Problem Solving with C++ Note: Selection and Repetition

Preprocessors

• Preprocessor commands, which begins with #, performs some actions before the complier does the translation.
  • The include command is to include a header file:
    • Files containing definitions of common variables and functions.
    • Written to be included by other programs.
  • #include <iostream>: Before the compilation, the complier looks for the iostream header file and copy the codes therein to replace this line.
  • We may define our own variables and functions into self-defined header files and include them by ourselves:
    • #include "myHeader"
    • Use double quotation marks instead of angle brackets.
    • A path must be specified.

Namespaces

• Suppose all roads in Taiwan have different names. In this case, we do not need to include the city/county name in our address.

• This is why we do not need to specify the district for an address in the Taipei city.

• But we need to specify the district for an address in the New Taipei County.

• A C++ namespace is a collection (space) of names.

  • For C++ variables, functions, object, etc.
  • The objects cout, cin, and all other items defined in the C++ standard library are defined in the namespace std.

• By writing using namespace std;, whenever the complier sees a name, it searchs whether it is defined in this program or the namespace std.

• The scope resolution operator (::)

  • We may specify the namespace of cout each time when we use it with the scope resolution operation ::

#include <iostream>
int main()
{
    std::cout << "Hello World!\n" << std::endl; // \a std::
    return 0;
}

Selection

• The if statement

if (condition)
{
    statements
}

• The if-else statement

if (condition)
{
    statements1
}
else
{
    statement2
}

• Example

int income = 0, tax = 0;

cout << "Please enter your income: ";
cin >> income;

if (income <= 10000)
{
    tax = 0.02 * 10000;
}
else
{
    tax = 0.08 * (income - 10000) + 200;
}

• An if or an if-else statement can be nested in an if block or/and else block.

#include <iostream>
using namespace std;

int main()
{
    int a = 0, b = 0, c = 0;

    cout << "Enter three numbers: ";
    cin >> a >> b >> c;

    if (a <= b)
    {
        if (a <= c)
        {
            cout << a << " is the smallest\n";
        }
        else
        {
            cout << c << " is the smallest\n";
        }
    }
    else
    {
        if (b <= c)
        {
            cout << b << " is the smallest\n";
        }
        else
        {
            cout << c << " is the smallest\n";
        }
    }
}

• Revised version:

#include <iostream>
using namespace std;

int main()
{
    int a = 0, b = 0, c = 0;
    
    cout << "Enter three numbers: ";
    cin >> a >> b >> c;
    
    int min = c;

    if (a <= b)
    {
        if (a <= c)
        {
            min = a;
        }
    }
    else
    {
        if (b <= c)
        {
            min = b;
        }
    }
    
    cout << min << " is the smallest";
}

• The ternary if operator ? :

• In many cases, what to do after an if-else selection is simple.

• The ternary if operator ? : can be helpful in this case.

• condition ? operation A : opertion B;: if condition is true, do operation A; otherwise, operation B.

• Second revised version:

#include <iostream>
using namespace std;

int main()
{
    int a = 0, b = 0, c = 0;
    
    cout << "Enter three numbers: ";
    cin >> a >> b >> c;

    int min = c;

    if (a <= b)
        a < c ? min = a : min = c;
    else
        min = b <= c ? b : c;

    cout << "The smallest number is " << min << endl;
}

• Ternary if operators can also be nested (but not suggested)

• min = a <= b ? a <= c? a : c : b <= c ? b : c;

• min = (a <= b ? (a <= c? a : c) : (b <= c ? b : c));

• Dangling if-else

  • What does this mean?

if (a == 10)
    if (b == 10)
        cout << "a and b are both ten. \n";
else
    cout << "a is not ten. \n";

• In the current C++ standard, it is actually:

if (a == 10)
{
    if (b == 10)
        cout << "a and b are both ten. \n";
    else
        cout << "a is not ten. \n";
}    

• When we drop {}， our programs may be grammatically ambiguous.

• In the field of Programming Languages, it is called the dangling program.

• To handle this, C++ defines that “one else will be paired to the closest if that has not been paired with an else.”

• Good programming style:

  • Drop { } only when you know what you are doing.
  • Align your { }.
  • Indent your codes properly.

• Logical operators

  • &&: and.
  • ||: or.
  • !: not.
  • These operators have their aliases (and, or, and not).

• Each of the two conditions must be complete by itself.

if (a >= 10 && <= 20) // error! \a
    cout << "a is between 10 and 20";

• Two conditions can be combined only with a logical operator.

if (10 <= a <= 20) // error! \a
    cout << "a is between 10 and 20";

• Associativity and precedence
  • The && and || operators both associate the two conditions from left to right.
  • It is possible that the second condition is not evaluated at all.
    • If evaluating the first one is enough.
  • There is a precedence rule for operators.
    • Use parentheses.

#include <iostream>
using namespace std;

int main()
{
    int a = 0, b = 0;

    if ((a > 10) && (b = 1))
    ;
    cout << b << endl;  // result: 0 \a

    if ((a > 10) || (b = 5))
    ;
    cout << b << endl; // result: 5 \a
}

• switch-case

switch (operation)
{
    case value 1:
        statements
        break;
    case value 2:
        statements
        break;
    ...
    default:
        statements
        break;
}

• it is particularly useful for responding to multiple values of a single operation.
• For the operatoion:
  • It can contain only a single operand.
  • It must return an integer.
  • After each case, there is a value.
  • If the returned value of the operation equals that value, those statements in the case block will be executed.
  • No curly brackets are needed for blocks.
  • A colon is needed after the value.
  • A break marks the end of a block.
    • The break of the last section is optional.
  • Restriction on those values:
    • Cannot be (non-constant) variables.
    • Must be different integers.
• What will happen if we enter 10?

int a;
cin >> a;

switch (a)
{
    case 10:
        cout << "ten";
    case 6:
        cout << "six";
        break
}

• Example:

• Given a year and a month, how many days is in that month?

• There are four possibilities:

  • 31 days: January, March, May, July, August, October, December.
  • 30 days: April, June, September, November.
  • 29 days: Februray in a leap year.
  • 28 days: Februray in a ordinary year.

• A year is a leap year if:

  • It is a multiple of 400, or
  • It is a multiple of 4 but not a multiple of 100.

• Version 1

#include <iostream>
using namespace std;

int main()
{
    int year = 0, month = 0;
    cout << "Enter year and month: ";
    cin >> year >> month;
    int days = 0;

    if (month ==1 || month == 3 || month == 5 || month == 7 || month == 8 || month == 10 || month == 12)
        days = 31;
    else if (month == 4 || month == 6 || month == 9 || month == 11)
        days = 30;
    else if ((year % 400 == 0) || (year % 4 == 0 && year % 100 != 0))
        days = 29;
    else
        days = 28;

    cout << "Number of days: " << days << endl;
}

• Version 2

#include <iostream>
using namespace std;

int main()
{
    int year = 0, month = 0;
    cout << "Enter year and month: ";
    cin >> year >> month;
    int days = 0;

    switch (month)
    {
        case 1: case 3: case 5: case 7: case 8: case 10: case 12:
            days = 31;
            break;
        case 4: case 6: case 9: case 11:
            days = 30;
            break;
        case 2:
            if ((year % 4 == 0 && year % 100 != 0) || year % 400 == 0)
                days = 29;
            else
                days = 28;
    }

    cout << "Number of days: " << days << endl;
}

Repetition

• while and do-while

while (operation)
{
    statements
}

do 
{
    statements
} while (operation); // semicolon \a

• loop counter

• Using the unary increment/decrement operator ++/-- can be more convenient.(NOTE: postfix/prefix?)

• Binary self-assigning operators (e.g., +=).

• For modifying i, i++ has the same effect as i = i + 1.

• For modifying i, i-- has the same effect as i = i -1.

• They can be applied on all basic data types.

  • But we should only apply them on integers.
  • Typically, using them is faster than using the corresponding addition/subtraction and assignment operation.

• Both can be put at the left or the right of the operand.

  • This changes the order of related operations.
  • i++: returns the value of i, and then increment i.
  • ++i: increments i, and then returns the incremented value of i.
  • So is i = i + 1 equivalent to i++ or ++i? (ans: ++i)

• Self-assigning operations

  • Typically a += b is ** ** than a = a + b, etc.

• for

for (init; condition; some)
{
    statements
}

• You need those two ; in the ( ).

• The typical way of using a for statement is:

  • init: Initialize a counter variable.
  • cond: Set up the condition on the counter variable for the loop to continue.
  • some: Modify (mostly increment or decrement) the counter variable.
  • statements: The things that we really want to do.

• Multi-counter for loops

  • Inside one for statement:
    • You may initialize multiple counters at the same time.
    • You may also check multiple counters at the same time.
    • You may also modify multiple counters at the same time.
  • Use && or || to connect operations on multiple counters.

for (int i = 0, j = 0; i < 10 && j > -5; i++, j--)
    cout << i << " " << j << endl;

• Good programming style:

  • When you need to execute a loop for a fixed number of iterations, use a for statement with a counter declared only for the loop
    • This also applies if you know the maximum number of iterations.
    • This avoids poetential conflicts on variable names.
  • Use the loop that makes your program the most readable.
  • Typically only the counter variable enters the () of a for statement.
  • You may use fractional numbers for a counters, but this not recommended.
    • Use integer only.
  • Drop {} only when you know what you are doing.
  • Align your {}. Indent your codes properly.

• Scope of variable

  • variables live only in the block in which they are declared.
  • Two variables declared in the same level cannot have the same name.

int i = 0;
for (; i< 10; i++)
    cout << i << endl;
// ...
int i = 0; // error! \a
for (; i < 10; i++)
     cout << i << endl;

• This is a good reasons to use for: All loops at the same level may use the same name for loop counters.

for (int i = 0; i< 10; i++)
    cout << i << endl;
// ...
for (int i = 0; i < 10; i++)
     cout << i << endl;

• However, a variable of an existing name is allowed to be declared in an inner block.
  • In the inner block, after the same variable name is used to declare a new variable, it “replace” the original one.
  • However, its life ends when the inner block ends.

int a = 0;
if (a == 0)
{
    cout << a << endl;
    int a = 10;
    cout << a << endl;
}
cout << a << endl;

• break and continue
  • When we implement a repetition process, sometimes we need to further change the flow of execution of the loop
  • A break statement brings us to exit the loop immediately.
  • When continue is executed, statements after it in the loop are skipped.
    • The looping condition will be checked immediately.
    • If it is satisfied, the loop starts from the beginning again.
  • How to write a program to print out all integers from 1 to 100 except multiples of 10.

for (int a = 1; a <= 100; a++)
{
    if (a % 10 != 0)
        cout << a << endl;
}

for (int a = 1; a <= 100; a++)
{
    if (a % 10 == 0)
        continue;
    cout << a << endl;
}

• The effect of break and continue is just on the current level.
  • If a break is used in an inner loop, the execution jumps to the outer loop
  • If a continue is used in an inner loop, the execution jumps to the condition check of the inner loop.
• What will be printed out at the end of this program

#include <iostream>

int main()
{
    using namespace std;

    int a = 0, b = 0;
    while (a <= 10)
    {
        while (b <= 10)
        {
            if (b == 5)
                break;
            cout << a * b << endl; // result: a = 0, b = 0: 0, 0, 0, 0, 0; a = 1, b = 5: 
            b++;
        }
        a++;
    }
    cout << a << endl; // result: 11
    return 0;
}

• Using break gives a loop multiple exits
  • It becomes harder to track the flow of a program.
  • It becomes harder to know the state after a loop
• Using continue highlights the need of getting to the next iteration.
  • Having too many continue still gets people confused.
• Be careful not to hurt the readability of a program too much.