Problem 2
Explain the distinction between an ambiguity in a proposed algorithm and an ambiguity in the representation of an algorithm.
Problem 3
Describe how the use of primitives helps remove ambiguities in an algorithm's representation.
Problem 4
Select a subject with which you are familiar and design a pseudocode for giving directions in that subject. In particular, describe the primitives you would use and the syntax you would use to represent them. (If you are having trouble thinking of a subject, try sports, arts, or crafts.)
Problem 5
Does the following program represent an algorithm in the strict sense? Why or why not? Count \(=0\) white (Count != 5): Count \(=\) Count \(+2\)
Problem 6
In what sense do the following three steps not constitute an algorithm? Step 1: Draw a circle with center coordinates \((2,5)\) and radius 3 . Step 2: Draw a circle with center coordinates \((6,5)\) and radius \(5 .\) Step 3: Draw a line segment whose endpoints are at the intersections of the previous two circles.
Problem 7
Rewrite the following program segment using a repeat structure rather than a while structure. Be sure the new version prints the same values as the original. Initialization: num \(=0\) while \((\) num \(<50)\) : if (num is Odd) : print (num is Odd) \(=\) num \(+1\) num \(=\) num \(+1\)
Problem 8
Rewrite the following program segment using a while structure rather than a repeat structure. Be sure the new version prints the same values as the original. num \(=100\) repeat: print (num) num \(=\) num \(-1\) until \((\) num \(>0)\)
Problem 9
What must be done to translate a posttest loop expressed in the form repeat: (...) until (...) into an equivalent posttest loop expressed in the form do: (...) while (...)
Problem 10
Design an algorithm that, when given an arrangement of the digits \(0,1,2,3,4,5,6,7\), 8,9 , rearranges the digits so that the new arrangement represents the next larger value that can be represented by these digits (or reports that no such rearrangement exists if no rearrangement produces a larger value). Thus 5647382901 would produce 5647382910 .
Problem 11
Design an algorithm for finding all the factors of a positive integer. For example, in the case of the integer 12 , your algorithm should report the values \(1,2,3,4,6\), and 12 .
