Условията и решенията на задачите за домашно от раздела масиви.
Array Index
Task: Write a program that allocates array of 20 integers and initializes each element by its index multiplied by 5. Print the obtained array on the console.
Array Comparison
Task: Write a program that reads two arrays from the console and compares them element by element.
Char Array Comparison
Task: Write a program that compares two char arrays lexicographically (letter by letter).
Maximal Sequence
Task: Write a program that finds the maximal sequence of equal elements in an array.
Example: {2, 1, 1, 2, 3, 3, 2, 2, 2, 1} -> {2, 2, 2}.
Maximal Increasing Sequence
Task: Write a program that finds the maximal increasing sequence in an array.
Example: {3, 2, 3, 4, 2, 2, 4} -> {2, 3, 4}.
Maximal Sum Array
Task: Write a program that reads two integer numbers N and K and an array of N elements from the console. Find in the array those K elements that have maximal sum.
Selection Sort Algorithm
Task: Sorting an array means to arrange its elements in increasing order. Write a program to sort an array. Use the „selection sort“ algorithm: Find the smallest element, move it at the first position, find the smallest from the rest, move it at the second position, etc.
Sequence of Maximal Sum
Task: Write a program that calculates the greatest common divisor (GCD) of given two numbers. Use the Euclidean algorithm (find it in Internet).Write a program that finds the sequence of maximal sum in given array. Example: {2, 3, -6, -1, 2, -1, 6, 4, -8, 8} -> {2, -1, 6, 4}
Most Frequent Number
Task: Write a program that finds the most frequent number in an array.
Example: {4, 1, 1, 4, 2, 3, 4, 4, 1, 2, 4, 9, 3} -> 4 (5 times)
Sequence of Given Sum
Task: Write a program that finds in given array of integers a sequence of given sum S (if present).
Example: {4, 3, 1, 4, 2, 5, 8}, S=11 -> {4, 2, 5}
Binary Search Algorithm
Task: Write a program that finds the index of given element in a sorted array of integers by using the binary search algorithm (find it in Wikipedia).
Index of Each Letter
Task: Write a program that creates an array containing all letters from the alphabet (A-Z). Read a word from the console and print the index of each of its letters in the array.
Merge Sort Algorithm
Task: Write a program that sorts an array of integers using the merge sort algorithm (find it in Wikipedia).
Quick Sort Algorithm
Task: Write a program that sorts an array of strings using the quick sort algorithm (find it in Wikipedia).
Sieve of Eratosthenes Algorithm
Task: Write a program that finds all prime numbers in the range [1…10 000 000]. Use the sieve of Eratosthenes algorithm (find it in Wikipedia).
Subset of Elements
Task: We are given an array of integers and a number S. Write a program to find if there exists a subset of the elements of the array that has a sum S.
Example: arr={2, 1, 2, 4, 3, 5, 2, 6}, S=14 -> yes (1+2+5+6)
Subset and Sum in Array
Task: Write a program that reads three integer numbers N, K and S and an array of N elements from the console. Find in the array a subset of K elements that have sum S or indicate about its absence.
Increasing Order Sort
Task: Write a program that reads an array of integers and removes from it a minimal number of elements in such way that the remaining array is sorted in increasing order. Print the remaining sorted array.
Example: {6, 1, 4, 3, 0, 3, 6, 4, 5} -> {1, 3, 3, 4, 5}
Number Permutations
Task: Write a program that reads a number N and generates and prints all the permutations of the numbers [1 … N].
Example: n = 3 -> {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}
Variations From Set
Task: Write a program that reads two numbers N and K and generates all the variations of K elements from the set [1..N].
Example: N = 3, K = 2 -> {1, 1}, {1, 2}, {1, 3}, {2, 1}, {2, 2}, {2, 3}, {3, 1}, {3, 2}, {3, 3}
Combinations From Set
Task: Write a program that reads two numbers N and K and generates all the combinations of K distinct elements from the set [1..N].
Example: N = 5, K = 2 -> {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 5}, {4, 5}