6.1 User-Defined Functions

1. Write a function for calculating the cube of integers, and calculate the cube difference between each number from 1 to 10 and its previous adjacent integer.

For example, 2, the previous adjacent number is 1, the cube difference between the two is equal to 7.

2. Write a function to convert Fahrenheit temperature to Celsius temperature, with the formula C=(F-32) * 5/9, and call the function to calculate the Celsius temperature corresponding to 73 ℉.

3. Write a function to calculate the area of a triangle using its side length.

Given three sides, determine if a triangle can be formed, and if so, calculate the area.

Tip: The formula for calculating the area of a triangle using its side length is Helen’s formula

, p is half of the perimeter.

4. Use a custom function to calculate the volume of a hollow cylinder. Enter the outer radius R, inner radius r, and height h to calculate the volume.

Tip: Volume of cylinder

5. Customize a function to calculate BMI, input height and weight, and output BMI

6. If a number is exactly equal to the sum of all its factors, it is called a “perfect number”. For example, 6=1+2+3.

How to determine the perfect number, Euclidean discovered that as long as 2ⁿ-1 is a prime number, 2^n-1（2ⁿ-1）must be a perfect number (n>=2). Write a program to find the smallest 5 perfect numbers. Require to use custom function to determine whether 2ⁿ-1 is a prime number.

7. Implement a function that can count the number of times a number appears in any integer. For example, in -21252, if 2 appears 3 times, the function should return 3.

8. Find the roots of equation ax^2 + bx + c = 0. The parameters a, b, and c are input from the main function.

6.2 Recursion

1. Write a recursive function that returns the maximum common divisor of integers x and y

2. The monkey picked a bunch of peaches and ate half of them on the first day, feeling unsatiated, the monkey ate another one; The next day, the monkey ate half of the remaining peaches and one extra; From then on, it was like this every day, by the tenth day, there was only one peach left. How many peaches were there initially?

3. A frog can jump up one or two steps at a time. How many jumping methods are there for the frog to jump up an n-level step.

4. Use recursive thinking to output a positive integer in reverse order. For example, given a positive integer n=12345, it is desired to output in reverse order of each digit, i.e. output 54321

5. Hanoi Tower problem: Given three pillars, denoted as a, b, c, where there are n plates on pillar a, and the plates on top must be smaller than those below. Question: How many times does it take to move the plates on pillar a through pillar b to pillar c at least?

When moving, attention should be paid to:

① Only one plate can be moved at a time

② A large plate cannot be placed on top of a small plate

6.3 Reusable script

1. Edit the method of calculating triangle area using side length into a reusable script and call it.

2. Edit the calculation method of BMI into a reusable script and call it.

Suggested answers:

6.1 User-Defined Functions

1.

	A	B
1	func	return A1*A1*A1
2	=10.(func(A1,~)-func(A1,~[-1]))

2.

	A	B
1	func	return (A1-32)*5/9
2	=func(A1,73)

3.

	A	B	C	D
1	func
2		if A1 + B1 > C1 && A1 + C1 > B1 && B1 + C1 > A1	=A1+B1+C1	=C2/2
3			=sqrt(D2*(D2-A1)*(D2-B1)*(D2-C1))
4			return C3
5		else	return “This side length group does not form a triangle”

4.

	A	B	C
1	func
2		return pi()*A1*A1*C1-pi()*B1*B1*C1

5.

	A	B
1	func
2		return B1/(A1*A1)

6.

	A	B	C	D	E
1	0	2
2	for A1<5	if func(A5,B1)==1	>output(int(power(2,B1-1)*(power(2,B1)-1)))	>A1+=1
3		>B1+=1
4
5	func	=power(2,A5)-1
6		if A5==2	return 1
7		else	for 2,sqrt(B5)	if B5%C7==0	return 0
8					break C7
9			return 1

7.

	A	B	C	D
1	func		0
2		if A1<0	>A1=-A1
3		if A1==0 && B1==0	return 1
4		for A1	if A1%10==B1	>C1+=1
5			>A1=10
6		return C1
7	=func(A1,-21252,2)

8.

	A	B	C	D
1	func
2		if A1==0	return -C1/B1
3		else	=B1*B1-4*A1*C1
4			if C3 >0	return [(-B1+sqrt(C3))/(2*A1),(-B1-sqrt(C3))/(2*A1)]
5			else if C3==0	return -B1/(2*A1)
6			else	return “There are no real roots”
7	=func(A1,3,8,5)

6.2 Recursion

1.

	A	B	C
1	func
2		if B1==0	return A1
3		else	return func(A1,B1,A1%B1)
4	=func(A1,54,63)

2.

	A	B	C
1	func
2		if A1==1	return 1
3		return (func(A1,A1-1)+1)*2
4	=func(A1,10)

3.

	A	B	C
1	func
2		if A1==1	return 1
3		elseif A1==2	return 2
4		else	return func(A1,A1-1)+func(A1,A1-2)
5	=func(A1,9)

4.

	A	B	C
1	func	if A1<10	return output(A1%10)
2		=output(A1%10)
3		return func(A1, A1\10),B2
4	=func(A1,12345)

Recursive thinking: First output the single digit of this number, and then output the single digit of the preceding number until there are no numbers before.

5.

	A	B	C
1	func	if A1==1	return 1
2		return 2*func(A1,A1-1)+1
3	=func(A1,10)