Chapter 7

State whether the following are true or false. If the answer is false, explain why. a. An array can store many different types of values. b. An array subscript should normally be of data type float. c. If there are fewer initializers in an initializer list than the number of elements in the array, the remaining elements are initialized to the last value in the initializer list. d. It is an error if an initializer list contains more initializers than there are elements in the array. e. An individual array element that is passed to a function and modified in that function will contain the modified value when the called function completes execution.

include ; b. arraySize = 10; // arraySize was declared const c. Assume that… # Find the error in each of the following program segments and correct the error: a. #include ; b. arraySize = 10; // arraySize was declared const c. Assume that int b[ 10 ] = { 0 }; for ( int i = 0; <= 10; i++ ) b[ i ] = 1; d. Assume that int a[ 2 ][ 2 ] = { { 1, 2 }, { 3, 4 } }; a[ 1, 1 ] = 5;

Determine whether each of the following is true or false. If false, explain why. a. To refer to a particular location or element within an array, we specify the name of the array and the value of the particular element. b. An array declaration reserves space for the array. c. To indicate that 100 locations should be reserved for integer array p, the programmer writes the declaration p[ 100 ]; d. A for statement must be used to initialize the elements of a 15- element array to zero. e. Nested for statements must be used to total the elements of a two- dimensional array.

Consider a 2-by-3 integer array t. a. Write a declaration for t. b. How many rows does t have? c. How many columns does t have? d. How many elements does t have? e. Write the names of all the elements in row 1 of t. f. Write the names of all the elements in column 2 of t. g. Write a single statement that sets the element of t in row 1 and column 2 to zero. h. Write a series of statements that initialize each element of t to zero. Do not use a loop. i. Write a nested for statement that initializes each element of t to zero. j. Write a statement that inputs the values for the elements of t from the terminal. k. Write a series of statements that determine and print the smallest value in array t. l. Write a statement that displays the elements in row 0 of t. m. Write a statement that totals the elements in column 3 of t. n. Write a series of statements that prints the array t in neat, tabular format. List the column subscripts as headings across the top and list the row subscripts at the left of each row.

(Bubble Sort) In the bubble sort algorithm, smaller values gradually "bubble" their way upward to the top of the array like air bubbles rising in water, while the larger values sink to the bottom. The bubble sort makes several passes through the array. On each pass, successive pairs of elements are compared. If a pair is in increasing order (or the values are identical), we leave the values as they are. If a pair is in decreasing order, their values are swapped in the array. Write a program that sorts an array of 10 integers using bubble sort.

Write a program that simulates the rolling of two dice. The program should use rand to roll the first die and should use rand again to roll the second die. The sum of the two values should then be calculated. [ Note: Each die can show an integer value from 1 to \(6,\) so the sum of the two values will vary from 2 to \(12,\) with 7 being the most frequent sum and 2 and 12 being the least frequent sums.] Figure 7.32 shows the 36 possible combinations of the two dice. Your program should roll the two dice 36,000 times. Use a onedimensional array to tally the numbers of times each possible sum appears. Print the results in a tabular format. Also, determine if the totals are reasonable (i.e., there are six ways to roll a \(7,\) so approximately one-sixth of all the rolls should be 7 ).

( Airline Reservations System) A small airline has just purchased a computer for its new automated reservations system. You have been asked to program the new system. You are to write a program to assign seats on each flight of the airline's only plane (capacity: 10 seats). Your program should display the following menu of alternativesplease type 1 for "First Class" and Please type 2 for "Econony". If the person types 1 , your program should assign a seat in the first class section (seats \(1-5\) ). If the person types \(2,\) your program should assign a seat in the economy section (seats \(6-10\) ). Your program should print a boarding pass indicating the person's seat number and whether it is in the first class or economy section of the plane. Use a one-dimensional array to represent the seating chart of the plane. Initialize all the elements of the array to 0 to indicate that all seats are empty. As each seat is assigned, set the corresponding elements of the array to 1 to indicate that the seat is no longer available. Your program should, of course, never assign a seat that has already been assigned. When the first class section is full, your program should ask the person if it is acceptable to be placed in the economy section (and vice versa). If yes, then make the appropriate seat assignment. If no, then print the message -Next flight leaves in 3 hours".

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, each salesperson passes in a slip for each different 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, each salesperson passes in between 0 and 5 sales slips per day. Assume that the information from all of the slips for last month is available. Write a program that will read all this information for last month's sales and summarize the total sales by salesperson by product. All totals should be stored in the two-dimensional array sales. After processing all the information for last month, print the results in tabular format with each of the columns representing a particular salesperson and each of the rows 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 printout should include these cross totals to the right of the totaled rows and to the bottom of the totaled columns.

When this process is complete, the array elements that are still set to one indicate that the subscript is a prime number. These subscripts can then be printed. Write a program that uses an array of 1000 elements to determine and print the prime numbers between 2 and \(999 .\) Ignore element 0 of the array. (Bucket Sort) A bucket sort begins with a one-dimensional array of positive integers to be sorted and a two-dimensional array of integers with rows subscripted from 0 to 9 and columns subscripted from 0 to \(n 1\), where \(n\) is the number of values in the array to be sorted. Each row of the twodimensional array is referred to as a bucket. Write a function bucketsort that takes an integer array and the array size as arguments and performs as follows: a. Place each value of the one-dimensional array into a row of the bucket array based on the value's ones digit. For example, 97 is placed in row 7,3 is placed in row 3 and 100 is placed in row \(0 .\) This is called a "distribution pass." b. Loop through the bucket array row by row, and copy the values back to the original array. This is called a "gathering pass." The new order of the preceding values in the one-dimensional array is 100,3 and \(97 .\) c. Repeat this process for each subsequent digit position (tens, hundreds, thousands, etc.). On the second pass, 100 is placed in row 0,3 is placed in row 0 (because 3 has no tens digit) and 97 is placed in row \(9 .\) After the gathering pass, the order of the values in the one-dimensional array is 100,3 and \(97 .\) On the third pass, 100 is placed in row 1,3 is placed in row zero and 97 is placed in row zero (after the 3 ). After the last gathering pass, the original array is now in sorted order. Note that the two-dimensional array of buckets is 10 times the size of the integer array being sorted. This sorting technique provides better performance than a insertion sort, but requires much more memory. The insertion sort requires space for only one additional element of data. This is an example of the spacetime trade-off: The bucket sort uses more memory than the insertion sort, but performs better. This version of the bucket sort requires copying all the data back to the original array on each pass. Another possibility is to create a second two-dimensional bucket array and repeatedly swap the data between the two bucket arrays.

(Selection Sort) A selection sort searches an array looking for the smallest element. Then, the smallest element is swapped with the first element of the array. The process is repeated for the subarray beginning with the second element of the array. Each pass of the array results in one element being placed in its proper location. This sort performs comparably to the insertion sortfor an array of \(n\) elements, \(n 1\) passes must be made, and for each subarray, \(n 1\) comparisons must be made to find the smallest value. When the subarray being processed contains one element, the array is sorted. Write recursive function selectionsort to perform this algorithm.