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Homework 4: Arrays

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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,…

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