1. Starting Out with C++: Early Objects 5/e © 2006 Pearson Education. All Rights Reserved Starting Out with C++: Early Objects 5 th Edition Chapter 9 배열 탐색과 정렬 (Searching and Sorting Arrays)

2. Chapter 9 Starting Out with C++: Early Objects 5/e slide 2 © 2006 Pearson Education. All Rights Reserved 목 차목 차 9.1 탐색 알고리즘 소개 선형탐색 / 이진탐색 9.2 Demetris Leadership Center ( 사례연구 I) 9.3 정렬 알고리즘 소개 버블정렬 / 선택정렬 9.4 Demetris Leadership Center ( 사례연구 II) 9.5 벡터의 탐색과 정렬

3. Chapter 9 Starting Out with C++: Early Objects 5/e slide 3 © 2006 Pearson Education. All Rights Reserved 9.1 탐색 알고리즘 소개 탐색 (Search): 자료 집합 (array, vector, etc ) 에서 특정 자료가 있는 위치를 찾아내는 방법 대표적인 두 방법 : – 선형 탐색 (Linear search) : 순차 탐색 – 이진 탐색 (Binary search)

4. Chapter 9 Starting Out with C++: Early Objects 5/e slide 4 © 2006 Pearson Education. All Rights Reserved 선형 탐색 알고리즘 Set found to false Set position to –1 Set index to 0 While index < number of elts and found is false If list [index] is equal to search value found = true position = index End If Add 1 to index End While Return position

5. Chapter 9 Starting Out with C++: Early Objects 5/e slide 5 © 2006 Pearson Education. All Rights Reserved 선형 탐색 예 배열 numlist 값 11 찾기 : 선형 검색은 17, 23, 5, 그리고 11 을 조사한다. 값 7 찾기 : 선형 검색은 17, 23, 5, 11, 2, 29, 그리고 3 순으로 조사한다.(not found!) 17235112293

6. Chapter 9 Starting Out with C++: Early Objects 5/e slide 6 © 2006 Pearson Education. All Rights Reserved 선형 탐색의 효율성 장점 – 이해하기 쉽다.  구현하기 쉽다. – 배열 내의 자료가 어떠한 순서로 있어야 할 필요가 없다. 단점 – 비효율성 ( 속도가 느리다.): for array of N elements, examines N/2 elements on average for value in array, N elements for value not in array

7. Chapter 9 Starting Out with C++: Early Objects 5/e slide 7 © 2006 Pearson Education. All Rights Reserved 이진 탐색 알고리즘 1. 정렬된 배열을 세 영역으로 나눈다. – 가운데 요소 – 가운데 요소보다 작은 값의 요소들 – 가운데 요소보다 큰 값의 요소들 2. 가운데 요소가 찾는 값이면 탐색 완료. 찾는 값이 가운데 요소와 비교하여 작은 값이면 작은 값 요소들에서 단계 1 을 수행. 큰 값이면 큰 값 요소들에서 단계 1 수행. 3. 값을 찾거나 더 이상의 탐색 요소가 없을 때까지 단계 1 과 2 를 수행한다.

8. Chapter 9 Starting Out with C++: Early Objects 5/e slide 8 © 2006 Pearson Education. All Rights Reserved 이진 탐색 예 배열 numlist2 값 11 탐색 : 이진 탐색은 11 과 비교하고 탐색을 마친다. 값 7 탐색 : 이진 탐색은 11, 3, 5 와 비교한 다음 탐색을 마친다 23511172329

9. Chapter 9 Starting Out with C++: Early Objects 5/e slide 9 © 2006 Pearson Education. All Rights Reserved 이진탐색 프로그램 9-2 // This program performs a binary search on an integer array // whose elements are in ascending order. #include using namespace std; // Function prototype int binarySearch(int [], int, int); const int SIZE = 20; int main() { int tests[SIZE] = {101, 142, 147, 189, 199, 207, 222, 234, 289, 296, 310, 319, 388, 394, 417, 429, 447, 521, 536, 600}; int results, empID; cout << "Enter the employee ID you wish to search for: "; cin >> empID; results = binarySearch(tests, SIZE, empID); if (results == -1) cout << "That number does not exist in the array.\n"; else { cout << "That ID is found at element " << results; cout << " in the array.\n"; } return 0; }

10. Chapter 9 Starting Out with C++: Early Objects 5/e slide 10 © 2006 Pearson Education. All Rights Reserved //************************************************************ // binarySearch * // This function performs a binary search on an integer array * // with numElems elements whose values are stored in ascending * // order. The array is searched for the number stored in the * // value parameter. If the number is found, its array subscript * // returned. Otherwise, -1 is returned. * //************************************************************ int binarySearch(int array[], int numElems, int value) { int first = 0, // First array element last = numElems - 1, // Last array element middle, // Midpoint of search position = -1; // Position of search value bool found = false; // Flag while (!found && first <= last) { middle = (first + last) / 2; // Calculate midpoint if (array[middle] == value) // If value is found at mid { found = true; position = middle; } else if (array[middle] > value) // If value is in lower half last = middle - 1; else first = middle + 1; // If value is in upper half } return position; }

11. Chapter 9 Starting Out with C++: Early Objects 5/e slide 11 © 2006 Pearson Education. All Rights Reserved 이진 탐색의 효율성 장점 – 선형 탐색에 비해 효율적이다. ( N 개 요소의 배열에 대해, performs at most log 2 N comparisons) 단점 – 탐색 전에 정렬을 요구한다.

12. Chapter 9 Starting Out with C++: Early Objects 5/e slide 12 © 2006 Pearson Education. All Rights Reserved // This program manages an array of product structures. It allows // the user to enter a product number, then finds and displays // information on that product. #include using namespace std; struct ProdStruct { int id; // Product number string title, // Product title description; // Product description double price; // Product unit price int sold; // Units sold during the past 6 months // Default constructor for a ProdStruct structure ProdStruct() { price = id = sold = 0; title = description = ""; } // Constructor to set initial data values ProdStruct(int i, string t, string d, double p, int s) { id = i; title = t; description = d; price = p; sold = s; } }; 사례연구 I : 이진탐색 프로그램 9-3

13. Chapter 9 Starting Out with C++: Early Objects 5/e slide 13 © 2006 Pearson Education. All Rights Reserved // Function prototypes int getProdNum(int, int); int binarySearch(ProdStruct [], int, int); void displayProd(ProdStruct [], int);

14. Chapter 9 Starting Out with C++: Early Objects 5/e slide 14 © 2006 Pearson Education. All Rights Reserved int main() { const int NUM_PRODS = 9, // Number of products carried by DLC MIN_PROD_NUM = 914, // Minimum product number MAX_PROD_NUM = 922; // Maximum product number ProdStruct product[NUM_PRODS] = { ProdStruct(914, "Six Steps to Leadership", "Book", 12.95, 842), ProdStruct(915, "Six Steps to Leadership", "Audio cassette", 14.95, 416), ProdStruct(916, "The Road to Excellence", "Video", 18.95, 127), ProdStruct(917, "Seven Lessons of Quality", "Book", 16.95, 514), ProdStruct(918, "Seven Lessons of Quality", "Audio cassette", 21.95, 437), ProdStruct(919, "Seven Lessons of Quality", "Video", 31.95, 269), ProdStruct(920, "Teams are Made, Not Born", "Book", 14.95, 97), ProdStruct(921, "Leadership for the Future","Book", 14.95, 492), ProdStruct(922, "Leadership for the Future","Audio cassette", 16.95, 212) };

15. Chapter 9 Starting Out with C++: Early Objects 5/e slide 15 © 2006 Pearson Education. All Rights Reserved int prodNum, // Product number the user wants index; // Array subscript where that product's record is found char again; // Does user want to look up another record (y/n)? do { // Get the desired product number prodNum = getProdNum(MIN_PROD_NUM, MAX_PROD_NUM); // Find the array index of the record for that product index = binarySearch(product, NUM_PRODS, prodNum); if (index == -1) cout << "That product number was not found.\n"; else displayProd(product, index); cout << "\nWould you like to look up another product? (y/n) "; cin >> again; } while (again == 'y' || again == 'Y'); return 0; }

16. Chapter 9 Starting Out with C++: Early Objects 5/e slide 16 © 2006 Pearson Education. All Rights Reserved //****************************************************************************** // getProdNum * // Passed in: legal minumum and maximum product numbers * // Returned : a valid product number * //****************************************************************************** int getProdNum(int min, int max) { int prodNum; cout << "Enter the item's product number " << min << " - " << max << ": "; cin >> prodNum; // Validate input while (prodNum max) { cout << "Invalid product number.\n" << "Enter the item's product number " << min << " - " << max << ": "; cin >> prodNum; } return prodNum; }

17. Chapter 9 Starting Out with C++: Early Objects 5/e slide 17 © 2006 Pearson Education. All Rights Reserved //******************************************************************************************* // binarySearch * // If the record is found, its array subscript is returned. If it is not found, -1 * // is returned. * //******************************************************************************************* int binarySearch(ProdStruct array[], int numElems, int value) { int first = 0, // First array element last = numElems - 1, // Last array element middle, // Midpoint of search position = -1; // Position of search value bool found = false; // Flag while (!found && first <= last) { middle = (first + last) / 2; // Calculate midpoint if (array[middle].id == value) // If value is found at mid { found = true; position = middle; } else if (array[middle].id > value) // If value is in lower half last = middle - 1; else first = middle + 1; // If value is in upper half } return position; }

18. Chapter 9 Starting Out with C++: Early Objects 5/e slide 18 © 2006 Pearson Education. All Rights Reserved //********************************************************************************** // displayProd * // Passed in: the product array and the index of a specific element * // of that array * // This function displays four fields (i.e., structure members) of * // the product array element whose index is passed to the function. * //********************************************************************************** void displayProd(ProdStruct product[], int index) { cout << "\nID: " << product[index].id; cout << "\nTitle: " << product[index].title; cout << "\nDescription: " << product[index].description; cout << "\nPrice: $" << product[index].price << endl; }

19. Chapter 9 Starting Out with C++: Early Objects 5/e slide 19 © 2006 Pearson Education. All Rights Reserved 9.3 정렬 알고리즘 소개 정렬 (Sort): 자료를 어떤 순서로 배치한다. – 알파벳 순 – 올림차순 – 내림차순 대표적인 두 알고리즘 – 버블 정렬 (Bubble sort) – 선택 정렬 (Selection sort)

20. Chapter 9 Starting Out with C++: Early Objects 5/e slide 20 © 2006 Pearson Education. All Rights Reserved 버블 정렬 알고리즘 1.Compare 1 st two elements and exchange them if they are out of order. 2.Move down one element and compare 2 nd and 3 rd elements. Exchange if necessary. Continue until end of array. 3.Pass through array again, repeating process and exchanging as necessary. 4.Repeat until a pass is made with no exchanges.

21. Chapter 9 Starting Out with C++: Early Objects 5/e slide 21 © 2006 Pearson Education. All Rights Reserved 버블 정렬 예 배열 numlist3 Compare values 17 and 23. In correct order, so no exchange. Compare values 23 and 11. Not in correct order, so exchange them. 1723511 Compare values 23 and 5. Not in correct order, so exchange them.

22. Chapter 9 Starting Out with C++: Early Objects 5/e slide 22 © 2006 Pearson Education. All Rights Reserved 버블 정렬 예 ( 계속 ) 첫 패스 이후, 배열 numlist3 Compare values 17 and 5. Not in correct order, so exchange them. Compare values 17 and 23. In correct order, so no exchange. 1751123 Compare values 17 and 11. Not in correct order, so exchange them. In order from previous pass

23. Chapter 9 Starting Out with C++: Early Objects 5/e slide 23 © 2006 Pearson Education. All Rights Reserved 버블 정렬 예 ( 계속 ) 두번 째 패스 후, 배열 numlist3 No exchanges, so array is in order Compare values 5 and 11. In correct order, so no exchange. Compare values 17 and 23. In correct order, so no exchange. 5111723 Compare values 11 and 17. In correct order, so no exchange. In order from previous passes

24. Chapter 9 Starting Out with C++: Early Objects 5/e slide 24 © 2006 Pearson Education. All Rights Reserved 버블 정렬 효율성 장점 – 이해하기 쉽고, 구현하기 쉽다. 단점 – 비효율성 : 대형 배열에서 느린 속도 (swap)

25. Chapter 9 Starting Out with C++: Early Objects 5/e slide 25 © 2006 Pearson Education. All Rights Reserved 버블 정렬 //********************************************************************* // Definition of function sortArray * // This function performs an ascending-order bubble sort on * // array. The parameter elems holds the number of elements * // in the array. * //********************************************************************* void sortArray(int array[], int elems) { int temp; bool swap; do {swap = false; for (int count = 0; count < (elems - 1); count++) { if (array[count] > array[count + 1]) { temp = array[count]; array[count] = array[count + 1]; array[count + 1] = temp; swap = true; } } while (swap); } const int SIZE = 6; int values[SIZE] = {7, 2, 3, 8, 9, 1}; sortArray(values, SIZE); 7 2 3 8 9 1 7 temp values [0] [1] [5] count count+1

26. Chapter 9 Starting Out with C++: Early Objects 5/e slide 26 © 2006 Pearson Education. All Rights Reserved 선택 정렬 알고리즘 1.Locate smallest element in array and exchange it with element in position 0. 2.Locate next smallest element in array and exchange it with element in position 1. 3.Continue until all elements are in order.

27. Chapter 9 Starting Out with C++: Early Objects 5/e slide 27 © 2006 Pearson Education. All Rights Reserved 선택 정렬 예 배열 numlist 1.Smallest element is 2. Exchange 2 with element in 1 st array position (i.e. element 0). 112293 211293 Now in order

28. Chapter 9 Starting Out with C++: Early Objects 5/e slide 28 © 2006 Pearson Education. All Rights Reserved 선택 정렬 예 ( 계속 ) 2.Next smallest element is 3. Exchange 3 with element in 2 nd array position. 3.Next smallest element is 11. Exchange 11 with element in 3 rd array position. 232911 23 29 Now in order

29. Chapter 9 Starting Out with C++: Early Objects 5/e slide 29 © 2006 Pearson Education. All Rights Reserved 선택 정렬 효율성 장점 –More efficient than Bubble Sort, due to fewer exchanges 단점 –Considered harder than Bubble Sort to understand

30. Chapter 9 Starting Out with C++: Early Objects 5/e slide 30 © 2006 Pearson Education. All Rights Reserved 선택 정렬 //************************************************************** // selectionSort * // This function performs an ascending-order selection sort on * // array. The parameter elems holds the number of elements * // in the array. * //************************************************************** void selectionSort(int array[], int elems) { int startScan, minIndex, minValue; for (startScan = 0; startScan < (elems - 1); startScan++) { minIndex = startScan; minValue = array[startScan]; for(int index = startScan + 1; index < elems; index++) { if (array[index] < minValue) { minValue = array[index]; minIndex = index; } array[minIndex] = array[startScan]; array[startScan] = minValue; } const int SIZE = 6; int values[SIZE] = {7, 2, 3, 8, 9, 1}; selectionSort(values, SIZE); 7 2 3 8 9 1 values [0] [1] [5] startScan minIndex minValue 721721

31. Chapter 9 Starting Out with C++: Early Objects 5/e slide 31 © 2006 Pearson Education. All Rights Reserved // 9.4 Demetris Leadership Center Page. P.566 struct ProdStruct { int id; // Product number string title, // Product title description; // Product description double price; // Product unit price int sold; // Units sold during the past 6 months // Default constructor for a ProdStruct structure ProdStruct() { price = id = sold = 0; title = description = ""; } // Constructor to set initial data values ProdStruct(int i, string t, string d, double p, int s) { id = i; title = t; description = d; price = p; sold = s; } };

32. Chapter 9 Starting Out with C++: Early Objects 5/e slide 32 © 2006 Pearson Education. All Rights Reserved struct SalesStruct { int id; // Product number double dollarAmt; // Dollar amount of sales in past 6 months }; // Function prototypes void calcSales(ProdStruct[], SalesStruct [], int); void sortBySales(SalesStruct [], int); void showOrder(SalesStruct [], int); void showTotals(ProdStruct[], SalesStruct [], int);

33. Chapter 9 Starting Out with C++: Early Objects 5/e slide 33 © 2006 Pearson Education. All Rights Reserved int main() { const int NUM_PRODS = 9; // Number of products carried ProdStruct product[NUM_PRODS] = { ProdStruct(914, "Six Steps to Leadership", "Book", 12.95, 842), ProdStruct(915, "Six Steps to Leadership", "Audio cassette", 14.95, 416), ProdStruct(916, "The Road to Excellence", "Video", 18.95, 127), ProdStruct(917, "Seven Lessons of Quality", "Book", 16.95, 514), ProdStruct(918, "Seven Lessons of Quality", "Audio cassette", 21.95, 437), ProdStruct(919, "Seven Lessons of Quality", "Video", 31.95, 269), ProdStruct(920, "Teams are Made, Not Born", "Book", 14.95, 97), ProdStruct(921, "Leadership for the Future","Book", 14.95, 492), ProdStruct(922, "Leadership for the Future","Audio cassette", 16.95, 212) }; SalesStruct sales[NUM_PRODS]; calcSales(product, sales, NUM_PRODS); sortBySales(sales, NUM_PRODS); cout << fixed << showpoint << setprecision(2); showOrder(sales, NUM_PRODS); showTotals(product, sales, NUM_PRODS); return 0; }

34. Chapter 9 Starting Out with C++: Early Objects 5/e slide 34 © 2006 Pearson Education. All Rights Reserved //************************************************************ // calcSales * // Passed in: the product array, the sales array, and the * // size of the arrays * // * // This function uses data in the product array to get the * // product id and to calculate the product dollarAmt to be * // stored for each product in the sales array. * //************************************************************ void calcSales(ProdStruct product[], SalesStruct sales[], int numProds) { for (int index = 0; index < numProds; index++) {sales[index].id = product[index].id; sales[index].dollarAmt = product[index].price * product[index].sold; }

35. Chapter 9 Starting Out with C++: Early Objects 5/e slide 35 © 2006 Pearson Education. All Rights Reserved void sortBySales(SalesStruct sales[], int elems) { int startScan, maxIndex; SalesStruct maxValue; // Holds the structure with largest dollarAmt so far for (startScan = 0; startScan < (elems - 1); startScan++) { maxIndex = startScan; maxValue = sales[startScan]; for (int index = startScan + 1; index < elems; index++) { if (sales[index].dollarAmt > maxValue.dollarAmt) { maxValue = sales[index]; maxIndex = index; } sales[maxIndex] = sales[startScan]; sales[startScan] = maxValue; } sales [0] [1] [8] startScan maxIndex maxValue

36. Chapter 9 Starting Out with C++: Early Objects 5/e slide 36 © 2006 Pearson Education. All Rights Reserved //************************************************************* // showOrder * // Passed in: the sales array and its size * // * // This function displays the product number and dollar sales * // amount of each product DLC sells. * //************************************************************* void showOrder(SalesStruct sales[], int numProds) { cout << "Product ID \t Sales\n"; cout << "----------------------------\n"; for (int index = 0; index < numProds; index++) { cout << sales[index].id << "\t\t $"; cout << setw(8) << sales[index].dollarAmt << endl; } cout << endl; }

37. Chapter 9 Starting Out with C++: Early Objects 5/e slide 37 © 2006 Pearson Education. All Rights Reserved //************************************************************ // showTotals * // Passed in: the product array, the sales array, and the * // size of the arrays * // * // This function calculates and displays the total quantity * // of items sold and the total dollar amount of sales. * //************************************************************ void showTotals(ProdStruct product[], SalesStruct sales[], int numProds) { int totalUnits = 0; double totalSales = 0.0; for (int index = 0; index < numProds; index++) { totalUnits += product[index].sold; totalSales += sales[index].dollarAmt; } cout << "Total units Sold: " << totalUnits << endl; cout << "Total sales: $" << totalSales << endl; }

38. Chapter 9 Starting Out with C++: Early Objects 5/e slide 38 © 2006 Pearson Education. All Rights Reserved 9.5 벡터의 정렬과 탐색 정렬, 탐색 알고리즘은 배열 뿐 아니라 벡터에도 적용된다. 벡터 인자를 사용하기 위해서 함수에서 약간의 변경이 필요하다. – vector & // 함수 원형 – No need to indicate vector size as functions can use size member function to calculate

39. Chapter 9 Starting Out with C++: Early Objects 5/e slide 39 © 2006 Pearson Education. All Rights Reserved // This program produces a sales report for the Demetris Leadership Center. // This is an object-oriented version of the program that uses STL vectors // instead of arrays and that reads the product data in from a file. #include #include // Needed to use vectors using namespace std; struct ProdStruct { int id; // Product number string title, // Product title description; // Product description double price; // Product unit price int sold; // Units sold during the past 6 months // Default constructor for a ProdStruct structure ProdStruct() { price = id = sold = 0; title = description = ""; } // Constructor to set initial data values ProdStruct(int i, string t, string d, double p, int s) { id = i; title = t; description = d; price = p; sold = s; } };

40. Chapter 9 Starting Out with C++: Early Objects 5/e slide 40 © 2006 Pearson Education. All Rights Reserved struct SalesStruct { int id; // Product number double dollarAmt; // Dollar amount of sales in past 6 months }; const int NUM_PRODS = 9; // Number of products carried class ProdMgr { private: // Declare vectors to hold product and sales records vector product; vector sales; // Private function prototypes void initVectors(); void calcSales(); void sortBySales(); public: // Default constructor ProdMgr() { initVectors(); calcSales(); sortBySales(); cout << fixed << showpoint << setprecision(2); } // Public function prototypes void showOrder(); void showTotals(); };

41. Chapter 9 Starting Out with C++: Early Objects 5/e slide 41 © 2006 Pearson Education. All Rights Reserved void ProdMgr::initVectors() { product.resize(NUM_PRODS); sales.resize(NUM_PRODS); ifstream fileData; fileData.open("product.dat"); if (!fileData) cout << "Error opening data file.\n"; else { for (int index = 0; index < product.size(); index++) { fileData >> product[index].id; fileData.ignore(); // Skip newline char getline(fileData, product[index].title); getline(fileData, product[index].description); fileData >> product[index].price; fileData >> product[index].sold; } fileData.close(); } void ProdMgr::calcSales() { for (int index = 0; index < product.size(); index++) {sales[index].id = product[index].id; sales[index].dollarAmt = product[index].price * product[index].sold; }

42. Chapter 9 Starting Out with C++: Early Objects 5/e slide 42 © 2006 Pearson Education. All Rights Reserved //************************************************************ // ProdMgr::sortBySales * // This function performs a selection sort, arranging vector * // elements in descending-order based on the value of the * // dollarAmt structure member. * //************************************************************ void ProdMgr::sortBySales() { int startScan, maxIndex; int elems = sales.size(); SalesStruct maxValue; // Holds the structure with largest dollarAmt so far for (startScan = 0; startScan < (elems - 1); startScan++) { maxIndex = startScan; maxValue = sales[startScan]; for (int index = startScan + 1; index < elems; index++) { if (sales[index].dollarAmt > maxValue.dollarAmt) { maxValue = sales[index]; maxIndex = index; } sales[maxIndex] = sales[startScan]; sales[startScan] = maxValue; }

43. Chapter 9 Starting Out with C++: Early Objects 5/e slide 43 © 2006 Pearson Education. All Rights Reserved void ProdMgr::showOrder() { cout << "Product ID \t Sales\n"; cout << "----------------------------\n"; for (int index = 0; index < sales.size(); index++) { cout << sales[index].id << "\t\t $"; cout << setw(8) << sales[index].dollarAmt << endl; } cout << endl; } //************************************************************** // ProdMgr::showTotals * // This function calculates and displays the total quantity of * // items sold and the total dollar amount of sales. * //************************************************************** void ProdMgr::showTotals() { int totalUnits = 0; double totalSales = 0.0; for (int index = 0; index < product.size(); index++) { totalUnits += product[index].sold; totalSales += sales[index].dollarAmt; } cout << "Total units Sold: " << totalUnits << endl; cout << "Total sales: $" << totalSales << endl; }

44. Chapter 9 Starting Out with C++: Early Objects 5/e slide 44 © 2006 Pearson Education. All Rights Reserved /***************************** CLIENT PROGRAM *************************/ int main() { ProdMgr DLCsales; // Create a ProdMgr object DLCsales.showOrder(); DLCsales.showTotals(); return 0; }

45. Starting Out with C++: Early Objects 5/e © 2006 Pearson Education. All Rights Reserved Starting Out with C++: Early Objects 5 th Edition Chapter 9 Searching and Sorting Arrays