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13.20 Add the following two member functions to the Vet tor class template: T min(); T max(>; // returns the minimum element in the vector // returns the minimum element in the vector

CHAP. 9]

y (b)

Use of these functions, of course, presume that the order operators <, >, etc., are defined for the type T. For example, they would not work on an instance of Vector<Complex>.

13.21 Add the following member function to the Vet t or class template: int find(T t);

Fig. 12-25

This function searches for the element t in the Vet tor. If found, it returns the index of the element; otherwise, it returns -1. Use the sequential search algorithm.

If one side of a triangle is parallel to either coordinate axis, the length of that side and the length of the altitude to that side can be found readily. Then the formula A 1bh can be used. 2 If no side of a triangle is parallel to either axis, then either 1. The triangle can be enclosed in a rectangle whose sides are parallel to the axes (Fig. 12-26), or 2. Trapezoids whose bases are parallel to the y-axis can be formed by dropping perpendiculars to the x-axis (Fig. 12-27).

class template:

Fig. 12-26

ostream&

Fig. 12-27

friend istream&

9.3 PROCESSING A DATA FILE All applications involving the use of data files are based upon the same overall sequence of events. Specifically, the following three tasks must be carried out. 1. 2. 3. Open the data file. Process the file, as required by the application. Close the file.

operator<< ostream&, operator>> istream&,

The area of the triangle can then be found from the areas of the figures so formed: 1. In Fig. 12-26, area (^ABC) 2. In Fig. 12-27, area (^ABC) area(rectangle ADEF) [area(^ ABD) area (^ BCE) area (^ACF)]. area(trapezoid ABED) area(trapezoid BEFC) area (trapezoid DFCA).

const Vector<T>&); Vector<T>&);

The trapezoid method described above can be extended to finding the area of a quadrilateral if its vertices are given.

13.23 Add the following member function to the Vet t or class template: void sort();

12.19 Area of a triangle having a side parallel to an axis Find the area of the triangle whose vertices are A(1, 2), B(7, 2), and C(5, 4).

This function rearranges the elements of the Vet t or so that they are in increasing order. Use your favorite sorting algorithm. Use of this function, of course, requires that the order operators C, >, etc., are defined for the type T.

From the graph of the triangle (Fig. 12-28), we see that b A 1bh 1(6)(2) 6. 2 2 7 1 6 and h 4 2 2. Then

13.24 Add the following member function to the Vet t or class template: int find(T t);

4 2 x O y 2 A(1, 2)

This function searches for the element t in the Vet tor. If found, it returns the index of the element; otherwise, it returns - 1. Use the binary search algorithm, assuming that the Vet tor has already been sorted.

Private Sub mnuOpen_Click() Dim OldFile As String, i As Integer CommonDialog1.ShowOpen OldFile = CommonDialog1.FileName Open OldFile For Input As #1 i = 0 Do Until EOF(1) . . . . . 'read each data item from the input file, then process the data item 'continue until an end-of-file (EOF) condition has been detected on channel #1 . . . . . i = i + 1 Loop Close #1 End Sub

Add a constructor to the Vet tor class template that replicates an ordinary array of elements of type T. This will allow the following simpler way to initialize a vector:

Fig. 12-28

that replaces the sz data member with one that holds the last subscript value. Your new Array class template should have the same member functions as the Array subclass template.

12.20 Area of a triangle having no side parallel to an axis Find the area of ^ABC whose vertices are A(2, 4), B(5, 8) and C(8, 2) (a) using the rectangle method; (b) using the trapezoid method.