Answered: Subject: Discrete Structures Question:…

Subject: Discrete Structures Question: The number of bacteria in a colony doubles every hour. If the colony begins with 5 bacteria, how many will be present in 30 hours?

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter19: Probabilistic Dynamic Programming

Section19.4: Further Examples Of Probabilistic Dynamic Programming Formulations

Problem 7P

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Please help with q2 and 3 please
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Python Language Q2: Ginormous Campus The campus is pretty big. There are n buildings scattered around it, numbered from 0 to n-1. These buildings are so far away from each other that the only way to get from one to another is to take a campus bus. There are m campus bus routes. The i-th one (0 <= i < m) takes you from building u_i to building v_i (but not the other way around). These buses run very frequently. Professor Zingaro is deciding where to hold his CS lectures. He believes a building x is accessible from a building y if you can get from y to x taking at most two buses. For his students’ convenience, he wants to hold his lectures in the most accessible building. Help him out by telling him how many buildings the most accessible building is accessible from. In addition, list all buildings that are the most accessible. Input The first line of the input contains two space-separated integers n and m, denoting the number of buildings and bus routes, respectively. m lines…
Code requirements: A robot is positioned on an integral point in a two-dimensional coordinate grid (xr, yr). There is a treasure that has been placed at a point in the same grid at (xt, yt). All x’s and y’s will be integral values. The robot can move up (North), down (South), left (West), or right (East). Commands can be given to the robot to move one position in one of the four direction. That is, “E” moves a robot one slot East (to the right) so if the robot was on position (3, 4), it would now be on (4, 4). The command N would move the robot one position north so a robot at position (4, 4) would be at (4, 5). Because the robot cannot move diagonally, the shortest distance between a robot at (xr, yr) and a treasure at (xt, yt) is | xr – xt | + | yr - yt | = ShortestPossibleDistance Write a recursive program which determines all the unique shortest possible paths from the robot to the treasure with the following stipulation: The robot may never move in the same direction more than…
Graph Theory: Graph theory in computer science uses a graphical matrix with nodes and edges to describe a data structure. These can be used for search trees, game theory, shortest path, and many other applications in math and computer science. An example of an application of a graph in computer science is the data structure used to hole the moves for a checkers game program. Each move can be represented by a node. The edges connecting the nodes are determined by the rules of the game, basically how to get to the node. This is a directed graph, because a player cannot take a move back. So the flow is always in one direction towards the end of the game. Cycles in a graph is when a node can go back to itself. This is not possible in this graph, because a move can only go to another position on the board. The only case where this would be correct is if a player were allowed to skip his turn, or move to the same spot that he is already in. A graph is said to be connected if there is a path…
Q2: Ginormous Campus The campus is pretty big. There are n buildings scattered around it, numbered from 0 to n-1. These buildings are so far away from each other that the only way to get from one to another is to take a campus bus. There are m campus bus routes. The i-th one (0 <= i < m) takes you from building u_i to building v_i (but not the other way around). These buses run very frequently. Professor Zingaro is deciding where to hold his CS lectures. He believes a building x is accessible from a building y if you can get from y to x taking at most two buses. For his students’ convenience, he wants to hold his lectures in the most accessible building. Help him out by telling him how many buildings the most accessible building is accessible from. In addition, list all buildings that are the most accessible. Input The first line of the input contains two space-separated integers n and m, denoting the number of buildings and bus routes, respectively. m lines follow. The i-th one…
Blue-Eyed Island: A group of individuals live on an island until a visitor arrives with an unusual order: all blue-eyed people must leave the island as quickly as possible. Every evening at 8:00 p.m., a flight will depart. Everyone can see everyone else's eye colour, but no one knows their own (nor is anyone allowed to tell them). Furthermore, they have no idea how many people have blue eyes, but they do know that at least one person does. How long will it take for the blue-eyed individuals to leave?
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…
Wooden FenceRecently, Vincent has just bought a farm. He plans to enjoy his retirement by raising horses and goats onhis new farm. In order to do that, he needs to build a fence to enclose his farm; otherwise, the horses andgoats may escape from his farm. Fortunately, he only needs to build a fence on one side of the farm; theremaining sides are naturally fenced.The fence must be exactly 2 unit high and form a perfect rectangle. Why a perfect rectangle? If the fencehas a hole on the upper part, then a horse might jump over it. On the other hand, if the fence has a hole onthe lower part, then a goat might crawl out of it.Vincent has N boards to be used to build the fence. Each board’s dimension is 1 × Li. Each board may beplaced horizontally (1 × Li) or vertically (Li × 1) as long as the resulting fence has a height of 2.Oh, have we told you that Vincent is infamous for his stinginess? Yes, he’s very stingy. He demands to useALL the available boards; he doesn’t care about the length of…
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A hungry mouse wants to eat all four fruits in a maze such as the one below, in as few moves as possible.. At each turn the mouse can move any number of squares in one of the directions up, down, left or right, but it is not allowed to enter (or jump over) any walls (i.e., the black squares). Thus, the mouse moves just like a rook in chess. To eat a fruit, the mouse has to stop at that square. Assume that the maze has 4 fruits, and the size of b xh squares. 1. Give a suitable representatión of the states in this searching problem. 2. How many possible actions can the mouse perform at each move? (1.e., what is the branching factor?)