set of tuples) 3pts ill. and matrix representation of R. 3pts pOwoll r fo rlasovilenb180 s Terd OS i. Draw the digraph representation of R. 3pts bre e wo RUAlD Write Yes or No in the blank after evaluating if R has the following properties: (1pt ea.) 4pts iv. Is R reflexive? 30. Use the following algorithm to answer the questions. Line numbering is given to the left. vii. Is R transitive? vi. antisymmetric? v. symmetric? procedure Linear search (x: integer, a, a,- an: distinct integers ) 1. i1 while (isn and x an) i : i1 if is n then Location := i else Location :e0 oi return Location Given the linear search algorithm above, in the worst case (integer x is not found), evaluate the number of comparisons the algorithm performs in terms of the input size, n. How many times is the comparison is n in line 3 performed? (including the final comparison to terminate the while loop) How many times is the comparison x a, in line 3 performed? llof2pts iii. How many times is the comparison i s n in line 5 performed? What is the total number of comparisons? Use Big-O notation to express the time complexity of the algorithm: procedure binary search(x: integer, di, a,-an: increasing integers) i 1 // is the Left endpoint of the search intervalL j : n //j is the right endpoint of the search interval while i<) 2. 3. 4. 5. 6. 7. i. 2pts ii. 2pts 2pts 2pts iv. v. 1 2. 3. 4. I14)/2) 5. m= if xs a, then i m+1 6. else i m 7. 8. if x a then Location 1 else location e 9. 10. return Location 31. Which algorithm, regardless of efficiency, can be used to find the index of integer x within sorted list of integers? (linear search, binary search, or both can be used) 32. Which is more efficient given a sorted list of integers? (Linear search /binary search both have the same time complexity) Page 6 of 6 16 13 12 15 32 27

Answer 1

29.

antisymmetric: Yes

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