S 5 D They start by making A the current vertex and assigning a tentative distance of 5 to B and a tentative distance of 6 to C. Then they mark A as visited, and since B has the lowest tentative distance, they mark B as the current vertex. Next, they update the tentative distance of C to be 5+2=7, and the tentative distance of D to be 5+3=8. Then they mark B as visited and select C (which has the lowest tentative distance) as current. What mistake did this student make? Answer in a sentence or two
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- You are given nn points in the plane: (x1,y1),(x2,y2),...,(xn,yn). On the page , in English, give an algorithm that determines if there is a circle on which all of the points lie. In English, write your algorithm to determine if there is a circle on which points(x_1, y_1), (x_2, y_2), . . ., (x_n, y_n) lie. Algorithm:The Python implementation updates the cost of reaching from the start vertex to each of the explored vertexes. In addition, when it decides on a route, A* considers the shortest path from the start to the target, passing by the current vertex, because it sums the estimate from the heuristic with the cost of the path computed to the current vertex. This process allows the algorithm to perform more computations than BFS when the heuristic is a proper estimate and to determine the best path possible.Write a program that reads three edges for atriangle and computes the perimeter if the input is valid. Otherwise, display that theinput is invalid. The input is valid if the sum of every pair of two edges is greaterthan the remaining edge.
- Computer Science Given a dataframe with two columns (x and y), I have found a function on Python that gives a local fit value (essentially between two set values x it gives the average of all values of y). Now the questions asks us to create 2 graphs - one that shows the average per value of x and another one that shows the difference to that average that we found. What does this mean?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.In hill-climbing algorithms there are steps that make lots of progress and steps that make very little progress. For example, the first iteration on the input given might find a path through the augmentation graph through which a flow of 30 can be added. It might, however, find the path through which only a flow of 2 can be added. How bad might the running time be when the computation is unlucky enough to always take the worst legal step allowed by the algorithm? Start by taking the step that increases the flow by 2 for the input. Then continue to take the worst possible step. You could draw out each and every step, but it is better to use this opportunity to use loop invariants. What does the flow look like after i iterations? Repeat this process on the same graph except that the four edges forming the square now have capacities 1,000,000,000,000,000 and the crossover edge has capacity 1. (Also move t to c or give that last edge a large capacity.)1. What is the worst case number of…
- Given is a strictly increasing function, f(x). Strictly increasing meaning: f(x)< f(x+1). (Refer to the example graph of functions for a visualization.) Now, define an algorithm that finds the smallest positive integer, n, at which the function, f(n), becomes positive. The things left to do is to: Describe the algorithm you came up with and make it O(log n).Consider an undirected graph G = (V,E), in which each node u 2 V may be colored with some color between 1 and C. Your task is to write a program that determine the colors for the uncolored nodes in the graph such that • For all edges (u, v) 2 E, u and v have different colors. • The number of additional colors needed is minimum. Input (Standard input): Includes multiples lines. The first line contains two integers 1 n 1000, 1 m 100000 that correspond to the number of nodes and edges, respectively. Each of the following m lines contain two integers u and v, separated by one space, to denote an edge from u to v. Nodes are numbered from 1 to n. The last line contains n integers that are the colors of the nodes. Uncolored nodes are indicated with color 0. Output (Standard output): The first line contains an integer 0 D n that is the number of additional colors needed to color all the uncolored nodes in the graph. The next line contains n positive integers that are colors of the nodes. Your…When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…
- When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…When faced with a difficult problem in mathematics, it often helps to draw a picture. If the problem involves a discrete collection of interrelated objects, it is natural to sketch the objects and draw lines between them to indicate the relationships. A graph (composed of dots called vertices connected by lines or curves called edges) is the mathematical version of such a sketch. The edges of a graph may have arrows on them; in this case, the graph is called a directed graph. When we draw a graph, it doesn’t really matter where we put the vertices or whether we draw the edges as curved or straight; rather, what matters is whether or not two given vertices are connected by an edge (or edges). The degree of a vertex is the number of edges incident to it (i.e., the number of times an edge touches it). This is different than the number of edges touching it, because an edge my form a loop; for instance, vertex ? in graph ? (above) has degree 5. In a directed graph, we can speak of the…