et G: (0,1)" (0,1)"+l be defined as follows: (X1. ....x,) = (X, x, OX2, X OX2 O X3,X x2 ... x, X). Prove or disprove is a PRG.
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- Consider eight points on the Cartesian two-dimensional xx-yy plane. For each pair of vertices uu and vv, the weight of edge uvuv is the Euclidean (Pythagorean) distance between those two points. For example, dist(a,h) = \sqrt{4^2 + 1^2} = \sqrt{17}dist(a,h)=42+12=17 and dist(a,b) = \sqrt{2^2 + 0^2} = 2dist(a,b)=22+02=2. Using the algorithm of your choice, determine one possible minimum-weight spanning tree and compute its total distance, rounding your answer to one decimal place. Clearly show your steps.Consider the set F = {1, −1, i, −i} with an operation ✕ defined by the table. ✕ 1 −1 i −i 1 1 −1 i −i −1 −1 1 −i i i i −i −1 1 −i −i i 1 −1 a ✕ b means find the entry in row a and column b; for example, −1 ✕ (−i) = i (the entry in row −1 and column −i). Find each of the following. (a) −1 ✕ i (b) i ✕ i (c) −i ✕ i (d) −i ✕ 1 (e) 1 ✕ i (f) −i ✕ −iProblem Alice was given a number line containing every positive integer, x, where 1<=x<=n. She was also given m line segments, each having a left endpoint, l (1<=l<=n), a right endpoint, r (1<=r<=n), and an integer weight, w. Her task is to cover all numbers on the given number line using a subset of the line segments, such that the maximum weight among all the line segments in the chosen subset is minimal. In other words, let S=(l1,r1,w1),(l2,r2,w2),....,(lk,rk,wk), represent a set of k line segments chosen by Alice, max(w1,w2,...,wk) should be minimized. All numbers 1,2,....n should be covered by at least one of k the chosen line segments. It is okay for the chosen line segments to overlap. You program should output the minimized maximum weight in the chosen subset that covers all the numbers on the number line, or -1 if it is not possible to cover the number line. Input format The first line of the input contains an integer, n - denoting the range of numbers…
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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.Implement a commonly used hash table in a program that handles collision using linear probing. Using (K mod 13) as the hash function, store the following elements in the table: {1, 5, 21, 26, 39, 14, 15, 16, 17, 18, 19, 20, 111, 145, 146}. Use c++Consider a graph that is represented as below in python D={'A':{'V','Z'},'K':{'R','V'}, 'R':{'A','Z','V'},'V':{'K','A','F'},'Z':{'A','F'},'F':{}} construct a function in PYTHON that takes a dict like D and a node N and get length of the lengthiest path from N to final state without repeating nodes which is the empty dictonary.It is F for dict d length_extreme(D,'A') should give us 6. for reference lengthiest path is A,V,K,R,Z,F CANNOT import any libraries, CAN use only loops,recursion,map,filter and fold.
- 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…The Virtual Weight (VW) of an integer number (which consists of more than 1 digit) is the sumof the individual digits that are composing the number. For example, consider the followingtwo numbers; 5638 and 1145, then the VW of each is calculated as following:VW(5638) = 5+6+3+8 = 22VW(1145) = 1+1+4+5 = 11Then, the VW can be classified as L (mean Low) or H (means High) using a specific cut-offvalue. For example, if the cut-off value is 15, then the VW of the number 5638 is H (High),and the VW of the number 1145 is L because 22 > 15 and 11 ≤ 15 respectivelyWrite a C++ program that: reads a positive integer n (where 5≤n≤20) from the user. If the user enters invalidnumber, then the program should continue prompting until he/she enters a valid numberwithin the specified range. Then, the program should generate n random numbers using the built-in rand()function. Every time a random number is generated, the program will classify that number as Lor H using the above method. Use a…Implement a program in python to solve the 8 Queens Problem using a genetic algorithm. The aim of the N-Queens Problem is to place N queens on an N x N board, in a way so that none of them can attack the other (means when any queen moves in directions vertical, horizontal and diagonal no other queen found in the path)