Give the initial state, goal test, successor function, and cost function to transform the following problem into a search problem. Choose a formulation that is precise enough to be implemented. You are not to supply the solutions. ● You have to color a planar map using only three colors, with no two adjacent regions having the same color.
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Q: Oh i forgot to add it must be c language. thank you so much.
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- You are a computer research scientist at Tesla, and your task is to create a computer vision application for self-driving cars to detect object and avoid collision. You know that Graham's scan is a method of computing the convex hull of a finite set of points in the plane. You decide to apply this algorithm to achieve the goal of your task. a) Suppose Graham's scan executes n points, where n >= 3. Prove that, at the end of the program, the stack S consists of, from bottom to top, exactly the vertices of convex hull in counter-clockwise order.The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors v,, v,, and v, because 0 = Ov, + Ov, + 0va. This is called the trivial solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v,, v,, and v. If not possible, enter IMPOSSIBLE.) v, = (1, 0, 1), v, = (-1, 1, 2), v3 = (0, 1, 2) 0 =This is for a Java Progrsm problem but If you could fully explain it to me then I should be okay to try to create this program based off your explaination. Thank you! Trigonometry is needed A pipe is to be carried around a right-angled corner of two intersecting corridors. Suppose that the widths of the two intersecting corridors are 5 feet and 8 feet. Your objective is to find the length of the lingest pipe, rounded to the nearest foot, that can be carried level around the right-angled corner. What I have to do is the following: Write a program that prompts the user to input the widths of both the hallways/ The program then outputs the length of the longest pipe, rounded to the nearest foot, that can be carried level around the right-angled cprner. Note that the length of the pipe os goven by l = AB + BC = 8 /SIN 0 (Omega) + 5 / cos 0(Omega), where 0 < > Omega < pi/ 2
- In a company, there are several branches. Let us consider a branch of that company having N employees, if the manager is allotted to that branch(s) then he is known to everyone else in that branch. Note that the property of "known to everyone" is unique to a manager. Your task is to find the manager in that branch. Input from the user in main ( ), the square matrix M where if an element of row i and column j is set to 1 it means that ith person knows jth person. You need to write a function managerId ( ) which returns the id of the manager if present or else returns -1. The function managerId ( ) takes two arguments - the square matrix of N *N and its size N. Call managerId ( ) from the main ( ) output the information about the manager. Assume all diagonal elements to be 1 (as everyone knows him/herself) and there is at most one manager in the company.Q1. Consider a square centred at (p, q) on a two-dimensional plane. It is subjected to a transformation that reduced the square to half of its original size, but the centre remained unchanged. Deduce the transformation matrix. Q2. Use midpoint method to derive the decision parameters to draw the outline of an arc of radius r, beginning angle α, and sweep angle β. Explain your designed algorithm with suitable examples.Implement an algorithmic solution, indicating which states are valid and which are not, and model the space of the following problem: An interest group from a small town decided to sue a company for commercial abuse. For this, the people have organized themselves and decided to send 3 representatives, who will have to travel in a Van to the city where the lawsuit will be filed. The company to be sued, upon learning of these actions, has decided to send 3 lawyers to persuade the representatives, who will also travel in the same Van for that purpose. The community must file the class action suit under these conditions: - The three applicants must reach the destination city; - Only two people can travel per trip in the Van (small town - city, city - small town); - There can never be more lawyers than plaintiffs in any one place (either in the small town or city) because the lawyers can persuade the plaintiffs and as a consequence, the lawsuit would not be made; - The Van cannot be…
- Here are the arrow diagrams of two maps: Is the map on the right the inverse of the map on the left? O Yes, the map on the right is the inverse of the map on the left. O No. the map on the right is not inverse of the map on the left.Although the plot function is designed primarily for plotting standard xy graphs, it can be adapted for other kinds of plotting as well. b. Make a plot of the curve, which is defined parametrically by the equations x = 2cosθ + cos2θ, y = 2sinθ - sin2θ, where 0 < θ < 2π. Take a set of values of θ between zero and 2π and calculate x and y for each from the equations above, then plot y as a function of x. b. Taking this approach a step further, one can make a polar plot r = f(θ) for some function f by calculating r for a range of values of θ and then converting r and θ to Cartesian coordinates using the standard equations x = r cosθ, y = r sinθ. Use this method to make a plot of the function r = ecosθ – 2 cos(4θ) + sin5 (θ/12) in the range 0 <= θ <= 24π. use python code to answer the highlight oneIN PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557. The following code format should help: def td(l, m, u, b): '''Solve a linear system Ax = b where A is tridiagonal Inputs: l, lower diagonal of A, n-1 vector m, main diagonal of A, n vector u,…
- Write a Python function that takes in three parameters - an adjacency matrix of a simple directed graph, a start node, and an end node; and returns "True" if there is a way to get from the start node to the end node using the provided edges. You can use this file as a starter code: path.py ↓ For example: Using the same graph given above. Consider your function with the same adjacency matrix given above as input and: If the start node is 1 and the end node is 4 then your function should return True. If the start node is 2 and the end node is 4 then your function should return False. Input: This function will have three parameters. First is an adjacency matrix in the form of a list of lists (as given above). Then the start_node and the end_node will be integers. Note that python indexing starts from 0 and not from 1, so the naming of the nodes will also follow the python convention and start from 0 instead of 1. Output: Boolean value: True or False.1. solve a system of ordinary differential equations of first order numerically using solve_ivp. 2. generate plots after "solving" the differential equations using matplotlib.pyplot. In that tutorial, the equations of motion described the dynamics of a simple pendulum. In this problem, you will investigate the motion of a satellite orbiting the Earth. This is modelled as a two-body dynamics system. A brief outline of what you need to do in this problem set is below and that is followed by a systematic set of questions towards achieving specific objectives. You will find the tutorial a handty reference here. In this problem, you will have to first create a Python function called twobody_dynamics_first_order_EOMS. Given a time t and a state vector X, this function will return the derivatives of the state vector. Mathematically, this means you are computing X using some dynamics equation X = f(t, X). Once you have this function in Python, you can solve the differential equations it…You will be given a square chess board with one queen and a number of obstacles placed on it. Determine how many squares the queen can attack. A queen is standing on an chessboard. The chess board's rows are numbered from to , going from bottom to top. Its columns are numbered from to , going from left to right. Each square is referenced by a tuple, , describing the row, , and column, , where the square is located. The queen is standing at position . In a single move, she can attack any square in any of the eight directions (left, right, up, down, and the four diagonals). In the diagram below, the green circles denote all the cells the queen can attack from : There are obstacles on the chessboard, each preventing the queen from attacking any square beyond it on that path. For example, an obstacle at location in the diagram above prevents the queen from attacking cells , , and : Given the queen's position and the locations of all the obstacles, find and print the number of…