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//############################################################################
// Programmation IV - 2002 - Week 01
//############################################################################
object M0 {
//##########################################################################
Console.println(87 + 145);
Console.println(1000 - 333);
Console.println(5 + 2 * 3);
//##########################################################################
def size = 2;
def pi = 3.14159;
def radius = 10;
def circumference = 2 * pi * radius;
Console.println(5 * size);
Console.println(2 * pi * radius);
Console.println(circumference);
Console.println((2 * pi) * radius);
//##########################################################################
def square(x: Double) = x * x;
Console.println(square(2));
Console.println(square(5 + 4));
Console.println(square(square(4)));
//##########################################################################
def sumOfSquares(x: Double, y: Double) = square(x) + square(y);
Console.println(sumOfSquares(3, 2+2));
//##########################################################################
def loop: Int = loop;
def first(x: Int, y: Int) = x;
def constOne(x: Int, y: => Int) = 1;
Console.println(constOne(1, loop));
//##########################################################################
def abs(x: Double) = if (x >= 0) x else -x;
Console.println(abs(737));
Console.println(abs(1));
Console.println(abs(0));
Console.println(abs(-1));
Console.println(abs(-76));
//##########################################################################
def sqrtIter0(guess: Double, x: Double): Double =
if (isGoodEnough0(guess, x)) guess
else sqrtIter0(improve0(guess, x), x);
def improve0(guess: Double, x: Double) =
(guess + x / guess) / 2;
def isGoodEnough0(guess: Double, x: Double) =
abs(square(guess) - x) < 0.001;
def sqrt0(x: Double) = sqrtIter0(1.0, x);
Console.println(sqrt0(2));
Console.println(sqrt0(3));
Console.println(sqrt0(4));
//##########################################################################
def sqrt1(x: Double) = {
def sqrtIter1(guess: Double, x: Double): Double =
if (isGoodEnough1(guess, x)) guess
else sqrtIter1(improve1(guess, x), x);
def improve1(guess: Double, x: Double) =
(guess + x / guess) / 2;
def isGoodEnough1(guess: Double, x: Double) =
abs(square(guess) - x) < 0.001;
sqrtIter1(1.0, x)
}
Console.println(sqrt1(2));
Console.println(sqrt1(3));
Console.println(sqrt1(4));
//##########################################################################
def sqrt2(x: Double) = {
def sqrtIter2(guess: Double): Double =
if (isGoodEnough2(guess)) guess
else sqrtIter2(improve2(guess));
def improve2(guess: Double) =
(guess + x / guess) / 2;
def isGoodEnough2(guess: Double) =
abs(square(guess) - x) < 0.001;
sqrtIter2(1.0)
}
Console.println(sqrt2(2));
Console.println(sqrt2(3));
Console.println(sqrt2(4));
//##########################################################################
}
//############################################################################
object M1 {
def abs(x: Double) = if (x >= 0) x else -x;
def sqrt(x: Double): Double = {
def sqrtIter(prev: Double, guess: Double): Double =
if (isGoodEnough(prev, guess)) guess
else sqrtIter(guess, improve(guess));
def improve(guess: Double) = (guess + x / guess) / 2;
def isGoodEnough(prev: Double, guess: Double) =
abs(prev - guess) / guess < 0.001;
sqrtIter(1.0, improve(1.0))
}
Console.println("sqrt(2) = " + sqrt(2));
}
//############################################################################
object M2 {
def abs(x: Double) = if (x >= 0) x else -x;
def sqrt(x:Double):Double = {
def sqrtIter(guess:Double):Double = {
val next = improve(guess);
if (isGoodEnough(guess,next)) next
else sqrtIter(next)
}
def improve(guess:Double) = (guess+x/guess)/2;
def isGoodEnough(prev:Double,guess:Double) = abs(prev-guess)/guess<0.001;
sqrtIter(1.0)
}
Console.println("sqrt(2) = " + sqrt(2));
}
//############################################################################
object M3 {
def abs(x: Double) = if (x >= 0) x else -x;
def cbrt(x:Double):Double = {
def cbrtIter(guess:Double):Double = {
val next = improve(guess);
if (isGoodEnough(guess,next)) next
else cbrtIter(next)
}
def improve(y:Double) = (x/(y*y)+2*y)/3;
def isGoodEnough(prev:Double,guess:Double) = abs(prev-guess)/guess<0.001;
cbrtIter(1.0)
}
Console.println("cbrt(2) = " + cbrt(2));
}
//############################################################################
object M4 {
def pascal(c: Int, l: Int): Int =
if (c <= 0 || c >= l) 1
else pascal(c - 1, l - 1) + pascal(c, l - 1);
Console.print(pascal(0,0));
Console.println;
Console.print(pascal(0,1));
Console.print(' ');
Console.print(pascal(1,1));
Console.println;
Console.print(pascal(0,2));
Console.print(' ');
Console.print(pascal(1,2));
Console.print(' ');
Console.print(pascal(2,2));
Console.println;
Console.print(pascal(0,3));
Console.print(' ');
Console.print(pascal(1,3));
Console.print(' ');
Console.print(pascal(2,3));
Console.print(' ');
Console.print(pascal(3,3));
Console.println;
Console.print(pascal(0,4));
Console.print(' ');
Console.print(pascal(1,4));
Console.print(' ');
Console.print(pascal(2,4));
Console.print(' ');
Console.print(pascal(3,4));
Console.print(' ');
Console.print(pascal(4,4));
Console.println;
}
//############################################################################
object Test {
def main(args: Array[String]): Unit = {
M0;
M1;
M2;
M3;
M4;
()
}
}
//############################################################################
|
