# 1 Problem Definition

In your first programming examination for C++, you will be dealing with keeping track of paths consisting of 2D vectors as coordinates. The path will start from (0,0) coordinate and you will be given a series of vectors to add to the end of the path and calculate the new distance and displacement of the path.

Displacement is defined to be the change in position of an object. It is the distance between the final position and the first position of the object. On the other hand, the distance of a path is the total length of the path.

(b) Distance = |*A*| + |*B*| + |*C*|

(a) Distance vs. Displacement Displacement = |*R*|

Figure 1: Difference between distance and displacement of a path.

## 1.1 General Specifications

- The signatures of the functions, their explanations and specifications are given in the following section. Read them carefully.
- Make sure that your implementations comply with the function signatures.
- You may define any number of helper function(s) as you need.
- You are not allowed to import any
*extra*library for this exam. - You should NOT make any change in header file. The one given to you will not be used in evaluation process.

## 1.2 Quick VPL Tips (In case youve forgotten them!)

- Evaluation is fast. If evaluation seems to hang for more than a few seconds, your code is entering an infinite loop or has an abnormal algorithmic complexity. Or youve lost your connection, which is
*much*less likely! - Although the run console does not support keyboard shortcuts, it should still be possible to copy and paste using the right-click menu (Tested on latest versions of Firefox and Chrome).
- Get familiar with the environment. Press the plus shapes button on the top-left corner to see all the options. You can download/upload files, change your font and theme, switch to fullscreen etc. Useful stuff!

# 2 Path Tracker

Path Tracker is a class keeping track of the final coordinate of the path and the distance and the displacement values.

PathTracker Class Properties

class PathTracker{ public:int final_x; | // | final | position on x-axis |

int final_y; | // | final | position on y-axis |

float displacement; | // | final | displacement |

float distance;} | // | final | distance |

There are 2 constructors you have to implement. If there is no argument, then PathTracker will start from the origin. If you are given an array of integers, then each couple in the array will be used as a vector and the path will be constructed using the list of couples. Besides, the distance and the displacement values will be updated.

For example, [1, 2, 3, 4, 5, 6] keeps three vectors: [1, 2], [3, 4], [5, 6]. These three vectors will be added end-to-end to construct the path.

PathTracker Class Constructors

class PathTracker{ .PathTracker(); // start the path from the origin// number_of_vectors: number of vectors to add end-to-end// existing_path: number_of_vectors*2 elements representing// [x1, y1, x2, y2, .., xn, yn], n=number_of_vectorsPathTracker(int *existing_path, int number_of_vectors);} | vectors |

There are 5 operator overloading functions to be implemented.

- PathTracker operator+=(const int *new_vector): takes an integer array with the length of 2, containing x and y components of the vector to be added to the end. During this operation, the final x and y coordinates, displacement and distance values of the path will be updated.
- bool operator==(const PathTracker rhs) const: takes a PathTracker object to compare displacements. If two objects displacements are equal, it will return true else will return false.
- bool operator
*>*(const PathTracker rhs) const: takes a PathTracker object to compare displacements. If the original objects displacement is longer, it will return true else will return false. - bool operator
*>*(const PathTracker rhs) const: takes a PathTracker object to compare displacements. If original objects displacement is shorter, it will return true else will return false. - bool operator==(float distance) const: takes a floating-point number and compare it with the objects distance. If they are equal, it will return true else will return false.

PathTracker Class Operator Overloading Functions

class PathTracker{ .// Adds new vector to the end// new_vector: keeping vector | components [x, y] | ||||||||

PathTracker &operator+=(const | int *new_vector); | ||||||||

// Comparing two PathTrackers | by displacements | ||||||||

// returns True if their displacements are equal bool operator==(const PathTracker &rhs) const;// returns True if original objects displacement | is | bigger then the | |||||||

// compared one bool operator>(const PathTracker &rhs) const;// returns True if original objects displacement// compared onebool operator<(const PathTracker &rhs) const; | is | less then the | |||||||

// Checks whether the distance | of the object | is | equal | to | the | given | |||

// floating-point number bool operator==(float distance)} | const; | ||||||||

There are 4 small helper functions to use while keeping track of the path.

- float calculate_displacement(): Calculates and returns the displacement of the path.
- void calculate_distance(int x, int y): takes two integer values as x and y components representing the newly added vector and updates the distance of the path.
- float calculate_l2(int x1, int y1, int x2, int y2): takes 4 integer values as 2 points on vector space. It calculates and returns Euclidean distance between two points.
- void summary(): prints the summary of the path as:

Final Position: [x, y] Displacement: #dsp# Distance: #dst#

Final Position: [25,30] Displacement: 39.051 Distance: 39.13

PathTracker Class Helper Functions

class PathTracker{ .// Calculates and returns displacement value float calculate_displacement();// Calculates and sets distance value void calculate_distance(int x, int y);// Calculates Euclidean distance between two points float calculate_l2(int x1, int y1, int x2, int y2);// Prints the summary of the pathvoid summary();} |

# 3 Examples

Example From Scratch and Adding A New Vector to the End

int main(){PathTracker pt = PathTracker(); int coord[2] = {3, 5}; pt.summary();pt += coord; pt.summary();coord[0] = -3; coord[1] = 1; pt += coord; pt.summary();coord[0] = -2; coord[1] = -6; pt += coord; pt.summary();return 0;}// OutputFinal Position: [0,0] Displacement: 0 Distance: 0Final Position: [3,5] Displacement: 5.831 Distance: 5.831Final Position: [0,6] Displacement: 6 Distance: 8.9932Final Position: [-2,0] Displacement: 2 Distance: 15.318 |

Example of Existing Path

int main(){int existing_path[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; // it is going to add all vectors end-to-end in constructor // [1, 2]// [3, 4]// [5, 6]// [7, 8]// [9, 10]PathTracker pt = PathTracker(existing_path, 5); pt.summary();return 0;}// OutputFinal Position: [25,30] Displacement: 39.051 Distance: 39.13 |

Examples of Operator Overloading Functions

int main(){int existing_path1[2] = {25, 30}; int existing_path2[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};PathTracker pt1 = PathTracker(existing_path1, 1);PathTracker pt2 = PathTracker(existing_path2, 5);pt1.summary(); pt2.summary();std::cout << pt1 == pt2: << (pt1 == pt2) << ; std::cout << pt1 > pt2: << (pt1 > pt2) << ; std::cout << pt1 < pt2: << (pt1 < pt2) << ;// notice that distance can be compared with a floating-point // not another PathTracker object. std::cout << distance comparison: << (pt1 == pt2.distance) << ;return 0;}// OutputFinal Position: [25,30] Displacement: 39.051 Distance: 39.051 Final Position: [25,30] Displacement: 39.051 Distance: 39.13 pt1 == pt2: 1 pt1 > pt2: 0 pt1 < pt2: 0 distance comparison: 0 |

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