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Quadratic Function and Factorial

Topics: Selection (conditional) statement, keyboard input using Scanner class, while loop, methods
Reading: Sec 2.2, Sec 3.1 (exclude pp104-109), Sec 3.2 (exclude pp112-114), pp 130-135 of Sec 3.3 (exclude the dowhile
loop)

Example: Quadratic function , re-visited

Write a program to find the minimum value of the quadratic function q(x)=x2+bx+c on the interval [L, R].

/* Min value of q(x) = x^2 + bx + c on interval [L,R]
*/
public class MinQuadratic {
public static void main (String[ ] args) {

final double b=2, c=-1.5;
double L=-3, R=5;
double qMin, qL, qR; // Min value of q, q(L), q(R)

double xc= -b/2;
if (L<=xc && xc<=R)
// qMin is q(xc)
qMin= xc*xc + b*xc + c;
else {
// qMin is q(L) or q(R)
qL= L*L + b*L + c;
qR= R*R + b*R + c;
if (qL < qR)
qMin= qL;
else
qMin= qR;
}

System .out.println("Min value is " + qMin);
}
}

User Input

We’ll use the class Scanner to read in user input from the keyboard. First, you need to import the class using the import
statement outside of the class body:

import java.util.Scanner;

Inside a method (e.g., main method), you create an object of the Scanner class. Below, we create such an object and
refer to it with the variable keyboard:

Scanner keyboard= new Scanner ( System .in);

Now we can use keyboard to read user input. Below are some example method calls. Read Sec 2.2 (Savitch) for more
information on the Scanner class.

Examples:

int var1= keyboard.nextInt ();
double var2= keyboard.nextDouble();
char var3= keyboard.nextChar();
boolean var4= keyboard.nextBoolean();

The Math class

A collection of basic mathematical functions .

double tmp = Math.exp(1);
tmp = 3*Math.sin(2);
tmp = Math.floor(3*Math.sin(2));
tmp = Math.random(); // in [0,1)

Shortcut expressions

Increment: i++;
Decrement: i--;
Assignment operators :

s += val;
s -= val;
s *= val;
s /= val;

Conditional Statement The while loop
if ( condition1 )
statement1;
while ( condition)

statement;
if ( condition1 )
statement1;
else
statement2;
Pattern for doing something n times
if ( condition1 )
statement1;
else if ( condition2 )
statement2;
else
statement3;
int i= 1;
while ( i<=n ) {
// do something
// increment counter
i= i + 1;
}
  Pattern for doing something an indefinite number of times
  % initialization

while ( not stopping signal ) {
// do something

// update status (variables)
}

Example: Factorial

Write a program fragment to calculate k ! (the factorial of k ). Assume k is given and k>=0. Use a while loop.

Method

/* = a random integer in [lo..hi]
*/
public static int randInt (int lo, int hi) {
return (int) Math.floor(
Math.random()*(hi-lo+1) + lo);
}
Method

A method is a named , parameterized group of statements
modifiers return-type method-name ( parameter-list ) {
statement-list
}


return-type void means nothing is returned from the method

There must be a return statement, unless return-type is
void

Method

A method is a named, parameterized group of statements
modifiers return-type method-name ( parameter-list ) {
statement-list
}


parameter-list : type-name pairs separated by commas

int randInt(int lo, int hi)

A parameter is a variable that is declared in the method

Calling a static method …

… that is in a different class :
classname.methodname(…)

Examples:

Math.random()
Math.pow(2.5,2)

… that is in the same class:
methodname(…)

Our class MyRandom has a static method
randInt, so an example method call within the
class can be
randInt(3,8)
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