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seed = 943364015 2948 15841 72 25506 30808 29709 13115 2527 seed = 943364119 17427 20464 13149 5702 12766 1424 16612 31746
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EXAMPLE 4.29 Generating Pseudo-Random Numbers in Given Range
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This program is the same as the one in Example 4.28 except that the pseudo-random numbers that it generates are restricted to given range: #include <cstdlib> #include <ctime> // defines the time() function #include <iostream> //#include <time.h> // use this if <ctime> is not recognized using namespace std; int main() { // prints pseudo-random numbers: unsigned seed = time(NULL); // uses the system clock cout << "seed = " << seed << endl; srand(seed); // initializes the seed int min, max; cout << "Enter minimum and maximum: "; cin >> min >> max; // lowest and highest numbers int range = max - min + 1; // number of numbers in range for (int i = 0; i < 20; i++) { int r = rand()/100%range + min; cout << r << " "; } cout << endl; } Here are two runs: seed = 808237677 Enter minimum and maximum: 1 100 85 57 1 10 5 73 81 43 46 42 17 44 48 9 3 74 41 4 30 68
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seed = 808238101 Enter minimum and maximum: 22 66 63 29 56 22 53 57 39 56 43 36 62 30 41 57 26 61 59 26 28 The first run generates 20 integers uniformly distributed between 1 and 100. The second run generates 20 integers uniformly distributed between 22 and 66.
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In the for loop, we divide rand() by 100 first to strip way the two right-most digits of the random number. This is to compensate for the problem that this particular random number generator has of producing numbers that alternate odd and even. Then rand()/100%range produces random numbers in the range 0 to range-1, and rand()/100%range + min produces random numbers in the range min to max.
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Review Questions
4.1 4.2 4.3 4.4 What happens in a while loop if the control condition is false (i.e., zero) initially When should the control variable in a for loop be declared before the loop (instead of within its control mechanism) How does the break statement provide better control of loops What is the minimum number of iterations that a. a while loop could make b. a do..while loop could make What is wrong with the following loop:
while (n <= 100) sum += n*n; If s is a compound statement, and e1, e2, and e3 are expressions, then what is the difference
between the program fragment:
for (e1; e2; e3) s;
and the fragment:
e1; while (e2) { s; e3; }
What is wrong with the following program:
int main() { const double PI; int n; PI = 3.14159265358979; n = 22; }
4.8 What is an infinite loop, and how can it be useful 4.9 How can a loop be structured so that it terminates with a statement in the middle of its block 4.10 Why should tests for equality with floating-point variables be avoided
Problems
4.1 Trace the following code fragment, showing the value of each variable each time it changes:
float x = 4.15; for (int i=0; i < 3; i++) x *= 2;
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Assuming that e is an expression and s is a statement, convert each of the following for loops into an equivalent while loop: a. for ( ; e; ) s b. for ( ; ; e) s Convert the following for loop into a while loop:
for (int i=1; i <= n; i++) cout << i*i << " ";
Describe the output from this program:
int main() { for (int i = 0; i < 8; i++) if (i%2 == 0) cout << i + 1 << "\t"; else if (i%3 == 0) cout << i*i << "\t"; else if (i%5 == 0) cout << 2*i - 1 << "\t"; else cout << i << "\t"; }
Describe the output from this program:
int main() { for (int i=0; i < 8; i++) { if (i%2 == 0) cout << i + 1 << endl; else if (i%3 == 0) continue; else if (i%5 == 0) break; cout << "End of program.\n"; } cout << "End of program.\n"; } In a 32-bit float type, 23 bits are used to store the mantissa and 8 bits are used to store the
4.8 4.9 4.10 4.11 4.12
4.13 4.14
exponent. a. How many significant digits of precision does the 32-bit float type yield b. What is the range of magnitude for the 32-bit float type Write and run a program that uses a while loop to compute and prints the sum of a given number of squares. For example, if 5 is input, then the program will print 55, which equals 12 + 22 + 32 + 42 + 52. Write and run a program that uses a for loop to compute and prints the sum of a given number of squares. Write and run a program that uses a do..while loop to compute and prints the sum of a given number of squares. Write and run a program that directly implements the quotient operator / and the remainder operator % for the division of positive integers. Write and run a program that reverses the digits of a given positive integer. (See Problem 3.13 on page 51.) Apply the Babylonian Algorithm to compute the square root of 2. This algorithm (so called because it was used by the ancient Babylonians) computes 2 by repeatedly replacing one estimate x with the closer estimate (x + 2/x)/2. Note that this is simply the average of x and 2/x. Write a program to find the integer square root of a given number. That is the largest integer whose square is less than or equal to the given number. Implement the Euclidean Algorithm for finding the greatest common divisor of two given positive integers. This algorithm transforms a pair of positive integers (m, n) into a pair (d, 0) by repeatedly dividing the larger integer by the smaller integer and replacing the larger with
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