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## Arrays

1. 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.
• Write a program that reads two arrays from the console and compares them element by element.
• Write a program that compares two char arrays lexicographically (letter by letter).
• 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}.
• Write a program that finds the maximal increasing sequence in an array. Example: {3, 2, 3, 4, 2, 2, 4} -> {2, 3, 4}.
• 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.
• 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.
• 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} Can you do it with only one loop (with single scan through the elements of the array)?
• 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)
• 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}
• Write a program that finds the index of given element in a sorted array of integers by using the Binary search algorithm.
• 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.
• *Write a program that sorts an array of integers using the Merge sort algorithm.
• *Write a program that sorts an array of strings using the Quick sort algorithm.
• Write a program that finds all prime numbers in the range [1...10 000 000]. Use the Sieve of Eratosthenes algorithm.
• * 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: {2, 1, 2, 4, 3, 5, 2, 6}, S=14 -> yes (1+2+5+6)
• * 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.
• * 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}
• * 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}
• 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}
• 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}
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