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- In computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem. Following is the problem statement: There are n people standing in a circle waiting to be executed. The counting out begins at some point (rear) in the circle and proceeds around the circle in a fixed direction. In each step, a certain number (k) of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. Given the total number of persons n and a number k which indicates that k-1 persons are skipped and kth person is killed in circle. The task is to choose the place in the initial circle so that you are the last one remaining and so survive. For example, if n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1…Please do not give solution in image formate thanku. Write a Python code for the following scenario : 1: Use Breadth First Search and Recursive Best First Search and implement the algorithms in Python. The program should be able to dynamically take in start and goal nodes from the user at run time. Compare to interpret the results in terms of the algorithm working, performance & shortest path if obtained relevant to the given problem 2: Print the minimum connections that keep the whole network up and running. For each incremental depth limit, the corresponding node generating sequence should be legibly printed in the result Consider Heuristic Value as : The edge cost is an approximation towards the transmission cost between any pair of nodes. For heuristic design, consider all the possible paths between any arbitrary node n to the goal node. The average of the total transmission cost across all these paths is the heuristic value h(n) Consider the following undirected graph…Sudoku is a popular logic puzzle that uses a 9 by 9 array of squares that are organized into 3 by 3 subarrays. The puzzle solver must fill in the squares with the digits 1 to 9 such that no digit is repeated in any row, any column, or any of the nine 3 by 3 subgroups of squares. Initially, some squares are filled in already and cannot be changed. For example, the following might be a starting configuration for a Sudoku puzzle: Create a class SudokuPuzzle.java Download SudokuPuzzle.java that has the attributes • board—a 9 by 9 array of integers that represents the current state of the puzzle, where 0 indicates a blank square • start—a 9 by 9 array of boolean values that indicates which squares in board are given values that cannot be changed and the following methods: • SudokuPuzzle—a constructor that creates an empty puzzle • toString—returns a string representation of the puzzle that can be printed • addInitial(row, col, value)—sets the given square to the given value as an…
- 4. Consider the function IndexEqual(A,i.j) that returns true if there exists an index x (i sx sj) such that A[x] = x; otherwise, retums false. You may assume A is a sorted integer array in which every element is unique. a. Write an efficient recursive algorithm for IndexEqual(A,i.j). b. What is the situation resulting in the best-case running time of your function, and give an expression for that running time? c. What is the situation resulting in the worst-case running time of your function, and give an expression for that running time in terms of n, where n=j-i+1?Implement the Greedy Algorithm discussed for the problem below, inC++. Using C++, implement the given problem below. (Greedy Algorithm) Given an array of size n that has the following specifications:1.Each element in the array contains either a policeman or a thief.2.Each policeman can catch only one thief.3.A policeman cannot catch a thief who is more than K units away from the policeman. We need to find the maximum number of thieves that can be caught. Examples: Input arr[] = {'P', 'T', 'T', 'P', 'T'}, k = 1.Output: 2.Here maximum 2 thieves can be caught, first policeman catches first thief and second police- man can catch either second or third thief.Input = arr[] = {'T', 'T', 'P', 'P', 'T', 'P'}, k = 2.Output: 3.Input arr[] = {'P', 'T', 'P', 'T', 'T', 'P'}, k = 3.Output: 3. Copy the code. Show the algorithm use. Don't copy code from other sites.Java: Consider the following algorithm for searching in an unsorted array. If the size of the array is 1, then check if it contains the element to be searched. Otherwise, divide the array into two halves, and recursively search both halves. Which of (a)–(c) is false? The running time of this algorithm is O(N) The actual running time of this algorithm is likely to be better than sequential search. This is an example of a divide‐and‐conquer algorithm all of the above are true none of the above is true
- 1. Analyze the word finder with wild card characters scenario to form the algorithm and compute the time complexity. You are given a list of characters with size n, m. You need to read character data provided as input into this list. There is also a list of p words that you need to find in the given problem. You can only search in left, right, up and down direction from a position. There are two wild characters *' and '+' ,if there is any instance of wild card characters for example '+' appears you can match whatever character in your word that you are searching at this position (only one character). Similarly, if you got wildcard *' you can skip any number of characters ( A sequence of characters not necessary same in between the characters) but the last character should be matched in the given data. This means you are not allowed to match a first and last character with *' wildeard. Input: The first line of the input will give you two integers n and m. From the next line you will get…Problem 5. Let A be an array of n integers, each of which comes from the domain [1, U]. Note that some of the integers may be identical. Design an algorithm to compute, for each distinct integer x in A, how many integers in A are at most x. For example, if A stores the sequence of integers (35, 12, 28, 12, 35, 7, 63, 35), you should output an array ((7, 1), (12, 3), (28, 4), (35, 7), (63, 8)). Your algorithm should terminate in O(n log n) time.4. Write the pseudocode for an algorithm that takes as input a list of numbers that are sorted in nondecreasing order, and finds the location(s) of the most frequently occurring element(s) in the list. If there are more than one element that is the most frequently occurring, then return the locations of all of them. Analyze the worst-case time complexity of this algorithm and give the O() estimate. (A list is in nondecreasing order if each number in the list is greater than or equal to the number preceding it.)
- Consider an n by n matrix, where each of the n2 entries is a positive integer. If the entries in this matrix are unsorted, then determining whether a target number t appears in the matrix can only be done by searching through each of the n2 entries. Thus, any search algorithm has a running time of O(n²). However, suppose you know that this n by n matrix satisfies the following properties: • Integers in each row increase from left to right. • Integers in each column increase from top to bottom. An example of such a matrix is presented below, for n=5. 4 7 11 15 2 5 8 12 19 3 6 9 16 22 10 13 14 17 24 1 18 21 23 | 26 | 30 Here is a bold claim: if the n by n matrix satisfies these two properties, then there exists an O(n) algorithm to determine whether a target number t appears in this matrix. Determine whether this statement is TRUE or FALSE. If the statement is TRUE, describe your algorithm and explain why your algorithm runs in O(n) time. If the statement is FALSE, clearly explain why no…The intersection of two sets contains the list of elements that are common to both, without repetition. As such, you are required to write an algorithm that finds and returns the intersection of two sets A and B. The sets A and B and the resulting intersection set are all lists. Assume the size of A is n and that of B is m. (a) Write an iterative algorithm that finds the intersection. (b) Prove the correctness of your algorithm; i.e. state its loop invariant and prove it by induc- tion. (c) Analyze the time complexity of your algorithm. (d) Think of a way to enhance the complexity of your algorithm by sorting both lists A and B before calculating their intersection. Write the enhanced version and prove that it has a better time complexity.In this programming assignment, you are expected to design an experimental study for thecomparison between Hoare’s partitioning and Lomuto’s partitioning in Quicksort algorithm.You must implement the recursive Quicksort algorithm using two partitioning algorithms inJava. You must design the experiments for the comparison of two algorithms both theoreticallyand empirically. You must write a detailed report including the pseudo-code of the algorithms,the time complexity of the algorithms, the experimental design, and your results. You canprovide some plots (scatter, line etc.) to illustrate your results.