## Description

4. Arrays

4.01. Write a function which takes two arguments – an array

and its size and prints all elements of the array on the

console.

4.02. Write a function which takes two arguments – an array

and its size and reverses the array. Example: {4,2,8,-6,12}-

{12,-6,8,2,4}.

4.03. Write a program which asks the user to enter n – the

number of numbers he will enter. Then the program should ask

for n numbers and print the contents of the array in reverse.

4.04. Write a program which asks the user to enter n – the

number of numbers he will enter. Then the program should ask

for n numbers and print only the even numbers.

4.05. Write a program which asks the user to enter n – the

number of numbers he will enter. Then the program should ask

for n numbers and print only the numbers that are smaller

than the average of all numbers.

4.06. Write a program which asks the user to enter n – the

number of numbers he will enter. Then the program should ask

for n numbers and print the maximum and minimum of them.

Example input Expected output

4 2 4 6 8 8 6 4 2

5 1 0 1 0 -1 -1 0 1 0 1

Example input Expected output

4 1 2 3 -4 2 -4

5 1 3 0 7 9 0

Example input Expected output

7 1 2 3 4 5 6 7 1 2 3

5 -2 4 -3 6 8 -2 -3

4.07. Write a function which takes three arguments – two

double arrays – source and destination and unsigned s – size

of the source. The function has to copy all elements from

source to destination (assume destination is big enough).

4.08. Write a program which inputs а sequence of integer

numbers and finds and prints the sum of those

elements from the sequence, which can be represented as

doubled odd number.

4.09. Write a program which checks whether there exist two

consecutive zeroes in a given sequence of integers.

4.10. Two sequences of numbers are given. Write a program

that detects how many times the second sequence contains the

first one.

4.11. Each subsequence of equal numbers in an array is called

a train. Write a program that finds the beginning and length

of the longest train in an array.

4.12. Write a program which check whether an array of chars

is symmetric.

4.13. Write a function which takes two arguments – an int

array and its size, and sorts the array (in ascending or

descending order).

4.14. (Cartesian Product) Write a program which reads an

array from the console and prints the product of each of its

elements with all elements. E.g. for the array {1, 7, 3}, the

result would be {1 * 1, 1 * 7, 1 * 3, 7 * 1, 7 * 7, 7 * 3, 3

* 1, 3 * 7, 3 * 3}, which gives us the array {1, 7, 3, 7, 49,

21, 3, 21, 9}, so for the input {1 7 3} the program should

print 1 7 3 7 49 21 3 21 9.

Example input Expected output

6 -2 -1 0 1 3 4 4 -2

1 4 4 4

N

a1, a2, . . . , aN

4.15. (Closest Numbers) Write a program which finds the two

closest (by value) integer numbers in an array and prints the

absolute difference between them.

4.16 Write a function which takes two arguments – an int

array and its size, and returns it’s median.

4.17 Write a function which takes two arguments – an int

array and its size, and returns its mode(s). “vector” and

“algorithm” libraries are allowed, because the array can have

more than one mode. Order of output does not matter.

Mode & Median of a set of data

[More about Median and Mode of a set of data values here]

(https://www.khanacademy.org/math/statistics-probability/

Example input Expected output

3

1 7 3 1 7 3 7 49 21 3 21 9

2

-1 4 1 -4 -4 16

1

42 1764

Example input Expected output Explanation

5

1 105 10 100 3 2 The closest number are 1 and 3, |1-3|=2

8

1 2 3 4 5 6 7 8 1 All numbers are exactly 1 unit apart

4

-1 -10 -90 3 4 The closest numbers are -1 and 3, |-1-3|=4, or equivalently |3-

(-1)|=|3+1|=4

Example input Expected output

1 2 3 4 4 5 4

22 3 11.9 22 3 4.5 -12 3 3 22

0 1 2 3 0 1 2 3

Type Description

Median Middle value separating the greater and lesser halves of a data set

Mode Most frequent value in a data set

summarizing-quantitative-data/mean-median-basics/a/meanmedian-and-mode-review “Markdown Tutorial”)

4.18. Write a program which asks the user to enter n – the

number of numbers he will enter. Then the program should ask

for n numbers and determine if the given array is hacksaw. We

call a sequence of numbers hacksaw if the following is true:

or

4.19. Write a function with signature bool checkDate(const

char* text), which verifies if the input parameter is a

correct date in DD.MM format. Do not use string.

4.20. Write a function which takes four arguments – a sorted

in increasing order int array, first index and last index of

the searched interval and wanted value x. Using the algorithm

“binary search”, the function should return the index of x if

it exists in the array, or -1 if it does not exist.

4.21. Write a program which prints on the console the

elements of the longest strictly increasing subsequence in a

locally defined array. In case there are two sequences with

the same length, print the first one.

4.22. Write a function which prints all the combinations of

elements from an array of integers arr, with sum equals to a

natural number N.

a0 < a1 a2 < a3 a4 < a5 . . . an a0 a1 < a2 a3 < a4 a5 . . . an

Example input Expected output

3 1 4 1 yes

3 4 1 4 yes

6 1 3 2 8 9 4 no

7 0 1 0 1 0 1 0 yes

4 4 -8 19 22 no

4 4 -8 19 19 no

Example input Expected output

-4 -2 8 9 0 1 2 3 -4 2 -4 2 8 9

3 9 0 2 1 3 4 6 9 1 3 4 6 9

4.23. Write a function with signature size_t checkNums(long

num1, long num2) , which returns a pointer to an array

containing all the digits encountered both in num1 and num2.

4.24. Write a bool function which checks whether a set is a

subset of another set.

4.25. Write a program that finds the most frequent number in

a given sequence of numbers. In case of multiple numbers with

the same maximal frequency, print all of them, ordered from

smallest to largest, separated by spaces.

4.26. Given two sequences (of numbers) and

sorted in ascending order. Write a function that

merges the two sequences in one new sequence with ascending

ordered elements consisting of the elements of the

first two sequences. Do not use sorting algorithms. Use the

condition that the first two sequences are sorted in

ascending order. The complexity of your function must be

.

4.27. In number theory, a Carmichael number is a composite

number n which satisfies the modular arithmetic congruence

relation: for all integers b which are relatively

prime to n. They are named after [Robert Carmichael](https://

en.wikipedia.org/wiki/Robert_Daniel_Carmichael “Markdown

Tutorial”). An alternative and equivalent definition of

Carmichael numbers is given by [Korselt’s criterion](https://

en.wikipedia.org/wiki/Carmichael_number “Markdown Tutorial”):

A positive composite integer n is a Carmichael number if and

only if n is square-free (a square-free integer is an integer

which is divisible by no perfect square other than 1), and

for all prime divisors p of n, it is true that .

Write a program that checks if a positive integer is a

Carmichael number using Korselt’s criterion.

Example input Expecte

d output Explanation

12

4 1 1 4 2 3 4 4 1 4 9 3 4 The number 4 is the most frequent (occurs 5 times)

8

2 2 2 2 1 2 2 2 2 The number 2 is the most frequent (occurs 7 times)

11

7 7 7 0 2 2 2 0 9 9 9 2 7 9 The numbers 2, 7 and 9 have the same maximal frequency (each

occurs 3 times)

a1, a2, . . . , an

b1, b2, . . . , bm

c1, c2, . . .

O(n + m)

bn ≡ b(modn)

p − 1 ∣ n − 1

4.28. Write a program which finds the sum of the polynomials

and

.

4.29. Write a program which finds the product of the

polynomials and

.

4.30. Write a program which finds the k-th power of the

polynomial , where

is a given number.

github.com/andy489

Pn(x) = an . xn + an−1 . xn−1 + . . . + a1 . x + a0

Qm(x) = bn . xn + bn−1 . xn−1 + . . . + b1 . x + b0

Pn(x) = an . xn + an−1 . xn−1 + . . . + a1 . x + a0

Qm(x) = bn . xn + bn−1 . xn−1 + . . . + b1 . x + b0

Pn(x) = an . xn + an−1 . xn−1 + . . . + a1 . x + a0 k = 0,1,2,…