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278 Arrays Chapter 7 As the turtle moves with the pen down, set the appropriate elements of array floorto 1s. When the 6 command (print) is given, wherever there is a 1in the array, display an asterisk or another character. Wherever there is a zero, display a blank. Write a program to implement the turtle graphics capabilities we have discussed. Write several turtle graphics programs to draw interesting shapes. Add commands to increase the power of your turtle graphics language. SPECIAL SECTION: RECURSION EXERCISES 7.7 (Palindromes) A palindrome is a string that is spelled the same forward and backward. Some examples of palindromes are radar, able was i ere i saw elba and, if blanks are ignored, a man a plan a canal panama. Write a recursive method testPalindrome that returns true if the string stored in the array is a palindrome and false otherwise. The method should ignore spaces and punctuation in the string. 7.8 (Linear Search) Modify Fig. 7.11 to use recursive method LinearSearch to perform a linear search of the array. The method should receive an integer array and the size of the array as arguments. If the search key is found, return the array subscript; otherwise, return 1. 7.9 (Binary Search) Modify the program in Fig. 7.12 to use a recursive method Binary- Search to perform the binary search of the array. The method should receive an integer array and the starting and ending subscript as arguments. If the search key is found, return the array subscript; otherwise, return 1. 7.10 (Quicksort) In this chapter, we discussed the sorting technique bubble sort. We now present the recursive sorting technique called Quicksort. The basic algorithm for a single-subscripted array of values is as follows: a) Partitioning Step. Take the first element of the unsorted array and determine its final location in the sorted array (i.e., all values to the left of the element in the array are less than the element, and all values to the right of the element in the array are greater than the element). We now have one element in its proper location and two unsorted subarrays. b) Recursive Step. Perform step 1 on each unsorted subarray. Each time Step 1 is performed on a subarray, another element is placed in its final location of the sorted array, and two unsorted subarrays are created. When a subarray consists of one element, it must be sorted; therefore, that element is in its final location. The basic algorithm seems simple, but how do we determine the final position of the first element of each subarray? Consider the following set of values (partitioning element in bold it will be placed in its final location in the sorted array): 37 2 6 4 89 8 10 12 68 45 a) Starting from the rightmost element of the array, compare each element to 37 until an element less than 37 is found, then swap 37 and that element. The first element less than 37 is 12, so 37 and 12 are swapped. The new array is 12 2 6 4 89 8 10 37 68 45 Element 12 is italicized to indicate that it was just swapped with 37. b) Starting from the left of the array, but beginning with the element after 12, compare each element to 37 until an element greater than 37 is found, then swap 37 and that element. The first element greater than 37 is 89, so 37 and 89 are swapped. The new array is 12 2 6 4 37 8 10 89 68 45
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Chapter 7 Arrays 277 of the salespeople earned salaries in each of the following ranges (assume that each salesperson s sal ary is truncated to an integer amount): a) $200 $299 b) $300 $399 c) $400 $499 d) $500 $599 e) $600 $699 f) $700 $799 g) $800 $899 h) $900 $999 i) $1000 and over 7.5 Use a single-subscripted array to solve the following problem: Read in 20 numbers, each of which is between 10 and 100, inclusive. As each number is read, print it only if it is not a duplicate of a number already read. Provide for the worst case (in which all 20 numbers are different). Use the smallest possible array to solve this problem. 7.6 (Turtle Graphics) The Logo language made famous the concept of turtle graphics. Imagine a mechanical turtle that walks around the room under the control of a program. The turtle holds a pen in one of two positions, up or down. While the pen is down, the turtle traces out shapes as it moves; while the pen is up, the turtle moves about without writing anything. In this problem, you will simulate the operation of the turtle and create a computerized sketchpad. Use a 20-by-20 array floor, which is initialized to zeros. Read commands from an array that contains them. At all times, keep track of the current position of the turtle and whether the pen is up or down. Assume that the turtle always starts at position 0,0 of the floor with its pen up. The set of turtle commands your program must process are as follows: Command Meaning 1 Pen up 2 Pen down 3 Turn right 4 Turn left 5,10 Move forward 10 spaces (or a number other than 10) 6 Print the 20-by-20 array 9 End of data (sentinel) Suppose that the turtle is somewhere near the center of the floor. The following program would draw and print a 12-by-12 square, leaving the pen in the up position: 2 5,12 3 5,12 3 5,12 3 5,12 1 6 9
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276 Arrays Chapter 7 g) arrays are maintained as arrays of arrays. h) A variable must be declared and initialized in the same statement, or a syntax error will occur. i) C# provides the repetition structure for iterating through values in data structures, such as arrays. j) When an invalid array reference is made, an is generated. 7.2 State whether each of the following is true or false. If false, explain why. a) An array can store many different types of values at the same time. b) An array subscript normally should be of data type float. c) An individual array element that is passed to a method and modified in that method will contain the modified value when the called method completes execution. d) The maximum number of comparisons needed for the binary search of any sorted array is the exponent of the first power of 2 greater than the number of elements in the array. e) There are two types of multiple-subscripted arrays square and jagged. f) A const variable must be declared and initialized in the same statement, or a syntax er ror will occur. g) After each comparison, the binary search algorithm eliminates from consideration one third of the elements in the portion of the array that is being searched. h) To determine the number of elements in an array, we can use the NumberOfElements property. i) The linear search method works well for small or unsorted arrays. j) In an m-by-n array, the m stands for the number of columns and the n stands for the num ber of rows. ANSWERS TO SELF-REVIEW EXERCISES 7.1 a) arrays. b) name, type. c) subscript, index or position number. d) sorting. e) searching. f) multiple-subscripted. g.) Jagged. h) const. i) foreach. j) IndexOutofRangeException. 7.2 a) False. An array can store only values of the same type. b) False. An array subscript must be an integer or an integer expression. c) False. For individual primitive-data-type elements of an array, they are passed by value. If a reference to an array element is passed, then modifications to that array element are reflected in the original. An individual element of a reference type is passed to a method by reference. d) True. e) False. The two different types are called rectangular and jagged. f) True. g) False. After each comparison, the binary search algorithm eliminates from consideration half the elements in the portion of the array that is being searched. h) False. To determine the number of elements in an array, we can use the Length property. i) True. j) False. In an m-by-n array, the m stands for the number of rows and the n stands for the number of columns. EXERCISES 7.3 Write statements to accomplish each of the following tasks: a) Display the value of the seventh element of character array f. b) Initialize each of the five elements of single-subscripted integer array gto 8. c) Total the elements of floating-point array c of 100 elements. d) Copy 11-element array ainto the first portion of array bcontaining 34 elements. e) Determine the smallest and largest values contained in 99-element floating-point array w. 7.4 Use a single-subscripted array to solve the following problem: A company pays its salespeople on a commission basis. The salespeople receive $200 per week, plus 9% of their gross sales for that week. For example, a salesperson who grosses $5000 in sales in a week receives $200 plus 9% of $5000, or a total of $650. Write a program (using an array of counters) that determines how many
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Chapter 7 Arrays 275 For rectangular arrays, the repetition of the foreach structure begins with the element whose indices are all zero, then iterates through all possible combinations of indices, incrementing the rightmost index first. When the rightmost index reaches its upper bound, it is reset to zero, and the index to the left of it is incremented by 1. TERMINOLOGY [], subscript operator multiple-subscripted array array allocated with new named constant array automatically initialized to zeros nested forloop array bounds new operator array declaration null array of arrays (jagged array) off-by-one error bar chart one-dimensional array binary search algorithm partition brute force partitioning step bubble sort pass of a bubble sort column passing array to method const passing array element to method constant variable position number declare an array read-only variable dice-rolling program rectangular array double-subscripted array search key element searching exception single-subscripted array foreach structure sinking sort graph information size of an array histogram sorting ignoring element zero square brackets, [] initializer list subarray initializing double-subscripted arrays sub-initializer list in declarations subscript innermost set of square brackets swap invalid array reference table jagged array table element key value TextBox length of an array walk past end of an array linear search zero-based counting lvalue ( left value ) zeroth element m-by-n array SELF-REVIEW EXERCISES 7.1 Fill in the blanks in each of the following statements: a) Lists and tables of values can be stored in . b) The elements of an array are related by the fact that they have the same and . c) The number that refers to a particular element of an array is called its . d) The process of placing the elements of an array in order is called the array. e) Determining if an array contains a certain key value is called the array. f) Arrays that use two or more subscripts are referred to as arrays.
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