Problem 20
(Total Sales) Use a two-dimensional array to solve the following problem: A company has four salespeople \((1 \text { to } 4)\) who sell five different products \((1 \text { to } 5) .\) Once a day, cach salesperson passes in a slip for each type of product sold. Each slip contains the following: a) The salesperson number b) The product number c) The total dollar value of that product sold that day Thus, cach salesperson passes in between 0 and 5 sales slips per day. Assume that the information from all the slips for last month is available. Write an application that will read all this information for last month's sales and summarize the total sales by salesperson and by product. All totals should be stored in the two-dimensional array sales. After processing all the information for last month, display the results in tabular format, with each column representing a particular salesperson and each row representing a particular product. Cross-total each row to get the total sales of each product for last month. Cross-total each column to get the total sales by salesperson for last month. Your tabular output should include these cross- totals to the right of the totaled rows and to the bottom of the totaled columns.
Problem 27
\( (\text { Sieve of Eratosthenes) } \text { A prime number is any integer greater than } 1\) that is evenly divisible only by itself and \(1 .\) The Sieve of Eratosthenes is a method of finding prime numbers. It operates as follows: a) Create a primitive type boolean array with all elements initialized to true. Array elements with prime indices will remain true. All other array elements will eventually be set to false. b) Starting with array index \(2,\) determine whether a given element is true. If so, loop through the remainder of the array and set to false every element whose index is a multiple of the index for the element with value true. Then continue the process with the next element with value true. For array index \(2,\) all elements beyond element 2 in the array that have indices which are multiples of 2 (indices \(4,6,8,10,\) etc.) will be set to false; for array index 3 , all elements beyond element 3 in the array that have indices which are multiples of 3 (indices 6,9,12,15 , etc.) will be set to \(f\) alse; and so on. When this process completes, the array elements that are still true indicate that the index is a prime number. These indices can be displayed. Write an application that uses an array of 1000 elements to determine and display the prime numbers between 2 and \(999 .\) Ignore array elements 0 and 1.
Problem 29
\(\quad\) (Fibonacci Series) The Fibonacci series \(0,1,1,2,3,5,8,13,21, \dots\) begins with the terms 0 and 1 and has the property that cach succeeding term is the sum of the two preceding terms. a) Write a method fibonacci ( \(n\) ) that calculates the \(n\) th Fibonacci number. Incorporate this method into an application that enables the user to enter the value of \(n\). b) Determine the largest Fibonacci number that can be displayed on your system. c) Modify the application you wrote in part (a) to use double instead of int to calculate and return Fibonacci numbers, and use this modified application to repeat part (b).
