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CSCI-1200 Computer Science II — Spring 2006
Lecture 4 — Vectors & Sorting; Statistical Computations
Review from Lecture 3
- Strings: subscripting and type declarations
- Problem solving: two methods of thinking about output along a diagonal.
4.1 Today’s Class
Koenig & Moo: Chapter 3
- vector container class,
- sort function,
- Applications in computing statistics
4.2 Problem: Grade Statistics
- Read an unknown number of grades.
- Compute:
- Mean (average)
- Standard deviation
- Median (middle value)
- We will write several programs to accomplish these.
4.3 Example: Reading Numbers and Computing the Average
// Program: average.cpp // Author: Chuck Stewart // Purpose: Compute the average of an input set of grades. This // demonstrates input of a sequence of integers, computing the // average, and manipulating the output precision.
#include #include #include
int main( int argc, char* argv[] ) {
if ( argc != 2 ) { std::cerr << "Usage: " << argv[0] << " grades-file\n"; return 1; }
std::ifstream grades_str( argv[1] ); if ( !grades_str ) { std::cerr << "Can not open the grades file " << argv[1] << "\n"; return 1; }
// Counting and summation variables. int count = 0; int sum = 0; // Input variable int x;
// Read in the scores one at a time. Add each score to the sum and // increment the count. // // The value of the expression grades_str >> x is a reference to the // input stream grades_str. The while condition uses this to test // grades_str to see if it is ok. If it is not, the test is false // and the loop ends. The most common cause of this is finding the // end of the input, but it would be false is something other than // an integer (or whitespace), such as a letter, is in the input // stream. while ( grades_str >> x ) { ++ count ; sum += x; }
// Output the result. Set the precision to 3. std::cout << "The average of " << count << " grades is " << std::setprecision(3) << double(sum) / count << std::endl;
return 0; }
4.6 Example: Using Vectors to Compute Standard Deviation
// Program: average_and_deviation.cpp // Author: Chuck Stewart // Purpose: Compute the average and standard deviation of an input // set of grades. This introduces the use of a vector to store // the grades upon input.
#include #include #include #include // to access the STL vector class #include // to use standard math library and sqrt
int main( int argc, char* argv[] ) {
if ( argc != 2 ) { std::cerr << "Usage: " << argv[0] << " grades-file\n"; return 1; } std::ifstream grades_str( argv[1] ); if ( !grades_str ) { std::cerr << "Can not open the grades file " << argv[1] << "\n"; return 1; }
std::vector scores; // Vector to hold the input scores; initially empty. int x; // Input variable
// Read the scores, appending each to the end of the vector while ( grades_str >> x ) { scores.push_back(x); }
// Quit with an error message if too few scores. if ( scores.size() == 0 ) { std::cout << "No scores entered. Please try again!" << std::endl; return 1; }
// Compute and output the average value. int sum=0; // Accumulation of the values for ( unsigned int i = 0; i < scores.size(); ++ i ) { sum += scores[i]; }
double average = double(sum) / scores.size(); std::cout << "The average of " << scores.size() << " grades is " << std::setprecision(3) << average << std::endl;
// Exercise: compute and output the standard deviation.
return 0; }
4.7 Median
- Intuitively, a median value of a sequence is a value that is less than half of the values in the sequence, and
greater than half of the values in the sequence.
- More technically, if a 0 , a 1 , a 2 ,... , an− 1 is a sequence of n values AND if the sequence is sorted such that
a 0 ≤ a 1 ≤ a 2 ≤ · · · ≤ an− 1 then the median is
a(n−1)/ 2 if n is odd
an/ 2 − 1 + an/ 2
2 if^ n^ is even
- Sorting is therefore the key to finding the median.
4.8 Standard Library Sort Function
- The standard library has a series of algorithms built to apply to container classes.
- The prototypes for these algorithms (actually the functions implementing these algorithms) are in header file
algorithm.
- One of the most important of the algorithms is sort.
- It is accessed by providing the beginning and end of the container’s interval to sort.
- As an example, the following code reads, sorts and outputs a vector of doubles
double x;
std::vector a;
while ( std::cin >> x ) a.push_back(x);
std::sort( a.begin(), a.end() );
for ( unsigned int i=0; i<a.size(); ++i )
std::cout << a[i] << ’\n’;
- a.begin() is an iterator referencing the first location in the vector, while a.end() is an iterator referencing
one past the last location in the vector.
- We will learn much more about iterators in the next few weeks.
- Every container has iterators: strings have begin() and end() iterators defined on them.
- The ordering of values by std::sort is least to greatest (technically, non-decreasing). We will see ways to
change this.
std::vector scores; // Vector to hold the input scores; initially empty.
// Read the scores, as before read_scores( scores, grades_str );
// Quit with an error message if too few scores. if ( scores.size() == 0 ) { std::cout << "No scores entered. Please try again!" << std::endl; return 1; }
// Compute the average, standard deviation and median double average, std_dev; compute_avg_and_std_dev( scores, average, std_dev ); double median = compute_median( scores );
// Output std::cout << "Among " << scores.size() << " grades: \n" << " average = " << std::setprecision(3) << average << ’\n’ << " std_dev = " << std_dev << ’\n’ << " median = " << median << std::endl;
return 0; }
4.10 Passing Vectors (and Strings) As Parameters
The following outlines rules for passing vectors as parameters. The same rules apply to passing strings.
- If you are passing a vector as a parameter to a function and you want to make a (permanent) change to the
vector, then you should pass it by reference.
- This is illustrated by the function read scores in the program median grade.
- This is very different from the behavior of arrays as parameters.
- What if you don’t want to make changes to the vector or don’t want these changes to be permanent?
- The answer we’ve learned so far is to pass by value.
- The problem is that the entire vector is copied when this happens!
- The solution is to pass by constant reference: pass it by reference, but make it a constant so that it can not
be changed.
- This is illustrated by the functions compute avg and std dev and compute median in the program median grade.
- As a general rule, you should not pass a container object such as a vector or a string, by value because of the
cost of copying. There are rare circumstances in which this rule may be violated, but not in CS II.
4.11 Initializing a Vector — The Use of Constructors
Here are several different ways to initialize a vector:
- This “constructs” an empty vector of integers. Values must be placed in the vector using push_back.
vector a;
- This constructs a vector of 100 doubles, each entry storing the value 3.14. New entries can be created using
push_back, but these will create entries 100, 101, 102, etc.
int n = 100;
vector b( 100, 3.14 );
- This constructs a vector of 10,000 ints, but provides no initial values for these integers. Again, new entries can
be created for the vector using push_back. These will create entries 10000, 10001, etc.
vector c( n*n );
- This constructs a vector that is an exact copy of vector b.
vector d( b );
- This is a compiler error because no constructor exists to create an int vector from a double vector. These are
different types.
vector e( b );
4.12 Exercises
1. After the above code constructing the three vectors, what will be output by the following statement?
cout << a.size() << endl
<< b.size() << endl
<< c.size() << endl;
2. Write code to construct a vector containing 100 doubles, each having the value 55.5.
3. Write code to construct a vector containing 1000 doubles, containing the values 0, 1,
5, etc.
Write it two ways, one that uses push_back and one that does not use push_back.
std::cout << ’[’ << std::setw(3) << lower << ".." << std::setw(3) << upper << "): " << std::setw(3) << histogram[b] << ’\n’; }
return 0; // Everything ok }
4.14 Example: Alphabetize Strings
// Program: alphabetize.cpp // Author: Chuck Stewart // Purpose: Demonstrate using a vector of strings and sorting.
#include #include #include #include #include
int main( int argc, char* argv[] ) {
if ( argc != 3 ) { std::cerr << "Usage: " << argv[0] << " names-in names-out\n"; return 1; } std::ifstream names_in_str( argv[1] ); if ( !names_in_str ) { std::cerr << "Can not open the names file " << argv[1] << "\n"; return 1; } std::ofstream names_out_str( argv[2] ); if ( !names_out_str ) { std::cerr << "Can not open the output names file " << argv[2] << "\n"; return 1; }
std::vector<std::string> names; std::string one_name;
// Read the strings one at a time and add them to the back of the // vector. The reading loop ends when the end of file has been reached. while ( names_in_str >> one_name ) { names.push_back( one_name ); }
// Sort the vector of strings in the same manner that we sorted the // vector of doubles. The sort function uses (automatically) the < // operator which is defined on strings. This operator compares // strings "lexicographically". std::sort( names.begin(), names.end() );
names_out_str << "\n" << "Here are the names in alphabetical order." << std::endl; for ( unsigned int i=0; i<names.size(); ++i ) { names_out_str << names[i] << std::endl; }
return 0; }
