Homework 6 - Spring 2022 Semester
Deadline: Thursday khordad 12th - 11:59 pm

In this homework, we are going to Solve 4 questions using functions in the C++ STL library. Read each question carefully and write down your code.

In this question, we want to implement the gradient descent algorithm in an STL way. As you know in gradient descent we aim to find where is the minimum of a function by moving in a way that our function is decreasing, like in the picture below:

implement a function called gradient_descent that calculates the minimum of any given math-function (like sine, cosine, ...). the math-function can be a pointer to function, lambda function or a functor (see tests 1 to 4). The first input of your function should be the initial value and the second input the step size.

Note. implement all your code in q1 namespace and q1.h file.

In this question, we want to read the resources/lung_cancer.csv file and sort the patients by the possibility of whether or not they have lung cancer (in increasing order). First, implement a struct called Patient containing the necessary variables for a patient - something like this:

struct Patient
{
	std::string name;
	size_t age;
	size_t smokes;
	size_t area_q;
	size_t alkhol;
};

Note. store both the first name and last name of the patients in the name variable in the above struct like "John Wick".

Then implement the read_file function and read the resources/lung_cancer.csv content and create a std::vector of the patients.

std::vector<Patient> read_file(std::string filename)

Finally, implement a function called sort and sort the patients by their possibility of having lung cancer. To sort them you have to compare the sum of the variables of each patient with the below weights:

3*age + 5*smokes + 2*area_q + 4*alkhol

Note. you are not allowed to use any for in your sort function.

Note. implement all your code in q2 namespace and q2.h file.

In this question, we want to store the flights in the resources/flights.txt file, in a std::priority_queue container. Like question2 create a struct for each flight like below:

struct Flight
{
	std::string flight_number;
	size_t duration;
	size_t connections;
	size_t connection_times;
	size_t price;
};

Note. each flight may have one or more connections and therefore connection-times. the variable named connection_times is the overall connection time of the flight.

Now implement a function called gather_flights and return a priority queue containing all the flights in the file. Your function has one input which is the filename i.e. flights.txt. To compare the flights you should compare the weighted sum of the properties of each flight with the below weights:

duration + connection_times + 3*price

Note. you are not allowed to use any for in your gather_flights function.

Note. implement all your code in q3 namespace and q3.h file.

In this question, we want to implement an algorithm called kalman_filter (at least a simple version of it). Kalman filter is used to find the best estimate of a state by combining measurements from various sensors. meaning, sometimes to have a more accurate measurement of a variable you would use multiple sensors instead of just one and calculate the mean of these sensors as your measurement. It is worth mentioning: your sensors do not always have the same accuracy so instead of calculating the pure mean of your sensor, you should calculate the weighted mean of your sensors based on their accuracy. The sensors we want to use in this question are position sensors that measure the position in a 2D plane. So, implement the struct below to represent our position sensors. (you can add constructors or other stuff if needed)

struct Vector2D
{
double x{};
double y{}; 
};

struct Sensor
{
	Vector2D pos;
	double accuracy;    
};

and implement the below function for the kalman-filter:

Vector2D kalman_filter(std::vector<Sensor> sensors)

this function calculates our final position measurement based on the kalman-filter of sensors.

Note. again you are not allowed to use any for in your gather_flights function.

Note. implement all your code in q4 namespace and q4.h file.

As mentioned before, do not alter other files already populated except otherwise indicated. In case you want to test your code you may use the debug section of the main.cpp.

if (true) // make false to run unit tests  
{ 
	// debug section 
}  
else  
{  
	::testing::InitGoogleTest(&argc, argv);  
	std::cout << "RUNNING TESTS ..." << std::endl;  
	int ret{RUN_ALL_TESTS()};  
	if (!ret)  
		std::cout << "<<<SUCCESS>>>" << std::endl;  
	else  
	  std::cout << "FAILED" << std::endl;  
}  
return 0;

GOOD LUCK