Lecture 4/13: Vectors and Grids

April 13, 2020

📂Associated files

• qa
• ToonShade.zip
• VectorsGrids.zip

• Questions and Answers

The Vector and Grid Classes

CS 106B: Programming Abstractions

Spring 2020, Stanford University Computer Science Department

Lecturers: Chris Gregg and Julie Zelenski

Slide 2

Announcements

• Section starts this week! Section assignments will be released on Tuesday (4/14) evening and sections will begin Wednesday (4/15) morning. Reminder: All section times are displayed in PDT.
• If you can no longer make the time to which you’re assigned (or if you were originally unassigned because you did not submit time preferences), go to this website and you’ll be able to switch into any section which still has space.
• The (virtual) LaIR is now open – this is a space where you can get live code debugging help from our fleet of awesome section leaders. The LaIR will be open Sunday-Thursday evenings, 5:00PM – 9:00PM PDT and Monday, Tuesday mornings, 9:00AM - 11:00AM PDT. This second time is newly added to accommodate those students that are in timezones where the typical LaIR time is inaccessible. Check the Zoom details page for information on how to get help at the LaIR.
• Please make your best effort to save code debugging questions for the LaIR or instructor office hours – while we will offer as much flexibility as we can to answer debugging questions on Ed, we only have a limited capacity to do so, and would like to reserve this for folks that are unable to make any of the synchronous help resources that have been offered.

Slide 3

Code Mystery

• In the last lecture, we introduced the idea of a C++ reference. What is the output of this code? Fill out the Zoom poll with your answer!

void mystery(int& b, int c, int& a) { 
    a++;
    b--;
    c += a; 
}

int main() { 
    int a = 5; 
    int b = 2;
    int c = 8;
    mystery(c, a, b);
    cout << a << " " << b << " " << c << endl;
    return 0;
}

Poll:

A. 5 2 8
B. 5 3 7
C. 6 1 8 
D. 61 13 
E. other

Slide 4

Poll answer:

output
A. 5 2 8
B. 5 3 7
C. 6 1 8 
D. 61 13 
E. other

Note: please don't obfuscate your code like this! :(

See the International Obfuscated C Contest for much, much worse examples

Slide 5

A function for Solving the Quadratic Equation

• A quadratic equation for variable x is one of the form:

ax2 + bx + c = 0

for some numbers a, b, and c.

• The two roots of a quadratic equation can be found using the quadratic formula above.

• Example: The roots of x2 - 3x - 4 = 0 are x=4 and x=-1

• How would we write a function named quadratic to solve quadratic equations?
  • What parameters should it accept?
  • Which parameters should be passed by value, and which by reference?
  • What, if anything, should it return?
• We have choices!

Slide 6

A Function for Solving the Quadratic Equation

/*
 * Solves a quadratic equation ax^2 + bx + c = 0,
 * storing the results in output parameters root1 and root2. 
 * Assumes that the given equation has two real roots.
 */
void quadratic(double a, double b, double c,
               double& root1, double& root2) {
    double d = sqrt(b * b - 4 * a * c);
    root1 = (-b + d) / (2 * a);
    root2 = (-b - d) / (2 * a);
}

• How are we "returning" the results? Answer: by using references to variables
• What other choices ccould we have made?

Slide 7

Collections

• One of the most powerful aspects of C++ is the ability to have a "collection": we will study the six collections shown above.

• We will talk about all of these as we go through CS 106B, but you will need to use the Vector and Grid classes for assignment 1.

Slide 8

The Vector Collection

• What is a Vector?
  • It is like a list in Python, or an ArrayList in Java.
  • It is a list of elements that can grow and shrink.
  • Each element has a place (or index) in the list.
• Important Details
  • The constructor creates an empty list (more on constructors soon)
  • The Stanford Vector class performs bounds checks, meaning that if you try to access an element that is outside the bounds of a Vector, the program crashes.
  • A Vector Knows its size.
  • To use Vectors, you #include "vector.h".
• Under the hood, a vector is an array, which means that in the computer's memory, one value follows the next.

Slide 9

Creating a Vector

• You must specify the type of your vector (e.g., int, string, etc.)

• When a vector is created it is initially empty.

• To create a vector called vec that can hold integers (ints), we write the following:

  Vector<int> vec; 
  

  This calls the default constructor, which just means that it initializes and creates (constructs) an empty vector for us.

Slide 10

Adding elements to a vector

• Here is an example where we create a vector called magic and add the numbers 4, 8, 15, and 16 to the vector, and then print out the elment at index 2:

  Vector<int> magic;
  magic.add(4);
  magic.add(8);
  magic.add(15);
  magic.add(16);
  cout << magic[2] << endl;
  

  Output:

  15
  

• Notice that the index ordering starts from zero!

• In the computer's memory, our vector is represented by one number after another, as follows:

magic:

    

        
index:
        
 0 
        
 1 
        
 2 
        
 3 
    
    

        
value:
        
4
        
8
        
15
        
16
    

Slide 11

Vectors have useful functions, like size()

magic:

    

        
index:
        
 0 
        
 1 
        
 2 
        
 3 
    
    

        
value:
        
4
        
8
        
15
        
16
    

• The following loops through the values in the vector and prints them:

  for(int i = 0; i < magic.size(); i++) {
   cout << magic[i] << endl;
  }
  

  Output:

  4
  8
  15
  16
  

Slide 12

A new type of for loop: the for each loop:

magic:

    

        
index:
        
 0 
        
 1 
        
 2 
        
 3 
    
    

        
value:
        
4
        
8
        
15
        
16
    

• The following is a loop that automatically gets the next value in a collection:

  for(int value : magic) {
   cout << value << endl;
  }
  

  Output:

  4
  8
  15
  16
  

Slide 13

Vector Functions

• The following functions are part of the vector collection, and can be useful:
  • vec.size(): Returns the number of elements in the vector.
  • isEmpty(): Returns true if the vector is empty, false otherwise.
  • vec[i]: Selects the i^th element of the vector.
  • vec.add(value): Adds a new element to the end of the vector.
  • vec.insert(index, value): Inserts the value before the specified index, and moves the values after it up by one index.
  • vec.remove(index): Removes the element at the specified index, and moves the rest of the elements down by one index.
  • vec.clear(): Removes all elements from the vector.
• For the exhaustive list, check out the Stanford Vector class

Slide 14

The Grid Container

• The Grid is a Stanford library class for 2-dimensional arrays, like a matrix in math:

    

        
a0
        
b0
        
c0
    
    

        
a1
        
b1
        
c1
    
    

        
a2
        
b2
        
c2
    

Slide 15

Grid

• What is it?
  • Advanced 2D array.
  • Think spread sheets, game boards
• Important Details
  • Default constructor makes a grid of size 0
  • Doesn’t support “ragged right”.
  • Bounds checks
  • Knows its size.
• We could use a combination of Vectors to simulate a 2D matrix, but a Grid is easier!

Slide 16

Grid Example Code

Grid<int> matrix(2,2); 
matrix[0][0] = 42;
matrix[0][1] = 6;
matrix[1][0] = matrix[0][1];
cout << matrix.numRows() << endl;
cout << matrix[0][1] << endl;
cout << matrix[1][1] << endl;
cout << matrix[2][3] << endl;

Let's draw what happens on each line.

Grid<int> matrix(2,2); // Create a 2x2 grid, with 0 as the default entries

    

        

        
0
        
1
    
    

        
0
        
0
        
0
    
    

        
1
        
0
        
0
    

matrix[0][0] = 42; // put 42 at row 0, column 0

    

        

        
0
        
1
    
    

        
0
        
42
        
0
    
    

        
1
        
0
        
0
    

matrix[0][1] = 6; // put 6 at row 0, column 1

    

        

        
0
        
1
    
    

        
0
        
42
        
6
    
    

        
1
        
0
        
0
    

matrix[1][0] = matrix[0][1]; // put the value from r0,c1 at r1,c0

    

        

        
0
        
1
    
    

        
0
        
42
        
6
    
    

        
1
        
6
        
0
    

cout << matrix.numRows() << endl;
cout << matrix[0][1] << endl;
cout << matrix[1][1] << endl;

Prints the number of rows, then the value at r0,c1, then the value at r1,c1:

2
6
0

cout << matrix[2][3] << endl; // attempts to print out the value at r2,c3

***
*** STANFORD C++ LIBRARY 
*** An ErrorException occurred during program execution: 
*** Grid::operator [][]: (2, 3) is outside of valid range [(0, 0)..(1, 1)]
***
libc++abi.dylib: terminate_handler unexpectedly threw an exception
15:25:55: The program has unexpectedly finished.
15:25:55: The process was ended forcefully.

Grids do bounds checking! If you want to bounds check without crashing, you should call the grid.inBounds(row, col) function, which returns true if the row and column are in bounds for the grid.

Slide 17

Grid Functions

• The following functions are part of the grid collection, and can be useful:
  • grid.numRows(): Returns the number of rows in the grid.
  • grid.numCols(): Returns the number of columns in the grid.
  • grid[i][j]: selects the element in the i^th row and j^th column.
  • grid.resize(rows, cols): Changes the dimensions of the grid and re-initializes all entries to their default values.
  • grid.inBounds(row, col): Returns true if the specified row, column position is in the grid, false otherwise.
• For the exhaustive list, check out the Stanford Grid class

Slide 18

Grid Example: Traversing a Grid

void printGrid(Grid<char> &grid) {
    for(int r = 0; r < grid.numRows(); r++) {
        for(int c = 0; c < grid.numCols(); c++) {
            cout << grid[r][c];
        }
        cout << endl;
    }
}

If we pass in the following grid, what will print?

    

        

        
0
        
1
    
    

        
0
        
a
        
b
    
    

        
1
        
c
        
d
    
    

        
2
        
e
        
f
    

Output:

ab
cd
ef

Slide 19

Common pitfalls when working with collections in C++

• Vector numbers;
  • Needs a type! Should be: Vector<int> numbers;
• void myFunction(Grid<bool> gridParam);
  • Two issues:
    • If you want the original gridParam to be changed in the calling function, you're out of luck.
    • Inefficient because you have to make a copy of gridParam.

void printOutGrid(Grid<bool> & grid) {
    for(int i = 0; i < grid.numRows(); i++) {
        for(int j = 0; j < grid.numCols(); j++) {
            cout << grid[j][i];
        }
    }

• Watch your variable ordering! Better to use r for rows, and c for columns.

Slide 20

Let's Code Instagram!

Slide 21

A color is an int, and and Image is just a Grid<int>!

Slide 22

Let's change the palette of the image

Slide 23

Let's Code!