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++i; if (i*i == n) return true; else return false; } 0 is square. 1 is square. 2 is not square. 3 is not square. 4 is square. 5 is not square. 6 is not square. 7 is not square. 8 is not square. 9 is square. 10 is not square. 11 is not square. This tests a boolean function that tests integers for pentangularity: int isPentagonal(int); int main() { const int MAX=40; for (int i=0; i<MAX; i++) if (isPentagonal(i)) cout << i << " is pentagonal.\n"; else cout << i << " is not pentagonal.\n"; } int isPentagonal(int n) { int x=0, y=0, dy=1; while (y < n) { y += dy; dy += 3; } if (y == n) return true; else return false; } 0 is pentagonal. 1 is pentagonal. 2 is not pentagonal. 3 is not pentagonal. 4 is not pentagonal. 5 is pentagonal. 6 is not pentagonal. 7 is not pentagonal. 8 is not pentagonal. 9 is not pentagonal. 10 is not pentagonal. 11 is not pentagonal. 12 is pentagonal. 13 is not pentagonal. This tests a function that has reference parameters: void computeCircle(double& area, double& circ, double r); int main() { double a, c, r; cout << "Enter the radius: "; cin >> r;
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FUNCTIONS
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computeCircle(a,c,r); cout << "The area of a circle of radius " << r << " is " << a << "\nand its circumference is " << c << endl; } void computeCircle(double& area, double& circ, double r) { const double PI=3.141592653589793; area = PI*r*r; circ = 2*PI*r; } Enter the radius: 10 The area of a circle of radius 10 is 314.159 and its circumference is 62.8319 This tests a function that has reference parameters: void computeTriangle(float& a, float& p, float x,float y,float z); int main() { float a, p, x, y, z; cout << "Enter the sides: "; cin >> x >> y >> z; computeTriangle(a,p,x,y,z); cout << "The area of the triangle is " << a << "\nand its perimeter is " << p << endl; } void computeTriangle(float& a, float& p, float x, float y, float z) { p = x + y + z; float s = p/2.0; // the semiperimeter of the triangle a = sqrt(s*(s-x)*(s-y)*(s-z)); // Heron's formula } Enter the sides: 30 50 40 The area of the triangle is 600 and its perimeter is 120 This tests a function that has reference parameters: void computeSphere(double& a, double& v, double r); int main() { double a, v, r; cout << "Enter the radius: "; cin >> r; computeSphere(a,v,r); cout << "The area of a sphere of radius " << r << " is " << a << "\nand its volume is " << v << endl; } void computeSphere(double& a, double& v, double r) { const double PI=3.141592653589793; a = 4.0*PI*r*r; v = a*r/3.0; } Enter the radius: 10 The area of a sphere of radius 10 is 1256.64 and its volume is 4188.79
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Arrays
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6.1 INTRODUCTION An array is a sequence of objects all of which have the same type. The objects are called the elements of the array and are numbered consecutively 0, 1, 2, 3, ... . These numbers are called index values or subscripts of the array. The term subscript is used because as a mathematical sequence, an array would be written with subscripts: a0, a1, a2, . The subscripts locate the element s position within the array, thereby giving direct access into the array. If the name of the array is a, then a[0] is the name of the element that is in position 0, a[1] is the name of the element that is in position 1, etc. In general, the ith element is in position i 1. So if the array has n elements, their names are a[0], a[1], a[2], , a[n-1]. We usually visualize an array as a series of adjacent storage compartments a 0 11.11 that are numbered by their index values. For example, the diagram here shows 1 33.33 an array named a with 5 elements: a[0] contains 11.11, a[1] contains 33.33, 2 55.55 a[2] contains 55.55, a[3] contains 77.77, and a[4] contains 99.99. The 3 77.77 diagram actually represents a region of the computer s memory because an 4 99.99 array is always stored this way with its elements in a contiguous sequence. The method of numbering the ith element with index i 1 is called zero-based indexing. It guarantees that the index of each array element is equal to the number of steps from the initial element a[0] to that element. For example, element a[3] is 3 steps from element a[0]. Virtually all useful programs use arrays. If several objects of the same type are to be used in the same way, it is usually simpler to encapsulate them into an array. 6.2 PROCESSING ARRAYS An array is a composite object: it is composed of several elements with independent values. In contrast, an ordinary variable of a primitive type is called a scalar object. The first example shows that array elements can be assigned and accessed the same as ordinary scalar objects. EXAMPLE 6.1 Using Direct Access on Arrays
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int main() { double a[3]; a[2] = 55.55; a[0] = 11.11; a[1] = 33.33; cout << "a[0] = " << a[0] << endl; cout << "a[1] = " << a[1] << endl; cout << "a[2] = " << a[2] << endl; }
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