For this assignment, you need to implement two different search algorithms to solve a puzzle problem. For this puzzle game, the GUI (graphical user interface) framework is provided that is is developed by C++ and OpenCV library. The technical details are described in the source files of the project. Below is a highlight of the structure.

**How to play:**

After you run the project, you should be able to see a puzzle game coming out. You can use your mouse to select one piece of sub-image by one click and move it to the blank area by clicking the blank area. At any time, you can hit “s” key to search a solution, which you need to implement.

**Classes Involved:**

1. **VisualDisplay** – This class deals with all the graphical or visual stuff, including pattern generation from an image, user mouse/keyboard interface, ext (**You do not need to modify this class**).

2. **RandomGenerator** – This class is used to generate a random sequence of numbers (from 0-8), which are used as the orders of different pieces of an image that present different patterns. (**You do not need to modify this class**).

3. **SolutionSearch** – This is the class that provides a solution for a given puzzle. The solution can be found by different search algorithms. (**You are required to implement the functions in this class**).

**Requirements:**

You need to implement the a functions in the “SolutionSearch.cpp” file: void SolutionSearch::AStarSearch(int *data, vector<int> &solution)

(1) For the A* search you need to maintain g(x) and h(x) for each node. (25%)

(2) For the heuristic function h(x), you need to use the Manhattan Distance as the metric. (25%)

(3) Use the correct data structure making sure the node with the smallest f(x) = g(x) + h(x) gets expanded first (25%)

(4) Terminate the search when the first goal node is expanded from the memory (15%)

(5) Successfully find the optimal solution. (10%)

**What should be submitted:**

You can put all your code inside the function “AStarSearch()”. But if you want to create any additional data or functions, you are suggested to put all the created data or functions inside the “SolutionSearch” class, which are considered as the members of this class. So you just need to submit two files: “SolutionSearch.h” and “SolutionSearch.cpp” from the Isidore online system.

**Explanation of “AStarSearch()” Function:**

For this function, there are two input parameters: the first parameter is the random order of the 9 numbers, which you need to re-organize to make them into the correct order; the second parameter is actually an output. It returns or stores the moving path of the “empty space” that it is involved to make all the sub-images in the correct position. The integer sequence variable “solution” should store all the steps along the “Optimal” path.

For example:

Input: data = {0, 4, 1, 3, 8, 2, 6, 7, 5 };

Goal: make it into the correct order {0, 1, 2, 3, 4, 5, 6, 7, 8}

You need to make the following changes on the number 8, since the number 8 represents the empty space, moving 8 to its neighboring numbers equals to moving the corresponding number to the empty space. Below it shows a demo of the steps:

0 4 1 swap with 4 0 8 1 swap with 1 0 1 8 swap with 2 0 1 2 swap with 5 0 1 2

3 8 2 —————–> 3 4 2 —————–> 3 4 2 —————–> 3 4 8 ——————> 3 4 5 ————> End

6 7 5 6 7 5 6 7 5 6 7 5 6 7 8

So from this example, the right path should be {1, 2, 5, 8}.

WHY? You may thought it was {4, 1, 2, 5}, since the number 8 has swapped with them in this order. That is true. However, we do not care which number it swapped with, but which position the number 8has gone through. As the numbers can be in any positions during different time, which give no hint about where the number 8 is. In contrast, the positions are fixed. So we assume the positions are in the same order as an increasing sequence:

**[0] [1] [2]**

Fixed Position = **[3] [4] [5]**

** [6] [7] [8]**

Here, I use “[]” to distinguish the positions from the numbers. So now you can see, the number 8 starts from position [4], then swapped with number 4, which goes to the position [1]; then swapped with number 1, which goes to the position [2]; then swapped with number 2, which goes to the position [5]; finally, swapped with number 5, which goes to the position [8]. So the path you should assign to the parameter “&solution” with the path sequence {1, 2, 5, 8}.

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