C++ FAQ

Q1: How to understand passing by reference and by value?

Answer: Passing by reference is a new language feature in C++, which allows you to modify the value of a variable INSIDE a function. It works like this: when calling a function, the address of the actual argument is copied to the formal argument, then you can use that address in your function to change the value of that argument, (though you use it like a normal variable, i.e., you don't need to know that it is a address and do extra works, that's why passing by reference is usually better than passing an address) You can think about this as two names (for actual and formal argument, resp.) referring to a single address.

Compared with arguments passed by value, when calling the function, the language will actually create a new variable of the same type (the formal variable), copy the value of the actual argument to this newly created variable, which is then passed to the function. Therefore, the formal argument is different from the actual argument. In this way, the function doesn't know the address of the actual argument and there is no way to modify the value of the actual argument. After the function ends (when it returns), the variable created when calling the function disappears.

Q2: What's the relationship between .h file and .cpp file

Answer:Usually, we use .h and .cpp file to separate the declaration and implementation (definition) of functions. From the view of design, the programmer or the designer sometimes don't want the user to know how they solve the problem, they just want the users to learn how to use the functions they provide. This is a kind of information hiding, which is common in commercial softwares.

So the programmer (here, you're the programmer) put the class declarations in the header file (.h) and the class implementation/definition in the source file (.cpp)

Information hiding is not restricted to class things. You can separate the declaration and implementation of functions using header file and source file, too.

Q3: Can you give me an example of operator overloading

Answer: My pleasure.

You need to build a new project to hold these three files.

Q4: The determinant function without parameters/arguments in lab 9 seems impossible, can you give me a hint?

Answer: No, it is possible to implement such recursive algorithm, with the help of a data structure called "Stack". Whatever, you're not required to accoomplish this "mission impossible", what you need to do in the assignment is to copy your old codes of determinant to your class, make it a member function, then in you parameter-free version of determinant function, make a call to the "good-old" determinant function, that's it.

MATLAB FAQ

Q5: Is it possible to input a matrix using the MALTAB's input function?

Answer: Yes, you should ask the user to put their matrix (therefore vector) in the MATLAB syntax, then MATLAB will recognize the string as a matrix. For example:
A = input("please input a 3 by 4 matrix");
and if the user input:
[1,2,3,4;5,6,7,8;9,10,11,12] then A will be a matrix, taking 1 2 3 4 as its first row, 5 6 7 8 as its second row, and so on. You should try it out in your assignment. Note that a "," is used to separate the columns and ";" is for separate the rows.

Q6: How to understand the example given in the Lab 10 assignment? What's a, b, and what's b(x)?

Answer: First, a and b are vectors of the same length, for example
a=5:14 % you should type this line in MATLAB to see what are in a b=ones(1,10) % the same as above, if you're serious, type in this line in MATLAB Second, the intention of the code
if (a < 10) then b = b + 1 else b = b + 10 means that for every element in a, if it is less than 10, then add 1 to the element in b in the same position. Otherwise, add 10 to that element. For example, the first element in a is 5, so you add 1 to the first element of b, i.e., we have b(1) equal to 2. the last element of a is 14, which is larger than 10, so add 10 to the last element of b, so b(10) equals to 11.
x = a < 10
is a logical vector with its elements indicating whether the corresponding element in a is less than 10 or not. The first element of x is false, and the last element of x is true. then
b(x)=b(x).+9 means that if you have true in some position(s) in x, then the element of b in that corresponding place will increased by 9. For example, the first element in x is false, so nothing happen to the first element of b, but the last element in x is true, then MATLAB adds 9 to the last element of b, which equals to 10 at last.

Q7:

Answer: suppose we have an vector containing some random numbers, for those who have values large than 0.5, I want to suppress them, so I multiple them by 0.5. For those with values less than 0.3, I want to enlarge them, so I multiple them by 2. How to do this without for loop and if/else statements?
a=rand(1,10); % generate a 1 by 10 random matrix
x=(a>0.5);
y=(a<0.3);
a(x)=a(x)*0.5;
a(y)=a(y)*2;
what if I want to add 2 to those elements in a with values between 0.3 and 0.5? I simply need to obtain another indicator vector like
z=(a<=0.5 & a>=0.3)
then you can do some operation to these elements in a according to z.

Q8: How to get input in a vector form?

Answer: In MATLAB, you should try your best to avoid using loop. For example, you are going to let the user input a series of numbers, like salaries, you can write:
salaries=input('please input salaries in vector format like [2000, 90, 1200]');
then salaries will be an vector with its elements specified in the user's input, though looked strange to the user, but it is more efficient.

Q9: How to understand the bacteria growth?

Answer: You can think of the growth process as a series of natural numbers, where the next one is stochastically determined by the previous one only. Each natural number (the t-th number is denoted by N(t)) is the population size at the t-th generation. So it is quite natural to understand that the size of the current population is indeed determined by the previous size.
The more subtle thing is the probability. N(t) is not deterministically given by some fixed function, rather, it is governed by some probability. For example, N(t) could be N(t-1) + 1 with probability 0.6 and be N(t-1) - 1 with probability 0.3 and be N(t-1) - 2 with probability 0.1.
Of course, we're not going to directly calculate such probabilities since it is quite complex, what we are going to do is to 'simulate' the bacteria growth to get N(t), though the simulation does involve some simpler probability calculation.
To get N(t), you can determined how each individual in the (t-1)-th generation behaves: whether it copies itself (then the size grows by 1) or it dies (then the size decreases by 1). After you have the behaviors of all individuals, you know how many bacteria are there in the t-th generation.
How do we know a bacterium behaves? Here the probability comes into play: with probability p, it copies itself, otherwise, it dies. The bacterium has to make a decision, it can't do both (though maybe a human can clone himself/herself even when he/she dies).

Q10: How to simulate the probability distribution

Answer: In the assignment, a bacterium copies itself with probability p, and dies with probability 1-p, you can simulate this process using uniform distribution function provided by MATLAB:
r=rand(1);
if (r<=p)
% copies itself
else
% dies
end