The 15-puzzle problem The 15-puzzle is a larger version of the 8-puzzle. Goal: 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Initial 11 5 2 1 14 8 10 15 4 13 6 9 12 3 7 For this assignment, you will implement the two uninformed search algorithms that find solutions to the 15-puzzle problem. You are requested to implement the programs to the 15-puzzle problem using: 1. Depth-first search (DFS) 2. Breadth-first search (BFS) For each of the search routines, avoid returning to states that have already been visited on the current solution path i.e., there should be no repeated states in a solution. CS580 only: Your programs should also be able to accept arbitrary initial states and find solutions for these states. Please give proper explanation and typed answer only.

The 15-puzzle problem The 15-puzzle is a larger version of the 8-puzzle. Goal: 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Initial 11 5 2 1 14 8 10 15 4 13 6 9 12 3 7 For this assignment, you will implement the two uninformed search algorithms that find solutions to the 15-puzzle problem. You are requested to implement the programs to the 15-puzzle problem using: 1. Depth-first search (DFS) 2. Breadth-first search (BFS) For each of the search routines, avoid returning to states that have already been visited on the current solution path i.e., there should be no repeated states in a solution. CS580 only: Your programs should also be able to accept arbitrary initial states and find solutions for these states. Please give proper explanation and typed answer only.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter16: Searching, Sorting And Vector Type

Section: Chapter Questions

Problem 16SA

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Assuming, starting from the top left, rows and columns are indexed from 0 on a chessboard, one can solve the N-queens problem, with N any positive integer, with the following pseudo code: placeQueen (row) { for(col = 0; col < N; ++col) { if board [row][col] is open { place queen in board [row][col] if(row < N) placeQueen(row+1) else done remove queen from board[row][col] } } } Is this an example of excessive recursion? Give a reason.
Computer Science There is an n × n grid of squares. Each square is either special, or has a positive integer costassigned to it. No square on the border of the grid is special.A set of squares S is said to be good if it does not contain any special squares and, starting fromany special square, you cannot reach a square on the border of the grid by performing up, down,left and right moves without entering a cell belonging to S. 5 3 4 9 4 X 3 6 1 9 X 4 1 2 3 5 - Design an algorithm which receives an arbitrary n × n grid, runs in time poly-nomial in n and determines a good set of squares with minimum total cost.
Problem 2: Search an ArrayConsidering the search problem, we have a list of n integers A = ⟨v1, v2, · · · vn⟩. We wantto design an algorithm to check whether an item v exists or not such that it should returneither the index, i, if it was found or −1 otherwise, when not found.a) Implement the algorithm in Pythonb) Empirically, show the performance curve of the algorithm using time measurements.c) Using the basics of the theoretical analysis, write the complexity of its worst-casetime.d) Prove your algorithm is correct—it terminates with the valid output in every case
PLEASE USE PYTHONGiven a jungle matrix NxM:jungle = [ [1, 0, 0, 0], [1, 1, 0, 1], [0, 1, 0, 0], [1, 1, 1, 1,]]Where 0 means the block is dead end and 1 means the block can be used in the path fromsource to destination.Task:Starting at position (0, 0), the goal is to reach position (N-1, M-1).Your program needs to build and output the solution matrix – a 4x4 matrix with 1’s inpositions used to get from the starting position (0,0) to the ending position (N-1,M-1)with the following constraints:You can only move one space at a timeYou can only in two directions: forward and down.You can only pass thru spaces on the jungle matrix marked ‘1’If you cannot reach the ending position – print a message that you’re trapped in thejungleAlgorithm:If destination is reachedprint the solution matrixElseMark current cell in the solution matrixMove forward horizontally and recursively check if this leads to a solution If there is no solution, move down and recursively check if this leads to a solution If…
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.
(b) Now assume that one is given another list Bn = {bi}ni=1 of n distinct positive integers whosemedian mB is already known. Develop an algorithm that returns the sum of the twoelements with value closest to mB, such that one of them is greater than mB and the otheris lower than mB. Although sorting Bn would yield a quick solution, we will see later onthat this is a exhorbitantly slow process and one can solve the problem without sortingBn in singnificantly faster time. Hence, in your solution, Do Not Sort Bn and propose asolution that goes without Sorting. (c) State a loop invariant for the algorithm you proposed in part (b) above.(d) Prove the loop invariant you proposed in part (c) above.
The code of a sequential search function is shown on textbook page 60. In fact, if the list is already sorted, the search can halt when the target is less than a given element in the list. For example, given my_list = [2, 5, 7, 9, 14, 27], if the search target is 6, the search can halt when it reaches 7 because it is impossible for 6 to exist after 7. Define a function linearSearchSorted, which is used to search a sorted list. This function displays the position of the target item if found, or ‘Target not found’ otherwise. It also displays the elements it has visited. To test your function, search for these targets in the list [2, 5, 7, 9, 14, 27]: 2, 6, 14, 27 and 28.
Written in C: Hello, I'm writing an insertion sort element, to insert countries from a text file into a list that's alphabetically ordered. I have a fully functioning sorting algorithm, but I'm experiencing a bug: The output should be: AustriaAustriaCanada ItalyJapanNew ZealandRepublic of IrelandRussiaScotlandUkraineUnited KingdomUnited States of AmericaWales PROBLEM: However, The output I'm receiving from this sort algorithm is AustriaAustriaCanadaItalyJapanNew ZealandRepublic of IrelandRussiaScotlandUkraineUnited KingdomUnited States of AmericaWales AS YOU CAN SEE, IT BUNCHES UP WORDS SUCH AS CANADA & ITALY Above. I have no idea why this is happening. It only happens with some words and not others. HERE IS MY SORTING ALGORITHM CODE for (int i = 0; i < count-1 ; i++)//sorting algorithm using selection sort{for (int j = i + 1; j < count; j++){if (strcmp(country[i], country[j]) > 0){strcpy(temp, country[i]);strcpy(country[i], country[j]);strcpy(country[j],…
Problem 1: Euclid’s algorithm (or the Euclidean algorithm) is an algorithm that computes thegreatest common divisor, denoted by gcd, of two integers. Below are the original versions ofEuclid’s algorithm that uses repeated subtraction and another one that uses the remainder.int gcd_sub(int a, int b){ if (!a) return b; while (b) if (a > b) a = a – b; else b = b – a; return a;}int gcd_rem(int a, int b){ int t; while (b) { t = b; b = a % b; a = t; } return a;}1. Trace each of the above algorithm using specific values for a and b.2. Compare both algorithms.Problem 2: Given a fixed integer B (B ≥ 2), we demonstrate that any integer N (N ≥ 0) can bewritten in a unique way in the form of the sum of p+1 terms as follows:N = a0 + a1×B + a2×B2 + … + ap×Bpwhere all ai, for 0 ≤ i ≤ p, are integer such that 0 ≤ ai ≤ B-1.The notation apap-1…a0 is called the representation of N in base B. Notice that a0 is theremainder of the Euclidean division of N by B. If Q is the quotient, a1 is the remainder…
You will analyze three algorithms to solve the maximum contiguous subsequence sum problem, and then evaluate the performance of instructor-supplied implementations of those three algorithms. You will compare your theoretical results to your actual results in a written report. What is the maximum contiguous subsequence sum problem? Given a sequence of integers A1, A2, ..., An (where the integers may be positive or negative), find a subsequence Aj, ... , Ak that has the maximum value of all possible subsequences. The maximum contiguous subsequence sum is defined to be zero if all of the integers in the sequence are negative. Consider the sequence shown below. A1: -2 A2: 11 A3: -4 A4: 13 A5: -5 A6: 2 The maximum contiguous subsequence sum is 20, representing the contiguous subsequence in positions 2, 3, and 4 (i.e. 11 + (-4) + 13 = 20). The sum of the values in all other contiguous subsequences is less than or equal to 20. Consider a second sequence, shown below. A1: 1…
Suppose that the first, second and third steps of the operation of the best first search algorithmresults in the following situations a. What node will be expanded at the next step?b. Can we guarantee that the best solution will be found?
1. You, Alice and Bob are working on recursive search algorithms and have been studying avariant of binary search called trinary search. Alice has created the following pseudocodefor this algorithm:TSearch(A[a...b], t)If a > b return -1Let p1 = a + Floor((b - a)/3)If A[p1] = t return p1If A[p1] > t return TSearch(A[a...p1-1],t)Let p2 = a + Ceiling(2(b - a)/3)If A[p2] = t return p2If A[p2] > t return TSearch(A[p1+1...p2-1],t)Return TSearch(A[p2+1...b],t)EndTSearcha) State a recurrence relation that expresses the number of operations carried out bythis recursive algorithm when called on an input array of size n.b) Bob has heard that trinary search is no more efficient than binary search whenconsidering asymptotic growth. Help prove him correct by using induction to showthat your recurrence relation is in Θ(log2 n) as well.i. Split the tight bound into and upper (big-O) and lower (big-Ω).ii. For each bound select a function from Θ(log2 n) to use in your proof, likea log2 n or a…