Question

Question: State if an algorithm (satisfying the formal definition of an algorithm) which is guaranteed to find a solution exists or not for each of the following problems by filling the blanks with “Yes” (an algorithm guaranteed to find a solution exists) or “No” (an algorithm guaranteed to find a solution does not exist).

1. Finding the average height of a person in a group, given the height of each person in the group

2. Finding all factors of a finite integer

3. Finding if a triangle is scalene or not, when the coordinates of its vertices are given

4. Finding a path from the given start location to the given goal location in a finite maze (the number of junctions is finite and the length of path connecting any two junctions is also finite) that changes unpredictably at any time

Answer 1

SOLUTION:

Yes - an algorithm guaranteed to find a solution exists

No - an algorithm guaranteed to find a solution does not exist

1. Finding the average height of a person in a group, given the height of each person in the group

            YES

            Average height = Sum of all heights / number of people in the group

            Using the above formula in an algorithm, the solution to the question exists

2. Finding all factors of a finite integer

            YES

            Using the below algorithm, the solution to the question exists

Loop from i=1 to i<=n            //n is the finite integer

        if ( n modulus i = =0)

            then “i is factor of n”

3. Finding if a triangle is scalene or not, when the coordinates of its vertices are given

YES

            Using the below algorithm, the solution to the question exists

                        //ABC is the triangle whose coordinates of vertices are given

Calculate distance between AB

                        Calculate distance between BC

                        Calculate distance between CA

                                    if( AB != BC and BC != CA)

                                                then “Given triangle is Scalene triangle”

4. Finding a path from the given start location to the given goal location in a finite maze (the number of junctions is finite and the length of path connecting any two junctions is also finite) that changes unpredictably at any time

            NO

            There exists no algorithm which can guarantee a solution to the question, because the maze changes unpredictably at any time.

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