Suppose that each row of an n x n array A consists of 1's and 0's such that in any row of A all the 1's come before any 0's in that row. Assuming that A is already in memory, describe an algorithm running in O(n) time for finding the row that contains the most 1's. Write the algorithm following the style of your course-notes.
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- Create an array of size one million (1,000,019). Fill it in reverse sequentially with values (e.g. array[0] should equal 1,000,018, array[1] should equal 1,000,017, etc). Then the computer should select a random target number between 0 and array size – 1. You should then search the array for this value twice – once with a linear search algorithm, and then with a binary search algorithm. Start searching from the end of the array, rather than the beginning. Keep track of how long each one took, using the following criteria: Linear Search: Number of loop iterations before the target number was found Binary Search: Number of midpoints chosen (a.k.a “guesses”) taken before the target number was found Once both algorithms have been run, display the results and print which algorithm found the number first (or if there was a tie). Once both algorithms have been run, display the results and print which algorithm found the number first (or if there was a tie). In the rest of this assignment,…You are given a two-dimensional array A with n rows and n columns such that every element is either 1 or 0, and for every row, the 1s are placed ahead of 0s. Find the quickest algorithm to find a row with the most significant number of 1s. Analyze the time complexity of your algorithm.You are given an array A[1, ., n] in which the elements A[2] to A[n] are already sorted, i.e., A[2, .., n] is a sorted array. Write down an efficient algorithm with proper pseudocode for moving A[1] in the correct place, so that the full array A[1, ..., n] is sorted.
- You are asked to sort n English words alphabetically. What is the best achievable complexity? (Note: we are talking about actual English words that can be found in a Marriam-Webster dictionary.) Describe the algorithm that achieves the best complexity.You are given an array in which every number from 1 to N appears precisely once with the exception of one. How is the missing number to be located in O(N) time and 0(1) space? What if two numbers were absent?By Implement a recursive algorithm to find factorial of n,implement a recursive algorithm to find the n-th Fibonacci number.Print all the elements of a given array recursively. Given base and n that are both 1 or more, compute recursively (no loops) the value of base to the n power, so powerN(3, 2) is 9 (3 squared). powerN(3, 1) → 3 powerN(3, 2) → 9 powerN(3, 3) → 27 please do not use any built-in function and complete this task using python 3.Do not copy-paste from other sources.
- There are n different sizes of boxes, from 1 to n. There is an unlimited supply of boxes of each size t, each with a value vt . A box of size t can hold several smaller boxes of sizes a1, a2, . . . , ak as long as the sum of sizes a1 + a2 + . . . + ak is strictly less than t. Each of these boxes may be filled with yet more boxes, and so on. Design an algorithm which runs in O(n2 ) time and finds the maximum value that can be attained by taking one box, potentially with smaller boxes nested inside it.discrete mathDesign an algorithm in pseudo code to rearrange elements of a given array of n real numbers so that all its negative elements precede all its positive elements. Your algorithm should be No worse than Θ(n). Sample input: A = {-1, 4, -4, 3, 5, -2, 7, 8, 9, -10}
- Assume that we are given n pairs of items as input, where the first item is a number and the second item is one of three colors (red, blue, or yellow). Further assume that the items are sorted by number. Give an O(n) algorithm to sort the items by color (all reds before all blues before all yellows) such that the numbers for identical colors stay sorted. For example: (1,blue), (3,red), (4,blue), (6,yellow), (9,red) should become (3,red), (9,red), (1,blue), (4,blue), (6,yellow).The Fibonacci algorithm is a famous mathematical function that allows us to create a sequence of numbers by adding together the two previous values. For example, we have the sequence:1, 1, 2, 3, 5, 8, 13, 21…Write your own recursive code to calculate the nth term in the sequence. You should accept a positive integer as an input, and output the nth term of the sequence.Once you have created your code, add comments describing how the code works, and the complexity of any code you have created.Devise a recursive algorithm for finding n! mod m where n and m are positive integers.