We are given a two-dimensional board of size N × M (N rows and M columns). Each field of the board can be empty ('.'), may contain an obstacle ('X') or may have a character in it. The character might be either an assassin ('A') or a guard. Each guard stands still and looks straight ahead, in the direction they are facing.Every guard looks in one of four directions (up, down, left or right on the board) and is represented by one of four symbols. A guard denoted by '<' is looking to the left; by '>', to the right; '^', up; or 'v', down. The guards can see everything in a straight line in the direction in which they are facing, as far as the first obstacle ('X' or any other guard) or the edge of the board.The assassin can move from the current field to any other empty field with a shared edge. The assassin cannot move onto fields containing obstacles or enemies.Write a function:bool solution(vector<string> &B);that, given an array B consisting of N strings denoting rows of the array, returns true if is it possible for the assassin to sneak from their current location to the bottom-right cell of the board undetected, and false otherwise.Examples:1. Given B = ["X.....>", "..v..X.", ".>..X..", "A......"], your function should return false. All available paths lead through a field observed by a guard.2. Given B = ["...Xv", "AX..^", ".XX.."], your function should return true. The guard in the second row is blocking the other one from watching the bottom-right square.3. Given B = ["...", ">.A"], your function should return false, as the assassin gets spotted right at the start.4. Given B = ["A.v", ..."], your function should return false. It's not possible for the assassin to enter the bottom-right cell undetected, as the cell is observed.Write an efficient algorithm for the following assumptions:N is an integer within the range [1..500];all strings in B are of the same length M from range [1..500];there is exactly one assassin on the board;there is no guard or wall on B[N−1][M−1];every string in B consists only of the following characters '.', 'X', '<', '>', 'v', '^' and/or 'A'.
Question
We are given a two-dimensional board of size N × M (N rows and M columns). Each field of the board can be empty ('.'), may contain an obstacle ('X') or may have a character in it. The character might be either an assassin ('A') or a guard. Each guard stands still and looks straight ahead, in the direction they are facing.Every guard looks in one of four directions (up, down, left or right on the board) and is represented by one of four symbols. A guard denoted by '<' is looking to the left; by '>', to the right; '^', up; or 'v', down. The guards can see everything in a straight line in the direction in which they are facing, as far as the first obstacle ('X' or any other guard) or the edge of the board.The assassin can move from the current field to any other empty field with a shared edge. The assassin cannot move onto fields containing obstacles or enemies.Write a function:bool solution(vector<string> &B);that, given an array B consisting of N strings denoting rows of the array, returns true if is it possible for the assassin to sneak from their current location to the bottom-right cell of the board undetected, and false otherwise.Examples:1. Given B = ["X.....>", "..v..X.", ".>..X..", "A......"], your function should return false. All available paths lead through a field observed by a guard.2. Given B = ["...Xv", "AX..^", ".XX.."], your function should return true. The guard in the second row is blocking the other one from watching the bottom-right square.3. Given B = ["...", ">.A"], your function should return false, as the assassin gets spotted right at the start.4. Given B = ["A.v", ..."], your function should return false. It's not possible for the assassin to enter the bottom-right cell undetected, as the cell is observed.Write an efficient algorithm for the following assumptions:N is an integer within the range [1..500];all strings in B are of the same length M from range [1..500];there is exactly one assassin on the board;there is no guard or wall on B[N−1][M−1];every string in B consists only of the following characters '.', 'X', '<', '>', 'v', '^' and/or 'A'.
Solution
To solve this problem, we can use a breadth-first search (BFS) algorithm. The idea is to start from the assassin's position and try to reach the bottom-right cell of the board. If we can reach the bottom-right cell without being detected by a guard, we return true; otherwise, we return false.
Here is a step-by-step guide on how to implement this:
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First, we need to find the position of the assassin. We can do this by iterating over the board. Once we find the assassin, we store its position.
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We create a queue for the BFS algorithm and add the assassin's position to it. We also create a visited array to keep track of the cells we have already visited.
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We start the BFS algorithm. While the queue is not empty, we take the first cell from the queue. If this cell is the bottom-right cell, we return true.
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We check the four possible directions the assassin can move (up, down, left, right). If a move leads to a valid and not yet visited cell, we add it to the queue. However, we also need to check if the move leads to a cell that is observed by a guard. We can do this by checking the cells in the direction the guard is looking until we hit an obstacle, another guard, or the edge of the board.
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If we have checked all cells and none of them is the bottom-right cell, we return false.
Here is a Python code snippet that implements this:
def solution(B):
N, M = len(B), len(B[0])
dx = [-1, 0, 1, 0]
dy = [0, 1, 0, -1]
dir = {'<': 3, '>': 1, '^': 0, 'v': 2}
vis = [[False]*M for _ in range(N)]
q = []
for i in range(N):
for j in range(M):
if B[i][j] == 'A':
q.append((i, j))
vis[i][j] = True
while q:
x, y = q.pop(0)
if x == N-1 and y == M-1:
return True
for i in range(4):
nx, ny = x + dx[i], y + dy[i]
while 0 <= nx < N and 0 <= ny < M and B[nx][ny] != 'X':
if B[nx][ny] in dir:
if dir[B[nx][ny]] == i:
break
if not vis[nx][ny]:
q.append((nx, ny))
vis[nx][ny] = True
nx += dx[i]
ny += dy[i]
return False
This algorithm runs in O(N*M) time, which is the best we can do for this problem since we have to check every cell on the board.
Similar Questions
def create_board(size): size = int(size) board = [[' '] * size for i in range(size)] return boarddef is_occupied(board, x, y): if x >= 0 and y >= 0 and board[x][y] != ' ': return True else: return False def place_on_board(board, stone, position): x = int(input('Please enter row line: ')) y = ord(input('Please enter column line: ')) if is_occupied(board, x, y): return False else: board[x][y] = stone return Trueboard = create_board(3)stone = "●"position = (1,2)place_on_board(board, stone, position)
There is rectangle of size 𝑁×𝑀N×M with opposite corners at (0,0)(0,0) and (𝑁,𝑀)(N,M); and a special point (𝑥+0.5,𝑦+0.5) (0≤𝑥<𝑁,0≤𝑦<𝑀)(x+0.5,y+0.5) (0≤x<N,0≤y<M).Two players play a game on the rectangle where each player takes alternate turns. In his/her turn, the player will choose a line, either 𝑥=𝑘x=k or 𝑦=𝑘y=k, such that:𝑘k is an integer;The chosen line divides the current rectangle into two non-empty parts.The part of rectangle that does not consist of the special point, is discarded for further moves.The player who cannot make a move loses. If both players play optimally, determine the number of special points such that the first player wins.Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case contains two space-separated integers 𝑁N and 𝑀M — the lengths of the sides of the rectangle.Output FormatFor each test case, print the number of special points (𝑥+0.5,𝑦+0.5)(x+0.5,y+0.5) for which the first player wins the game.Note that 0≤𝑥<𝑁0≤x<N and 0≤𝑦<𝑀0≤y<M.Constraints1≤𝑇≤1041≤T≤10 4 1≤𝑁,𝑀≤1061≤N,M≤10 6 The sum of 𝑁N as well as the sum of 𝑀M over all test cases does not exceed 10610 6 .Sample 1:InputOutput42 12 23 51 120100Explanation:Test case 11 : There are 22 possible special points (0.5,0.5)(0.5,0.5) and (1.5,0.5)(1.5,0.5). In both cases, the first player can select the line 𝑥=1x=1 on his first move, and then the second player is left with no moves. Thus, the first player wins for both the special points.Test case 22 : There are 44 possible special points, all of them end up losing for the first player.
Given an m x n grid of characters board and a string word, return true if word exists in the grid.The word can be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once.
Given a 2D grid consists of 0s (land) and 1s (water). An island is a maximal 4-directionally connected group of 0s and a closed island is an island totally (all left, top, right, bottom) surrounded by 1s.Return the number of closed islands.Input FormatThe First line contains two integers denoting the value of n and mThe Next N lines contains M integers denoting the elements of the matrix.Constraints1 <= grid.length, grid[0].length <= 1000 <= grid[i][j] <=1Output FormatPrint a integer which is the answer to the question.Sample Input 03 50 0 1 0 00 1 0 1 00 1 1 1 0Sample Output 01Sample Input 13 41 0 1 1 1 1 1 1 1 1 1 1 Sample Output 10
My First Geometry ProblemYou are on a 22-dimensional grid, where you start at (0,0)(0,0).You are given a binary string 𝑆S of length 44 where:𝑆1S 1 refers to left direction;𝑆2S 2 refers to right direction;𝑆3S 3 refers to up direction;𝑆4S 4 refers to down direction.𝑆𝑖=1S i =1 denotes that you are allowed to make a move in the respective direction and vice-versa.Find the number of cells (𝑥,𝑦)(x,y) you can possibly visit which satisfy −10≤𝑥,𝑦≤10−10≤x,y≤10.Note that:You always include the cell (0,0)(0,0) in your answer.If you can visit (𝐴1,𝐵1)(A 1 ,B 1 ) and (𝐴2,𝐵2)(A 2 ,B 2 ) individually, but not both at the same time, you will still include both of them in your answer.Moves are defined as:A move in left direction is a move from cell (𝐴,𝐵)(A,B) to (𝐴−1,𝐵)(A−1,B).A move in right direction is a move from cell (𝐴,𝐵)(A,B) to (𝐴+1,𝐵)(A+1,B).A move in up direction is a move from cell (𝐴,𝐵)(A,B) to (𝐴,𝐵+1)(A,B+1).A move in down direction is a move from cell (𝐴,𝐵)(A,B) to (𝐴,𝐵−1)(A,B−1).Input FormatThe first line of input will contain a single integer 𝑇T, denoting the number of test cases.Each test case consists of a binary string 𝑆S of length 44 - denoting the directions in which moves are allowed.Output FormatFor each test case, output on a new line, the number of cells you can visit as mentioned in statement.Constraints1≤𝑇≤151≤T≤15∣𝑆∣=4∣S∣=4𝑆𝑖∈{0,1}S i ∈{0,1}𝑆𝑖=1S i =1 for at least one 1≤𝑖≤41≤i≤4.Sample 1:InputOutput5001011000110111011111121121231441Explanation:Test case 11: The only allowed direction is up. Thus, you can only visit cells (0,0),(0,1),(0,2),…,(0,10)(0,0),(0,1),(0,2),…,(0,10); which are a total of 1111 cells.Test case 22: The allowed directions are left and right. Thus, you can visit cells (−10,0),(−9,0),…,(0,0),…,(9,0),(10,0)(−10,0),(−9,0),…,(0,0),…,(9,0),(10,0), which are a total of 2121 cells.Test case 33: The allowed directions are right and up. You can visit all cells (𝑥,𝑦)(x,y) such that 𝑥≥0x≥0 and 𝑦≥0y≥0, which are a total of 121121 cells.Accepted195Submissions293
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