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4.36 Implement the f ac tori al ( )
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function with a for loop. Determine which values of n will
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factorial (n)
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4.37 The combinations function C(n,k) can be computed from the formula p (n, k) w&k) = --g. Use this formula to rewrite and test the comb ( > function implemented in Problem 4.15.
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4.38 A more efficient way to compute C(n,k) is shown by the formula
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C(n,k) = (n/l) ((n- 1)/2) ((n- 2)/3)...((n-k+2)/(k-1))
((n-k+l)/k)
This alternates divisions and multiplications. Use this formula to rewrite and test the comb ( > function implemented in Problem 4.15. Hint: Use a for loop like the one in Problem 4.14.
4.39 Pascal s Trianak is a triangular arrav of numbers that begins like this:
1 1 1 12 1 13 3 1 14 6 4 1 1 5 10 10 5 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 4.15 and Problem 4.38.) If we count the rows and the diagonal columns starting with 0, then the number in row ~1 and column k is C(n,k). For example, the number in row number 6 and column number 2 is C(6,2) = 15. Write a program that uses the comb ( ) function to print Pascal s Triangle down to row number 12. 4.40 Write and test a function that implements the Euclidean Algorithm to return the greatest common divisor of two given positive integers. See Example 3.19. 4.41 Write and test a function that uses the greatest common divisor function (Problem 4.40) to return the least common multiple of two given positive integers.
BOOLEAN FUNCTIONS 4.42 Write and test the following i ~Square ( ) is a square number:
int isSquare(int n)
function that determines whether the given integer
The first ten square numbers are 1,4,9, 16,25, 36,49,64, 8 1 , and 100. 4.43 Write and test the following i sPentagona1 integer is a pentagonal number:
int jsPentagonal(int n)
function that determines whether the given
The first ten pentagonal numbers are 1,5, 12,22, 35,51,70,92,
117, and 145.
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OVERLOADING 4.44 Write and test the following drawsquare void drawSquare(int w).
function that prints a combination of asterisks and blanks so that the asterisks form the boundary of a square of width W:
4.45 Write and test the following drawRec void drawSquare(int w,
tang1 e ( ) function that prints a combination of asterisks and blanks so that the asterisks form the boundary of a rectangle of width w and height h: int h). \
4.46 Write and test the following average ( >
function that returns the average of four numbers:
float average(float xl, float x2, float x3, float x4) 4.47 Write and test the following average ( )
function that returns the average of up to four posi-
tive numbers:
float average(float xl, float x2=0, float x3=0, float x4=0)
PASSING BY REFERENCE 4.48 Write and test the following compu t eC i rc 1 e ( > cumference c of a circle with given radius r : void computeCircle(float&
function that returns the area a and the cir-
a, float& c, float r).
4.49 Write and test the following compu t eRec tang1 e ( > function that returns the area a and the perimeter p of a rectangle with given side width w and height h: void computeRectangle(float& a, float& p, float w, float h).
4.50 Write and test the following compu t eTr i angl e ( > function that returns the area a and the perimeter p of a triangle with given side lengths a, b, and c: void computeTriangle(float& a, float& p, float a, float b, float c).
4.51 Write and test the following c ompu t esphere void computeSphere(float& 4.52 Write and test the following computecyl
(> surface area s of a sphere with given radius r:
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