Monkey problem: A little monkey is allowed to jump k times between n branches labeled with the integers in {0, 1, 2..., n-1}, for some even integer n> 5, starting from branch 0. The branches are arranged evenly each forming a radius of a circle. If the monkey is at branch i, then it will jump to one of branches branch (i-1) mod n and (i+1) mod n each with probability 1/2. The game is to predict at which branch will the monkey be after 10 jumps, if it started from the branch 0. Let f(i) be the probability that the monkey arrives at the branch i after 10 jumps from the branch 0, where i ranges from 0 to n - 1. i) Create a SAGE code that computes f.(i) by simulations, and plots all three graphs of for fe(i). fs(i) and fio(i). ii) Create a SAGE code that computes f. (i) using the Markov Chain method, and plots all three graphs of for fe(i). fs(i) and fio(i). iii) Provide reasons explaining the behaviour of the graph for odd i.

Monkey problem: A little monkey is allowed to jump k times between n branches labeled with the integers in {0, 1, 2..., n-1}, for some even integer n> 5, starting from branch 0. The branches are arranged evenly each forming a radius of a circle. If the monkey is at branch i, then it will jump to one of branches branch (i-1) mod n and (i+1) mod n each with probability 1/2. The game is to predict at which branch will the monkey be after 10 jumps, if it started from the branch 0. Let f(i) be the probability that the monkey arrives at the branch i after 10 jumps from the branch 0, where i ranges from 0 to n - 1. i) Create a SAGE code that computes f.(i) by simulations, and plots all three graphs of for fe(i). fs(i) and fio(i). ii) Create a SAGE code that computes f. (i) using the Markov Chain method, and plots all three graphs of for fe(i). fs(i) and fio(i). iii) Provide reasons explaining the behaviour of the graph for odd i.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter18: Deterministic Dynamic Programming

Section18.4: Resource-allocation Problems

Problem 3P

See similar textbooks

Similar questions

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. in its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring.", Wikipedia a) Apply your algorithm in the graph below. What is the accuracy ratio? b) Show that the performance ratio of your algorithm can go unbounded above or never at all.
Q1) how many graphs are there on 20 nodes? (To make this question precise, we have to make sure we known what it mean that two graphs are the same . For the purpose of this exercise,we consider the nodes given and labeled,say,asAlice ,Bob,...... The graph consisting of a single edge connecting Alice and Bob is different from the graph consisting of a single edge connecting Eve and frank.) Q2) Formulate the following assertion as a theorem about graphs and prove it :At every party one can find two people who know the same number of other people (like Bob and Eve in our first example).
4.1.44 Real-world graphs. Find a large weighted graph on the web—perhaps a mapwith distances, telephone connections with costs, or an airline rate schedule. Write a program RandomRealGraph that builds a graph by choosing V vertices at random and E edges at random from the subgraph induced by those vertices. 4.1.45 Random interval graphs. Consider a collection of V intervals on the real line(pairs of real numbers). Such a collection defines an interval graph with one vertex corresponding to each interval, with edges between vertices if the corresponding intervals intersect (have any points in common). Write a program that generates V random intervals in the unit interval, all of length d, then builds the corresponding interval graph.Hint: Use a BST.
Your task for this assignment is to identify a spanning tree in a connected undirected weighted graph using C++. 1. Implement a spanning tree algorithm using C++. A spanning tree is an acyclic spanning subgraph of the of a connected undirected weighted graph. Your program will be interactive. Graph edges with respective weights (i.e., v1 v2 w) are entered at the command line and results are displayed on the console. 2. Each input transaction represents an undirected edge of a connected weighted graph. The edge consists of two unequal uppercase letters representing graph vertices that the edge connects. Each edge has an assigned weight. The edge weight is a positive integer in the range 1 to 99. The three values on each input transaction are separated by a single space. An input transaction containing the string “end-of-file” signals the end of the graph edge input. After the edge information is read, the spanning tree evaluation process begins. Use an adjacency matrix for recording…
Computer Science Please do a simple JAVA code for the Monty Hall problem. Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? Please have the following Main allows the person playing to choose any door class door: should have data member methods Class person: should have data methods
Is the following statement true or false? a. Performing one rotation always preserves the AVL property. b. For any two functions f and g, we always have either f = O(g) or g = O(f). c. We run the breadth-first search algorithm (BFS) on a undirected graph G such that all edges have the same weight. BFS returns the shortest path from a source vertex s to any other vertex.
y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Comment on the results from the graph and determine the value of the time when the waves are with the same phase and assemble constructively and the time when they are with phase of opposite and interfere destructively.
A) Give the minimum spanning tree using Prim’s algorithm (starting at vertex A). B) Give the minimum spanning tree using Kruskal’s algorithm. C) What is the total weight of the minimum spanning tree?
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…
(3) Using the following graph, draw the Minimum Spanning Tree, and by using Dijkstra’s Algorithm give the shortest path from A to F (do not confuse F with E). You may either draw the shortest path, or write out the steps needed to follow the route you find.
Using Java, create and implement an iterative improvement algorithm that will find the approximation of a vertex in a parabola. The x-coordinate needs to be within 0.01 of the actual value. The algorithm must work for any quadratic function.Sample Run:Enter the coefficients for the parabola ax^2+bx+c: 2, 3, 1The vertex for the parabola is approximately:(-0.75, -0.125)
A robot can move horizontally or vertically to any square in the same row or in the same column of a board. Find the number of the shortest paths by which a robot can move from one corner of a board to the diagonally opposite corner. The length of a path is measured by the number of squares it passes through, including the ﬁrst and the least squares. Write the recurrence relation if you solve the problem by a dynamic programming algorithm.