Practice 4: Loop and Iteration

Guide (Please read!!!)

There are 3+1 levels of difficulty of practice problems which will help guide you on how you do the assignment. 1.-3. are mandatory. If it is too easy, try speed-running the easy ones.

Concept (💀) will help you recheck yourself whether you understood the content.
Apply (💀💀) will step up some difficulty where you have to apply several concepts.
Technique (💀💀💀) is more challenging.
Real-world Examples (😈) are optional.

The problems will state inputs and outputs of the program. Inputs and outputs can be more than one, one each, see examples for more details.

Special instructions for this and further problems

Keep in mind that in Python, there is print('x', end='') which removes the newline character when printing on the screen. Further problems may require that.

Problems

(💀) 1. Print from m to n

Write a program that prints integers from m to n

Input:

Integer m
Integer n

Output:

Integers from m to n separated by space

Examples

Input:  4
        10
-----
Output: 4 5 6 7 8 9 10

(💀) 2. Print capped

Write a program that prints k * characters per line with total of n *.

Input:

Integer n
Integer k

Output:

Stars (See examples)

Examples

Input:  30
        8
-----
Output: * * * * * * * *
        * * * * * * * *
        * * * * * * * *
        * * * * * *

Because: print k stars per line with total of n stars

(💀) 3. Sum until n

Write a program that finds maximum k such that sum of 1..k is strictly less than n.

Input:

Integer n

Output:

Integer k
Sum of 1..k (1 + 2 + 3 + … + k)

Examples

Input:  20
-----
Output: 5
        15

(💀) 4. Is it prime?

A prime number p is a number that only p and 1 can divide while p > 1. Write a program that check if the integer that user inputs is a prime or not.

Input:

Integer n

Output:

PRIME or NOT PRIME

Examples

Input:  7
-----
Output: PRIME

(💀) 5. Sum of n numbers as the user wishes

Write a program that takes n as an input. Then, for the next n lines, user can input integer in each line. The program should output the sum of that list of numbers by user.

Input:

Integer n
Next n lines: integers to be summed

Output:

Sum of those integers

Examples

Input:  5
        2
        4
        5
        9
        9
-----
Output: 29

(💀) 6. Multiplication Table

Write a program that prints the multiplication table of n from 1 to 12:

n x 1 = ...

n x 2 = ...

...

n x 12 = ...

Input:

Integer n

Output:

Multiplication Table of n

Examples

Input:  13
-----
Output: 13 x 1 = 13
        13 x 2 = 26
        13 x 3 = 39
        13 x 4 = 52
        13 x 5 = 65
        13 x 6 = 78
        13 x 7 = 91
        13 x 8 = 104
        13 x 9 = 117
        13 x 10 = 130
        13 x 11 = 143
        13 x 12 = 156

(💀) 7. Find maximum and minimum

Write a program that takes n as an input. Then, for the next n lines, user can input integer in each line. The program should output the max and min of that list of numbers by user. Do it however you want to do.

Input:

Integer n
Next n lines: integers to be summed

Output:

Minimum number in the list
Maximum number in the list

Examples

Input:  5
        4
        2
        5
        9
        9
-----
Output: 2
        9

(💀) 8. Count Odd-even

Write a program that takes n as an input. Then, for the next n lines, user can input integer in each line. The program should output the count of odd numbers in the list.

Input:

Integer n
Next n lines: integers to be summed

Output:

Number of odd numbers

Examples

Input:  5
        4
        2
        5
        8
        9
-----
Output: 2

(💀) 9. Selected sum

Write a function that takes a list as a parameter, then returns a sum of that list with condition that the number is even.

Template (copy and fill code)

# Your code begin
def f(inp):
    ...
# Your code end

print(f([1, 2, 3, 4, 5, 6, 7]))
print(f([1, 1, 2, 3, 5, 8]))
print(f([]))

Input:

None

Output:

None

Examples

Input:  -
-----
Output: 12
        10
        0

(💀💀) 10. Cycle the list

Write a function that takes a number n and a list as parameters. The function shall cycle the first element to the back for n times. The function should return the new list and should not change anything in the list from parameter.

Template (copy and fill code)

# Your code begin
x = [1, 2, 3, 4, 5, 6, 7, 8, 9]

def f(n, inp):
    ...
# Your code end

print(f(0, x))
print(f(1, x))
print(f(3, x))

print(x)

Input:

None

Output:

None

Examples

Input:  -
-----
Output: [1, 2, 3, 4, 5, 6, 7, 8, 9]  # cycle 0 times
        [2, 3, 4, 5, 6, 7, 8, 9, 1]  # cycle 1 times
        [4, 5, 6, 7, 8, 9, 1, 2, 3]  # cycle 3 times
        [1, 2, 3, 4, 5, 6, 7, 8, 9]  # print x

(💀💀) 11. Split the list

Write a function that takes a list as a parameter. The function shall split the list into 3 lists. Each result list will have the member from the original list every 3 members. See examples for more details.

E.g.,

list1 = [x[0], x[3], x[6], ...]
list2 = [x[1], x[4], x[7], ...]
list3 = [x[2], x[5], x[8], ...]

Template (copy and fill code)

# Your code begin
x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

def f(inp):
    list1 = []
    list2 = []
    list3 = []

    ...
    
    return list1, list2, list3
# Your code end

for e in f(x):
    print(e)

Input:

None

Output:

None

Examples

Input:  -
-----
Output: [1, 4, 7, 10]
        [2, 5, 8]
        [3, 6, 9]

(💀) 12. Factorial

Write a n factorial function.

Template (copy and fill code)

# Your code begin

def factorial(n):
    ...

# Your code end

print(factorial(0))
print(factorial(3))
print(factorial(5))

Input:

None

Output:

None

Examples

Input:  -
-----
Output: 1
        6
        120

(💀💀) 13. Binomial Coefficient

Write a program that print binomial coefficients of order n.

Lookup on how you can use combinatorial formula to calculate the coefficient.

Use the factorial function from the problem above.

Input:

Integer n

Output:

Binomial coefficients of order n

Examples

Input:  1
-----
Output: 1 1

=====

Input:  2
-----
Output: 1 2 1

=====

Input:  3
-----
Output: 1 3 3 1

=====

Input:  5
-----
Output: 1 5 10 10 5 1

=====

Input:  0
-----
Output: 1

(💀) 14. Print Square n

Write a program that prints a square dimension n x n from stars *.

Input:

Integer n

Output:

Square

Examples

Input:  5
-----
Output: * * * * *
        * * * * *
        * * * * *
        * * * * *
        * * * * *

(💀) 15. Print Rectangle m x n

Write a program that prints a rectangle dimension m x n from stars *.

Input:

Integer m (width)
Integer n (height)

Output:

Rectangle

Examples

Input:  7
        3
-----
Output: * * * * * * *
        * * * * * * *
        * * * * * * *

(💀) 16. Print Symmetrical Triangle n

Write a program that prints a triangle dimension n x n from stars *.

Input:

Integer n

Output:

Triangle

Examples

Input:  5
-----
Output: *
        * *
        * * *
        * * * *
        * * * * *

(💀) 17. Print Upside-down Symmetrical Triangle n

Write a program that prints a triangle dimension n x n from stars *.

Input:

Integer n

Output:

Upside down Triangle

Examples

Input:  5
-----
Output: * * * * *
        * * * *
        * * *
        * *
        *

(💀) 18. Print Symmetrical Triangle n with column number

Write a program that prints a triangle dimension n x n from column number.

Input:

Integer n

Output:

Triangle

Examples

Input:  5
-----
Output: 1
        1 2
        1 2 3
        1 2 3 4
        1 2 3 4 5

(💀) 19. Print Symmetrical Triangle n with row number

Write a program that prints a triangle dimension n x n from row number.

Input:

Integer n

Output:

Triangle

Examples

Input:  5
-----
Output: 1
        2 2
        3 3 3
        4 4 4 4
        5 5 5 5 5

(💀) 20. Print Symmetrical Triangle n with increasing number

Write a program that prints a triangle dimension n x n from increasing number.

Input:

Integer n

Output:

Triangle

Examples

Input:  5
-----
Output: 1
        2 3
        4 5 6
        7 8 9 10
        11 12 13 14

(💀) 21. Print Double Triangle

Write a program that prints a triangle with stars *. (See examples.)

Input:

Integer n

Output:

Triangle

Examples

Input:  5
-----
Output: *
        * *
        * * *
        * * * *
        * * * * *
        * * * *
        * * *
        * *
        *

(💀) 22. Print Symmetrical Triangle (Flipped) n

Write a program that prints a flipped triangle dimension n x n from stars *.

Input:

Integer n

Output:

Triangle

Examples

Input:  5
-----
Output:         *
              * *
            * * *
          * * * *
        * * * * *

Hint: try replacing space ' ' with '-' so you can see what’s going on.

(💀) 23. Print Symmetrical Triangle (Flipped) n with numbers

Write a program that prints a triangle with numbers. (See examples.)

Input:

Integer n

Output:

Triangle

Examples

(💀) 24. Print Hollow Square n

Write a program that prints a hollow square dimension n x n from stars *.

Input:

Integer n

Output:

Hollow Square

Examples

Input:  5
-----
Output: * * * * *
        *       *
        *       *
        *       *
        * * * * *

(💀) 25. Print Hollow Symmetrical Triangle n

Write a program that prints a hollow triangle dimension n x n from stars *.

Input:

Integer n

Output:

Hollow Triangle

Examples

Input:  5
-----
Output: *
        * *
        *   *
        *     *
        * * * * *

(💀) 26. Print Diamond

Write a program that prints a diamond with stars *. (See examples.)

Input:

Integer n

Output:

Diamond

Examples

Input:  4
-----
Output:       *
            * * *
          * * * * *
        * * * * * * *
          * * * * *
            * * *
              *

(💀💀) 27. Print X

Write a program that prints an X with stars *. (See examples.)

Input:

Integer n

Output:

Examples

Input:  4
-----
Output: *           *
          *       *
            *   *
              *
            *   *
          *       *
        *           *

(💀💀) 28. Print Pyramid

Write a program that prints a pyramid with stars *. (See examples.)

Input:

Integer n

Output:

Pyramid

Examples

Input:  4
-----
Output:    * 
          * * 
         * * * 
        * * * *

(💀) 29. Harmonic sum n

Write a program that finds the harmonic sum 1..n.

Input:

Integer n

Output:

Harmonic sum of 1..n (1/1 + 1/2 + 1/3 + … + 1/n)

Examples

Input:  5
-----
Output: 2.283333333333333

(💀) 30. Print Symmetrical Triangle n with alternating binary

Write a program that prints a triangle dimension n x n from binary.

The leftmost element is always 1.

Input:

Integer n

Output:

Triangle

Examples

Input:  5
-----
Output: 1
        0 1
        1 0 1
        0 1 0 1
        1 0 1 0 1

(💀) 31. Series sum

Write a program that finds the series sum of 1 + 11 + 111 + 1111 + … ; n terms.

Input:

Integer n

Output:

Series sum

Examples

Input:  5
-----
Output: 12345

Because 1 + 11 + 111 + 1111 + 11111

(💀) 32. Perfect Square

Write a program that check if the number n is the perfect square or not.

Input:

Integer n

Output:

YES or NO

Examples

Input:  88
-----
Output: NO

Because 88 is not a perfect square.

(🍍) 33. Fibonacci Sequence

Write a program that print first n Fibonacci numbers.

Fibonacci sequences can be defined as:

F(n) = F(n - 1) + F(n - 2); F(0) = 1, F(1) = 1, n >= 0 and is integer.

Input:

Integer n

Output:

Fibonacci sequence

Examples

Input:  8
-----
Output: 1 1 2 3 5 8 13 21

(💀💀) 34. Print Symmetrical Triangle n from alphabets

Write a program that prints a triangle dimension n x n from alphabets.

Input:

Integer n

Output:

Triangle

Examples

Input:  5
-----
Output: A
        A B
        A B C
        A B C D
        A B C D E

(💀💀💀) 35. GCD

Write a program that find the Greatest Common Divisor (GCD) of two integers.

Input:

Integer a
Integer b

Output:

GCD(a, b)

Examples

Input:  6
        21
-----
Output: 3

=====

Input:  6
        5
-----
Output: 1

=====

Input:  20000
        20002
-----
Output: 2

(💀💀💀) 36. List Sliding

Write a function that takes a list as a parameter. The function shall return the maximum sum of 3 consecutive numbers in the list.

Explanation

[1, 2, 3, 4, 5, 6, 7, 8, 99, 10, 11, 12, 13]
 ~~~~~~~        -> 1 + 2 + 3 = 6
    ~~~~~~~     -> 2 + 3 + 4 = 9
       ~~~~~~~  -> 3 + 4 + 5 = 12
 ...

Template (copy and fill code)

# Your code begin
x = [1, 2, 3, 4, 5, 6, 7, 8, 99, 10, 11, 12, 13]
y = [1, 1, 1, 1, 1, 1, 1]

def f(inp):
    ...
# Your code end

print(f(x))
print(f(y))

Input:

None

Output:

None

Examples

Input:  -
-----
Output: 120      # 99 + 10 + 11 is maximum
        3        # 1 + 1 + 1 is maximum

(💀💀) 37. Pair Sum

Write a function that takes a list as a parameter. The function shall return the maximum sum of 2 numbers from the list.

E.g., the list [1, 2, 3, 4] can have a pair sum of:

+ 2
+ 3
+ 4
+ 3
+ 4
+ 4

Template (copy and fill code)

# Your code begin
x = [1, 2, 3, 4, 5, 6, 7, 8, 99, 10, 11, 12, 13]
y = [1, 1, 1, 1, 1, 1, 1]

def f(inp):
    ...
# Your code end

print(f(x))
print(f(y))

Input:

None

Output:

None

Examples

Input:  -
-----
Output: 112      # 99 + 13 is maximum
        2        # 1 + 1 is maximum

(💀💀💀) 38. Value Pairs

Write a function that takes 2 lists as parameters. The function shall print every combination of cartesian product of list1 X list2.

Explanation

list1 = [1, 2, 3]
list2 = [a, b]

The function should print:
1 a
1 b
2 a
2 b
3 a
3 b

Template (copy and fill code)

x = [1, 2, 3]
y = [8, 9, 0]

# Your code begin

def f(list1, list2):
    ...
# Your code end

f(x, y)

Input:

None

Output:

Next len(list1) * len(list2) lines: Cartesian product’s elements in each line

Examples

Input:  -
-----
Output: 1 8
        1 9
        1 0
        2 8
        2 9
        2 0
        3 8
        3 9
        3 0

(😈😈😈) 39. Closest distance

Write a program that finds a pair of coordinates that are closest to each other.

Template (copy and fill code)

n = int(input())
coords = [list(map(float, input().strip().split())) for i in range(n)]

# Your code begin

...

# Your code end

Tips: You can iterate through 2 values at the same time in for loop:

for x, y in coords:
    # you can use value x and y here now.

Tips: You can iterate through value in the list and counting at the same time in for loop with enumerate:

for i, x in enumerate(inp):
    # i will be the index 0, 1, 2, ... , len(inp)-1
    # x will be the value in inp list

Tips: Combining with above two, you get:

for i, (x, y) in enumerate(coords):
    # i will be the index 0, 1, 2, ... , len(inp)-1
    # you can use value x and y here now.

Input:

Integer n indicating number of coordinates
Next n lines: coordinate x, y separated by space.

Output:

(x1, y1) (x2, y2) that are closest to each other
distance between those two coordinates

Examples

Input:  3
        3.0 4.0
        9.4 5.5
        6.7 -10.9
-----
Output: (3.0, 4.0) (9.4, 5.5)
        6.573431371817919

(😈😈) 40. Collatz Conjecture

Write a function that prints a sequence satisfying Collatz Conjecture.

(💀💀) 41. Insert Sorted

Write a function that takes a list and an element k to be inserted as parameters. The function will insert an element into the list without returning anything. The order of list after insertion will be sorted in ascending order.

Explanation

list1 = []

insert(list1, 5)  # list1 becomes [5]
insert(list1, 9)  # list1 becomes [5, 9]
insert(list1, 10)  # list1 becomes [5, 9, 10]
insert(list1, 10)  # list1 becomes [5, 9, 10, 10]
insert(list1, 2)  # list1 becomes [2, 5, 9, 10, 10]
insert(list1, 3)  # list1 becomes [2, 3, 5, 9, 10, 10]

Template (copy and fill code)

x = []

# Your code begin

def insert(list1, k):
    ...

# Your code end

print(x)
for e in [5, 9, 10, 10, 2, 3]:
    f(x, e)
    print(x)

Input:

None

Output:

None

Examples

Input:  -
-----
Output: []
        [5]
        [5, 9]
        [5, 9, 10]
        [5, 9, 10, 10]
        [2, 5, 9, 10, 10]
        [2, 3, 5, 9, 10, 10]

(💀) 42. Insert if not exist

Write a function that takes a list and an element k to be inserted as parameters. The function will insert an element into the list without returning anything. If k already exists, in the list, the function should not do anything.

In Python, you can use expression x in y to check if an element x is in the collection y or not. This expression is either True or False.

Explanation

list1 = []

insert(list1, 5)  # list1 becomes [5]
insert(list1, 9)  # list1 becomes [5, 9]
insert(list1, 10)  # list1 becomes [5, 9, 10]
insert(list1, 10)  # list1 becomes [5, 9, 10]
insert(list1, 2)  # list1 becomes [5, 9, 10, 2]
insert(list1, 3)  # list1 becomes [5, 9, 10, 2, 3]
insert(list1, 3)  # list1 becomes [5, 9, 10, 2, 3]

Template (copy and fill code)

x = []

# Your code begin

def insert(list1, k):
    ...

# Your code end

print(x)
for e in [5, 9, 10, 10, 2, 3, 3]:
    f(x, e)
    print(x)

Input:

None

Output:

None

Examples

Input:  -
-----
Output: []
        [5]
        [5, 9]
        [5, 9, 10]
        [5, 9, 10]
        [5, 9, 10, 2]
        [5, 9, 10, 2, 3]
        [5, 9, 10, 2, 3]

Vivatsathorn Thitasirivit

Guide (Please read!!!)

Special instructions for this and further problems

Problems

(💀) 1. Print from m to n

(💀) 2. Print capped

(💀) 3. Sum until n

(💀) 4. Is it prime?

(💀) 5. Sum of n numbers as the user wishes

(💀) 6. Multiplication Table

(💀) 7. Find maximum and minimum

(💀) 8. Count Odd-even

(💀) 9. Selected sum

(💀💀) 10. Cycle the list

(💀💀) 11. Split the list

(💀) 12. Factorial

(💀💀) 13. Binomial Coefficient

(💀) 14. Print Square n

(💀) 15. Print Rectangle m x n

(💀) 16. Print Symmetrical Triangle n

(💀) 17. Print Upside-down Symmetrical Triangle n

(💀) 18. Print Symmetrical Triangle n with column number

(💀) 19. Print Symmetrical Triangle n with row number

(💀) 20. Print Symmetrical Triangle n with increasing number

(💀) 21. Print Double Triangle

(💀) 22. Print Symmetrical Triangle (Flipped) n

(💀) 23. Print Symmetrical Triangle (Flipped) n with numbers

(💀) 24. Print Hollow Square n

(💀) 25. Print Hollow Symmetrical Triangle n

(💀) 26. Print Diamond

(💀💀) 27. Print X

(💀💀) 28. Print Pyramid

(💀) 29. Harmonic sum n

(💀) 30. Print Symmetrical Triangle n with alternating binary

(💀) 31. Series sum

(💀) 32. Perfect Square

(🍍) 33. Fibonacci Sequence

(💀💀) 34. Print Symmetrical Triangle n from alphabets

(💀💀💀) 35. GCD

(💀💀💀) 36. List Sliding

(💀💀) 37. Pair Sum

(💀💀💀) 38. Value Pairs

(😈😈😈) 39. Closest distance

(😈😈) 40. Collatz Conjecture

(💀💀) 41. Insert Sorted

(💀) 42. Insert if not exist