Chegg code hanoi towers plus#

Numerous myths regarding the ancient and mystical nature of the puzzle popped up almost immediately, including one about an Indian temple in Kashi Vishwanath containing a large room with three time-worn posts in it, surrounded by 64 golden disks. The puzzle was introduced to the West by the French mathematician Édouard Lucas in 1883.

4.4 General shortest paths and the number 466/885.

2.2.1 Logical analysis of the recursive solution.

2.1.1 Simpler statement of iterative solution.

The minimal number of moves required to solve a Tower of Hanoi puzzle is 2 n − 1, where n is the number of disks. With 3 disks, the puzzle can be solved in 7 moves.

No disk may be placed on top of a disk that is smaller than it.

Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.

The objective of the puzzle is to move the entire stack to the last rod, obeying the following rules: The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top, thus approximating a conical shape. The Tower of Hanoi (also called The problem of Benares Temple or Tower of Brahma or Lucas' Tower and sometimes pluralized as Towers, or simply pyramid puzzle ) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod. The output of your program should contain (1) a count of the total number of steps to be taken to reach the goal and (2) a path list showing the disk positions at each level of the search.Tower of Hanoi interactive display at Mexico City's Universum Museum

Similar to your work solving the 8-Puzzle with BFS and A, both algorithms should be implemented into the same file. Your final code must implement both Breadth-First Search and A* Search solutions. Consequently, at the start of the program execution, the integer N should be taken as an input. Trace the heuristic search process using the state space created in 2.04 Step 2 - Coding As previously discussed, your program must be capable of solving the problem of any number of disks. Briefly discuss how is the heuristics function defined in your assignment. As discussed previously, the definition of the heuristic function may vary.

Chegg code hanoi towers plus#

Create the first four levels (i.e., the root node plus next three levels) of the state space. Which scheme have you selected in your implementation? Why? 2. You are required to answer following questions: 1. Disk Class: Diameter Number of Rod, Index on the Rod While either scheme can be selected, scheme 2 may lead to a cleaner and more readable implementation. , Bottom Top Scheme 2 Another approach is to treat the disks individually, defining a Disk class to store their diameter, current rod, and the index in that rod. For a, instance, the state in Figure 3 can be represented as c0 clc2. The elements of the inner list represent disks stacked on this rod.

Each element of the list is a list by itself.

Consider the following figure for our problem: 3 S Figure 3 a state of the tower with 6 disks 3 a Scheme 1 A state is represented by a list of 3 elements where each element represents a rod. Step 1 - Problem Analysis Before writing the python code, we are required to perform an analysis in order to conclude the best methodology. The completion of the task consists of two steps as listed below. Note: the problem must be solved using State Space Search algorithms. You are required to solve the problem using TWO search algorithms to achieve the objective: (1) a blind (Breadth-First) search and (2) a heuristic (A*) search algorithms. A state space representation of the 2-disk problem is shown in Figure 2 Initial State III ITI' Goal State Figure 2 State Space of 2-Disk Problem In this task, we aim to solve the Towers of Hanoi problem of 6 disks, though your final algorithm will most likely be capable of solving more complex versions. The objective of this problem is to move the entire stack of disks from the first to the last rods. No disk may be placed on top of a disk that is smaller than it. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod. The objective of the puzzle is to move the entire stack to the last rod, obeying the following rules: 1. Transcribed image text: Solving the Towers of Hanoi Problem based on State Space Search Towers of Hanoi (Tower of Hanoi - Wikipedia) is a puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod as shown in Figure 1.