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question:If you have ever played Genshin Impact, you must remember “Divine Ingenuity: Collector’s Chapter” event. In this event, players can create custom domains by arranging components, including props and traps, between the given starting point and exit point. Paimon does not want to design a difficult domain; she pursues the ultimate “automatic map”. In the given domain with a size of m × n, she only placed Airflow and Spikes. Specifically, Spikes will eliminate the player (represented by ‘x’), while the Airflow will blow the player to the next position according to the wind direction (up, left, down, right represented by ‘w’, ‘a’, ‘s’, ‘d’, respectively). The starting point and exit point are denoted by ‘i’ and ‘j’, respectively. Ideally, in Paimon’s domain, the player selects a direction and advances one position initially; afterward, the Airflow propels the player to the endpoint without falling into the Spikes. The player will achieve automatic clearance in such a domain. However, Paimon, in her slight oversight, failed to create a domain that allows players to achieve automatic clearance. Please assist Paimon by making the minimum adjustments to her design to achieve automatic clearance. Given that the positions of the starting point and exit point are fixed, you can only adjust components at other locations. You have the option to remove existing component at any position; then, place a new direction of Airflow, or position a Spikes. 1.2 Input The first line of input contains two integers m and n, representing the size of the domain. m lines follow, each containing n characters. The characters must be one of ‘w’, ‘a’, ‘s’, ‘d’, ‘x’, ‘i’ and ‘j’. It is guaranteed that there is only one ‘i’ and ‘j’ on the map, and they are not adjacent. 1.3 Output Output a single integer, representing the minimum number of changes needed. Sample Input 1 3 3 dsi ssd jdd Sample Output 1 1
answer:To achieve automatic clearance in Paimon's domain, we need to make the minimum adjustments to the design. The starting point is represented by 'i' and the exit point is represented by 'j'. We can adjust the components at other locations to create a path without any Spikes in the way. In the given example, the domain is of size 3x3 and the layout is as follows: d s i s s d j d d To achieve automatic clearance, we can make the following adjustment: Change the 'd' at position (3, 2) to 's': d s i s s s j d d By making this adjustment, the player can now choose the 's' direction initially and be blown by the Airflow to the exit point without falling into any Spikes. Therefore, the minimum number of changes needed in this case is 1.
question:请写一个python程序来解决这个问题
answer:以下是解决这个问题的 Python 程序示例： ```python def find_min_adjustments(m, n, domain): # Find the positions of the starting point and exit point start_point = None exit_point = None for i in range(m): for j in range(n): if domain[i][j] == 'i': start_point = (i, j) elif domain[i][j] == 'j': exit_point = (i, j) # Create a function to check if a position is within the domain def is_valid_position(i, j): return 0 <= i < m and 0 <= j < n # Create a function to count the number of spikes adjacent to a position def count_adjacent_spikes(i, j): count = 0 directions = [(0, -1), (-1, 0), (0, 1), (1, 0)] # up, left, down, right for dx, dy in directions: ni, nj = i + dx, j + dy if is_valid_position(ni, nj) and domain[ni][nj] == 'x': count += 1 return count # Create a function to check if a position can be blown to the exit point without falling into spikes def can_reach_exit(i, j): if (i, j) == exit_point: return True spikes = count_adjacent_spikes(i, j) if spikes >= 2: return False directions = {'w': (-1, 0), 'a': (0, -1), 's': (1, 0), 'd': (0, 1)} # wind directions for direction, (dx, dy) in directions.items(): ni, nj = i + dx, j + dy if is_valid_position(ni, nj) and domain[ni][nj] != 'x': if can_reach_exit(ni, nj): return True return False # Count the number of adjustments needed to achieve automatic clearance adjustments = 0 i, j = start_point if not can_reach_exit(i, j): for dx, dy in [(-1, 0), (0, -1), (0, 1), (1, 0)]: ni, nj = i + dx, j + dy if is_valid_position(ni, nj) and domain[ni][nj] != 'x': domain[ni][nj] = 's' adjustments += 1 if can_reach_exit(ni, nj): break return adjustments # Read the size of the domain m, n = map(int, input().split()) # Read the domain layout domain = [] for _ in range(m): row = list(input()) domain.append(row) # Call the function to find the minimum number of adjustments needed result = find_min_adjustments(m, n, domain) # Print the result print(result) ``` 你可以将示例输入粘贴到程序中运行，然后它将输出结果。注意，在输入中的每一行字符之间都有空格。
question:Assume X ∼ Unif(0, 1), Y ∼ EXPO(1) and they are independent. Calculate the pdf of Z = X + Y .
answer:To calculate the probability density function (pdf) of Z = X + Y, where X is a uniform random variable on the interval (0, 1) and Y is an exponential random variable with parameter λ = 1, we need to find the expression for the pdf of Z. Let's start by finding the cumulative distribution function (CDF) of Z and then differentiate it to get the pdf. The CDF of Z is given by: F_Z(z) = P(Z ≤ z) = P(X + Y ≤ z) Since X and Y are independent, we can rewrite the above equation as: F_Z(z) = ∫[0,1] P(X + Y ≤ z | X = x) * f_X(x) dx Note that P(X + Y ≤ z | X = x) is the conditional probability of Y being less than or equal to z - x given that X = x, which is simply P(Y ≤ z - x) since Y is independent of X. Also, f_X(x) is the pdf of X, which is a constant 1 on the interval (0, 1). Therefore, the CDF becomes: F_Z(z) = ∫[0,1] P(Y ≤ z - x) dx = ∫[0,1] (1 - e^(-λ(z - x))) dx Integrating the above expression gives: F_Z(z) = 1 - e^(-λz) * ∫[0,1] e^(λx) dx Evaluating the integral, we get: F_Z(z) = 1 - e^(-λz) * (e^(λ) - 1) Finally, differentiating the CDF with respect to z gives us the pdf of Z: f_Z(z) = d/dz (F_Z(z)) = λe^(-λz) Substituting the value of λ, we get: f_Z(z) = e^(-z) Therefore, the pdf of Z is e^(-z).
question:立方体卫星如何发射，发射平台是什么，用于北极光研究的三个立方体卫星星座应该从什么坐标发射，经纬度是多少
answer:立方体卫星的发射通常是通过火箭将其送入太空。发射平台可以是地面的发射场，也可以是海上的发射平台。 对于用于北极光研究的三个立方体卫星星座，最佳的发射方式是通过极轨卫星发射。极轨卫星是按照南北极方向运行的卫星，其轨道倾角接近于90°，因此能够覆盖极地区域的观测需求。 至于具体的发射经纬度，这取决于发射场的选择以及任务需求。一般来说，北极地区附近的发射场（例如俄罗斯的普列谢茨克发射场）可能更适合发射北极光研究卫星。这些发射场的具体经纬度如下： - 普列谢茨克发射场：位于俄罗斯西部伊尔库茨克州，大约位于北纬62.927°，东经40.577°。 请注意，实际发射经纬度仍然取决于具体的任务规划和发射方案，因此可能不限于上述经纬度。