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- In order to beat AlphaZero, Grandmaster Hikaru is improving her chess calculation skills.Today, Hikaru took a big chessboard with N rows (numbered 1 through N) and N columns (numbered 1 through N). Let's denote the square in row r and column c of the chessboard by (r,c). Hikaru wants to place some rooks on the chessboard in such a way that the following conditions are satisfied:• Each square of the board contains at most one rook.• There are no four rooks forming a rectangle. Formally, there should not be any four valid integers r1, c1, r2, c2 (≠r2,c1≠c2) such that there are rooks on squares (r1,c1), (r1,c2 (r2,c1)and (r2,c2).• The number of rooks is at least 8N.Help Hikaru find a possible distribution of rooks. If there are multiple solutions, you may find any one. It is guaranteed that under the given constraints, a solution always exists.InputThe first line of the input contains a single integer T denoting the number of test cases. The first and only line of each test case contains…You are given a grid having N rows and M columns. A grid square can either be blocked or empty. Blocked squares are represented by a '#' and empty squares are represented by '.'. Find the number of ways to tile the grid using L shaped bricks. A L brick has one side of length three units while other of length 2 units. All empty squares in the grid should be covered by exactly one of the L shaped tiles, and blocked squares should not be covered by any tile. The bricks can be used in any orientation (they can be rotated or flipped). Input Format The first line contains the number of test cases T. T test cases follow. Each test case contains N and M on the first line, followed by N lines describing each row of the grid. Constraints 1 <= T <= 501 <= N <= 201 <= M <= 8Each grid square will be either '.' or '#'. Output Format Output the number of ways to tile the grid. Output each answer modulo 1000000007. Sample Input 3 2 4 .... .... 3 3 ...…5. Let R = {1, 3, π, 4, 1, 9, 10}, S = {{1}, 3, 9, 10}, T = {1, 3, π}, and U = {{1, 3, π}, 1}. Which of thefollowing are true? For those that are not, why not? (d) 1 ⊆ U(e) {1} ⊆ T(f) {1} ⊆ S(g) {1} ∈ S
- Can you help me with this code because I am struggling how to do this, I added the code that need to be work with in the photo.: question: Develop a solver for the n-queens problem: n queens are to be placed on an n x n chessboard so that no pair of queens can attack each other. Recall that in chess, a queen can attack any piece that lies in the same row, column, or diagonal as itself. A brief treatment of this problem for the case where n = 8 is given below (from the 3rd edition of AIMA). N-queens is a useful test problem for search, with two main kinds of formulation. An incremental formulation involves operators that augment the state description, starting with an empty state; for the 8-queens problem, this means that each action adds a queen to the state. A complete-state formulation starts with all 8 queens on the board and moves them around. (In either case, the path cost is of no interest because only the final state counts.) The first incremental formulation one might try is…Correct answer will be upvoted else downvoted. Computer science. first move is made by Alice, the second — by Bob, the third — by Alice, etc. During their turn, the player should pick one of the chips from the board and move it any sure number of cells to one side (along these lines, if the chip was in segment I, it can move to any segment j<i, and the chips in the furthest left segment can't be picked). Alice and Bob have q sets of numbers Li and Ri. For each such pair, they need to figure out who will be the victor of the game if l=Li and r=Ri. Note that these games ought to be thought about freely (they don't influence the condition of the board for the following games), and both Alice and Bob play ideally. Input The main line contains two integers n and m (1≤n,m≤2⋅105) — the number of lines and segments on the board, separately. The subsequent line contains n integers c1,c2,… ,cn (1≤ci≤m), where ci is the file of the segment where the chip in the I-th line is…To have random-access lookup, a grid should have a scheme for numbering the tiles.For example, a square grid has rows and columns, which give a natural numberingfor the tiles. Devise schemes for triangular and hexagonal grids. Use the numberingscheme to define a rule for determining the neighbourhood (i.e. adjacent tiles) of agiven tile in the grid. For example, if we have a four-connected square grid, wherethe indices are i for rows and j for columns, the neighbourhood of tile i, j can bedefined asneighbourhood(i, j) = {i ± 1, j,i, j ± 1}
- Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b}, Find A1 × A2, (A1 × A2) × A3, A1 × A2 × A3.Correct answer will be upvoted else downvoted. Computer science. You are given a network a comprising of positive integers. It has n lines and m segments. Build a lattice b comprising of positive integers. It ought to have a similar size as a, and the accompanying conditions ought to be met: 1≤bi,j≤106; bi,j is a numerous of ai,j; the outright worth of the contrast between numbers in any adjoining pair of cells (two cells that share a similar side) in b is equivalent to k4 for some integer k≥1 (k isn't really something similar for all sets, it is own for each pair). We can show that the appropriate response consistently exists. Input The primary line contains two integers n and m (2≤n,m≤500). Every one of the accompanying n lines contains m integers. The j-th integer in the I-th line is ai,j (1≤ai,j≤16). Output The output ought to contain n lines each containing m integers. The j-th integer in the I-th line ought to be bi,j.Given X = {1, 2, 5, 8, 9}, Y = {3, 4, 6, 7, 8}, Z = {1, 2, 4, 6, 8} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Findthe following: 1. (X -Z̅) ∪ Y2. (X̅ ∪ Z) ∩ Y3. (Y ∩̅Z) ∩ X4. (X ∩ Z) - (X ∪ Y)5. Z̅ – (Y ∩ X)
- There’s a famous puzzle intended to demonstrate the surprising growth of exponentiation sequences,sometimes called the “Wheat and chessboard problem”:If a chessboard were to have wheat placed upon each square such thatone grain was placed on the first square, two on the second, four on thethird, and so on (doubling the number of grains on each subsequentsquare), how many grains of wheat would be on the chessboard at thefinish?There are 64 squares on a chessboard. Write a program that uses a for loop to calculate the answerComputer 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.As discussed in Class 05, cryptography is the area of mathematics intended for the study of techniques and principles for transforming information from its original form to another, unintelligible form, so that it can be used only when authorized. According to the definition of encryption, carefully analyze the following situation presented below: For the transmission of encrypted messages between two points A and B, A generates a private key and forwards it to B, A encrypts the message using this same private key and sends this message to B, upon receiving the message, B decrypts the message with the same private key. Regarding the situation presented above, mark the alternative that corresponds to the encryption mode used. A) Cryptographic Abstract;B) Asymmetrical;C) Digital Certification;D) Symmetrical;E) Digital Signature.