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In other words, all optional parameters must be listed last.
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[CHAP. 5
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5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 What are the advantages of using functions to modularize a program What is the difference between a function s declaration and its definition Where can the declaration of a function be placed When does a function need an include directive What is the advantage of putting a function s definition in a separate file What is the advantage of compiling a function separately What are the differences between passing a parameter by value and by reference What are the differences between passing a parameter by reference and by constant reference 5.9 Why is a parameter that is passed by value referred to as read-only Why is a parameter that is passed by reference referred to as read-write 5.10 What is wrong with the following declaration:
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int f(int a, int b=0, int c);
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5.1 In Example 5.14, the following expression was used to test whether y is a leap year:
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y % 4 == 0 && y % 100 != 0 || y % 400 == 0 This expression is not the most efficient form. If y is not divisible by 4, it will still test the condition y % 400 == 0 which would have to be false. C++ implements short circuit-
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5.2 5.3 5.4 5.5 5.6 5.7
ing, which means that subsequent parts of a compound condition are tested only when necessary. Find an equivalent compound condition that is more efficient due to short circuiting. Describe how a void function with one reference parameter can be converted into an equivalent non-void function with one value parameter. Write a simple program like the one in Example 5.2 on page 88 to check the trigonometry cos2x = 2 cos2 x 1. Write a program like the one in Example 5.2 that checks the identity: cos2x + sin2x = 1. Write a program like the one in Example 5.2 that checks the identity: bx = e(x log b). Write and test the following min function that returns the smallest of four given integers:
int min(int,int,int,int);
Write and test the following max() function that uses the max(int,int) function from Example 5.5 on page 91 to find and return the largest of four given integers:
int max(int,int,int);
Write and test the following min() function that uses a min(int,int) function to find and return the smallest of four given integers:
int min(int,int,int,int); Write and test the following average() function that returns the average of four numbers: float average(float x1, float x2, float x3, float x4) Write and test the following average() function that returns the average of up to four pos-
5.9 5.10
itive numbers:
float average(float x1, float x2=0, float x3=0, float x4=0)
Implement the factorial function fact() with a for loop. (See Example 4.9 on page 65.) Determine which values of n will cause fact(n) to overflow. 5.12 A more efficient way to compute the permutations function P(n,k) is by the formula P(n,k) = (n)(n 1)(n 2) (n k+2)(n k+1)
TeamLRN
CHAP. 5]
FUNCTIONS
This means the product of the k integers from n down to n k + 1. Use this formula to rewrite and test the perm() function from Example 5.10. 5.13 The combination function C(n,k) gives the number of different (unordered) k-element subsets that can be found in a given set of n elements. The function can be computed from the formula n! C ( n, k ) = ---------------------k! ( n k )! Implement this formula. 5.14 The combinations function C(n,k) can be computed from the formula P ( n, k ) C ( n, k ) = ---------------k! Use this formula to rewrite and test the comb() function implemented in Problem 5.13. 5.15 A more efficient way to compute C(n,k) is shown by the formula C(n,k) = ((((((((n/1)(n 1))/2)(n 2))/3) (n k+2))/(k 1))(n k+1))/k This alternates divisions and multiplications, each time multiplying by the next decremented value from n and then dividing by the next incremented value from 1. Use this formula to rewrite and test the comb() function implemented in Problem 5.13. Hint: Use a for loop like the one in Problem 5.12. 5.16 Pascal s Triangle is a triangular array of numbers that begins like this:
1 1 1 1 1 1 5 1 4 10 3 6 10 2 3 4 5 1 1 1 1
1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1
Each number in Pascal s Triangle is one of the combinations C(n,k). (See Problem 5.13.) If we count the rows and the diagonal columns starting with 0, then the number C(n,k) is in row n and column k. For example, the number C(6,2) = 15 is in row number 6 and column number 2. Write a program that uses the comb() function to print Pascal s Triangle down to row number 12. 5.17 Write and test the digit() function:
int digit(int n, int k)
This function returns the kth digit of the positive integer n. For example, if n is the integer 29,415, then the call digit(n, 0) would return the digit 5, and the call digit(n, 2) would return the digit 4. Note that the digits are numbered from right to left beginning with the zeroth digit. 5.18 Write and test a function that implements the Euclidean Algorithm to return the greatest common divisor of two given positive integers. See Problem 4.14 on page 67. 5.19 Write and test a function that uses the greatest common divisor function (Problem 5.18) to return the least common multiple of two given positive integers. 5.20 Write and test the following power() function that returns x raised to the power n, where n can be any integer:
double power(double x, int p);
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