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author | Martin Odersky <odersky@gmail.com> | 2005-10-05 11:08:17 +0000 |
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committer | Martin Odersky <odersky@gmail.com> | 2005-10-05 11:08:17 +0000 |
commit | 0a6b2c44cbdcea9e9c248b6a5b9970ad4cd86001 (patch) | |
tree | c008a12ea7e928b3f34e0c345c84832d90c1c8ad /test-nsc/files/run/Course-2002-02.scala | |
parent | 041a971eb7f89d2976bee5512a6caf7de7bff27c (diff) | |
download | scala-0a6b2c44cbdcea9e9c248b6a5b9970ad4cd86001.tar.gz scala-0a6b2c44cbdcea9e9c248b6a5b9970ad4cd86001.tar.bz2 scala-0a6b2c44cbdcea9e9c248b6a5b9970ad4cd86001.zip |
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Diffstat (limited to 'test-nsc/files/run/Course-2002-02.scala')
-rwxr-xr-x | test-nsc/files/run/Course-2002-02.scala | 554 |
1 files changed, 554 insertions, 0 deletions
diff --git a/test-nsc/files/run/Course-2002-02.scala b/test-nsc/files/run/Course-2002-02.scala new file mode 100755 index 0000000000..00f43501f4 --- /dev/null +++ b/test-nsc/files/run/Course-2002-02.scala @@ -0,0 +1,554 @@ +//############################################################################ +// Programmation IV - 2002 - Week 02 +//############################################################################ +// $Id$ + +object M0 { + def gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b); + def factorial(n: Int): Int = if (n == 0) 1 else n * factorial(n - 1); + + Console.println(gcd(14,21)); + Console.println(factorial(5)); + Console.println; +} + +//############################################################################ + +object M1 { + def cube(x: Int): Double = x * x * x; + + def sumInts(a: Int, b: Int): Double = + if (a > b) 0 + else a + sumInts(a + 1, b); + + def sumCubes(a: Int, b: Int): Double = + if (a > b) 0 + else cube(a) + sumCubes(a + 1, b); + + def sumReciprocals(a: Int, b: Int): Double = + if (a > b) 0 + else 1.0/a + sumReciprocals(a + 1, b); + + def sumPi(n: Int): Double = { + def element(x: Int): Double = 4.0/(4*x+1) - 4.0/(4*x-1); + def sumElements(a: Int, b: Int): Double = + if (a > b) 0 + else element(a) + sumElements(a + 1, b); + 4 + sumElements(1,n) + } + + Console.println(sumInts(1,4)); + Console.println(sumCubes(1,4)); + Console.println(sumReciprocals(1,4)); + Console.println(sumCubes(1, 10) + sumReciprocals(10, 20)); + Console.println("pi = " + sumPi(20)); + Console.println; +} + +//############################################################################ + +object M2 { + def id(x: Int): Double = x; + def cube(x: Int): Double = x * x * x; + def reciprocal(x: Int): Double = 1.0/x; + + def sum(f: Int => Double, a: Int, b: Int): Double = + if (a > b) 0 + else f(a) + sum(f, a + 1, b); + + def sumInts(a: Int, b: Int): Double = sum(id, a, b); + def sumCubes(a: Int, b: Int): Double = sum(cube, a, b); + def sumReciprocals(a: Int, b: Int): Double = sum(reciprocal, a, b); + def sumPi(n: Int): Double = { + def element(x: Int): Double = 4.0/(4*x+1) - 4.0/(4*x-1); + 4 + sum(element, 1, n) + } + + Console.println(sumInts(1,4)); + Console.println(sumCubes(1,4)); + Console.println(sumReciprocals(1,4)); + Console.println(sumCubes(1, 10) + sumReciprocals(10, 20)); + Console.println("pi = " + sumPi(20)); + Console.println; +} + +//############################################################################ + +object M3 { + def sum(f: Int => Double, a: Int, b: Int): Double = + if (a > b) 0 + else f(a) + sum(f, a + 1, b); + + def sumInts(a: Int, b: Int): Double = sum((xXXXXX => xXXXXX), a, b); + def sumCubes(a: Int, b: Int): Double = sum((x => x * x * x), a, b); + def sumReciprocals(a: Int, b: Int): Double = sum((x => 1.0/x), a, b); + def sumPi(n: Int): Double = 4 + sum((x => 4.0/(4*x+1) - 4.0/(4*x-1)), 1, n); + + Console.println(sumInts(1,4)); + Console.println(sumCubes(1,4)); + Console.println(sumReciprocals(1,4)); + Console.println(sumCubes(1, 10) + sumReciprocals(10, 20)); + Console.println("pi = " + sumPi(20)); + Console.println; +} + +//############################################################################ + +object M4 { + def sum(f: Int => Double) = { + def sumF(a: Int, b: Int): Double = + if (a > b) 0 + else f(a) + sumF(a + 1, b); + sumF + } + + def sumInts = sum(x => x); + def sumCubes = sum(x => x * x * x); + def sumReciprocals = sum(x => 1.0/x); + def sumPi = (n: Int => 4 + sum(x => 4.0/(4*x+1) - 4.0/(4*x-1))(1, n)); + + Console.println(sumInts(1,4)); + Console.println(sumCubes(1,4)); + Console.println(sumReciprocals(1,4)); + Console.println(sumCubes(1, 10) + sumReciprocals(10, 20)); + Console.println("pi = " + sumPi(20)); + Console.println; +} + +//############################################################################ + +object M5 { + def sum(f: Int => Double): (Int, Int) => Double = { (a, b) => + if (a > b) 0 + else f(a) + sum(f)(a + 1, b) + } + + def sumInts = sum(x => x); + def sumCubes = sum(x => x * x * x); + def sumReciprocals = sum(x => 1.0/x); + def sumPi = (n: Int => 4 + sum(x => 4.0/(4*x+1) - 4.0/(4*x-1))(1, n)); + + Console.println(sumInts(1,4)); + Console.println(sumCubes(1,4)); + Console.println(sumReciprocals(1,4)); + Console.println(sumCubes(1, 10) + sumReciprocals(10, 20)); + Console.println("pi = " + sumPi(20)); + Console.println; +} + +//############################################################################ + +object M6 { + def sum(f: Int => Double)(a: Int, b: Int): Double = + if (a > b) 0 + else f(a) + sum(f)(a + 1, b); + + def sumInts = sum(x => x); + def sumCubes = sum(x => x * x * x); + def sumReciprocals = sum(x => 1.0/x); + def sumPi = (n: Int => 4 + sum(x => 4.0/(4*x+1) - 4.0/(4*x-1))(1, n)); + + Console.println(sumInts(1,4)); + Console.println(sumCubes(1,4)); + Console.println(sumReciprocals(1,4)); + Console.println(sumCubes(1, 10) + sumReciprocals(10, 20)); + Console.println("pi = " + sumPi(20)); + Console.println; +} + +//############################################################################ + +object M7 { + def sum(f: Int => Double)(a: Int, b: Int): Double = { + def iter(a: Int, result: Double): Double = + if (a > b) result + else iter(a + 1, f(a) + result); + iter(a, 0) + } + + def sumInts = sum(x => x); + def sumCubes = sum(x => x * x * x); + def sumReciprocals = sum(x => 1.0/x); + def sumPi = (n: Int => 4 + sum(x => 4.0/(4*x+1) - 4.0/(4*x-1))(1, n)); + + Console.println(sumInts(1,4)); + Console.println(sumCubes(1,4)); + Console.println(sumReciprocals(1,4)); + Console.println(sumCubes(1, 10) + sumReciprocals(10, 20)); + Console.println("pi = " + sumPi(20)); + Console.println; +} + +//############################################################################ + +object M8 { + def product(f: Int => Double)(a: Int, step: Int, b: Int): Double = + if (a > b) 1 + else f(a) * product(f)(a + step, step, b); + + def productPi = (n: Int => product(x=>4.0*x*x/(2*x-1)/(2*x-1))(1,1,n)/n); + + val pi = 2 * product(x => x * x)(2, 2, 40) / product(x => x * x)(1, 2,40)/40; + + Console.println("pi = " + productPi(20)); + Console.println("pi = " + pi); + Console.println; +} + +//############################################################################ + +object M9 { + def accumulate[t](combiner: (t, t) => t, nullValue: t, f: Int => t, next: Int => Int) + (a: Int, b: Int): t = + if (a > b) nullValue + else combiner(f(a), accumulate(combiner, nullValue, f, next)(next(a), b)); + + def inc(x: Int) = x + 1; + + def sum(f: Int => Double) = + accumulate((x: Double, y: Double) => x + y, 0d, f, inc); + def product(f: Int => Double) = + accumulate((x: Double, y: Double) => x * y, 1d, f, inc); + + def sumInts = sum(x => x); + def sumCubes = sum(x => x * x * x); + def sumReciprocals = sum(x => 1.0/x); + def sumPi = (n: Int => 4 + sum(x => 4.0/(4*x+1) - 4.0/(4*x-1))(1, n)); + + def productPi = (n: Int => product(x=>4.0*x*x/(2*x-1)/(2*x-1))(1,n)/n); + + val pi = 2*product(x => 2*x*2*x)(1,20)/product(x =>(2*x-1)*(2*x-1))(1,20)/40; + + Console.println(sumInts(1,4)); + Console.println(sumCubes(1,4)); + Console.println(sumReciprocals(1,4)); + Console.println(sumCubes(1, 10) + sumReciprocals(10, 20)); + Console.println("pi = " + sumPi(20)); + Console.println("pi = " + productPi(20)); + Console.println("pi = " + pi); + Console.println; +} + +//############################################################################ + +object MA { + val tolerance = 0.0001; + def abs(x: Double) = if (x < 0) -x else x; + def isCloseEnough(x: Double, y: Double) = abs((x - y) / x) < tolerance; + def fixedPoint(f: Double => Double)(firstGuess: Double) = { + def iterate(guess: Double): Double = { + val next = f(guess); + Console.println(next); + if (isCloseEnough(guess, next)) next + else iterate(next) + } + iterate(firstGuess) + } + def sqrt(x: Double) = fixedPoint(y => (y + x / y) / 2)(1.0); + + Console.println("sqrt(2) = " + sqrt(2)); + Console.println +} + +//############################################################################ + +object MB { + val tolerance = 0.0001; + def abs(x: Double) = if (x < 0) -x else x; + def isCloseEnough(x: Double, y: Double) = abs((x - y) / x) < tolerance; + def fixedPoint(f: Double => Double)(firstGuess: Double) = { + def iterate(guess: Double): Double = { + val next = f(guess); + Console.println(next); + if (isCloseEnough(guess, next)) next + else iterate(next) + } + iterate(firstGuess) + } + def averageDamp(f: Double => Double)(x: Double) = (x + f(x)) / 2; + def sqrt(x: Double) = fixedPoint(averageDamp(y => x/y))(1.0); + + Console.println("sqrt(2) = " + sqrt(2)); + Console.println +} + +//############################################################################ + +object MC { + def sum(f: Int => Double)(a: Int, b: Int): Double = { + def iter(a: Int, result: Double): Double = { + if (a > b) result + else iter(a + 1, result + f(a)) + } + iter(a, 0) + } + + def product(f: Int => Double)(a: Int, b: Int): Double = { + def iter(a: Int, result: Double): Double = { + if (a > b) result + else iter(a + 1, result * f(a)) + } + iter(a, 1) + } + + def factorial(n: Int) = product(x => x)(1 , n); + + Console.println( + "1 + 2 + .. + 5 = " + sum(x => x)(1, 5)); + Console.println( + "1 * 2 * .. * 5 = " + product(x => x)(1, 5)); + Console.println; + + Console.println( + "1^2 + 2^2 + .. + 5^2 = " + sum(x => x*x)(1, 5)); + Console.println( + "1^2 * 2^2 * .. * 5^2 = " + product(x => x*x)(1, 5)); + Console.println; + + Console.println( + "factorial(0) = " + factorial(0)); + Console.println( + "factorial(1) = " + factorial(1)); + Console.println( + "factorial(2) = " + factorial(2)); + Console.println( + "factorial(3) = " + factorial(3)); + Console.println( + "factorial(4) = " + factorial(4)); + Console.println( + "factorial(5) = " + factorial(5)); + Console.println; +} + +//############################################################################ + +object MD { + def reduce(op: (Double,Double) => Double, zero:Double) + (f: Int => Double)(a: Int,b: Int): Double = { + def iter(a: Int, result: Double): Double = { + if (a > b) result + else iter(a + 1, op(result, f(a))) + } + iter(a, zero) + } + + def plus (x:Double,y:Double) = x+y; val sum = reduce(plus , 0); + def times(x:Double,y:Double) = x*y; val product = reduce(times, 1); + + def factorial(n: Int) = product(x => x)(1 , n); + + Console.println( + "1 + 2 + .. + 5 = " + sum(x => x)(1, 5)); + Console.println( + "1 * 2 * .. * 5 = " + product(x => x)(1, 5)); + Console.println; + + Console.println( + "1^2 + 2^2 + .. + 5^2 = " + sum(x => x*x)(1, 5)); + Console.println( + "1^2 * 2^2 * .. * 5^2 = " + product(x => x*x)(1, 5)); + Console.println; + + Console.println( + "factorial(0) = " + factorial(0)); + Console.println( + "factorial(1) = " + factorial(1)); + Console.println( + "factorial(2) = " + factorial(2)); + Console.println( + "factorial(3) = " + factorial(3)); + Console.println( + "factorial(4) = " + factorial(4)); + Console.println( + "factorial(5) = " + factorial(5)); + Console.println; +} + +//############################################################################ + +object ME { + def reduce(op: (Double,Double) => Double, zero:Double) + (f: Int => Double)(a: Int,b: Int): Double = { + def iter(a: Int, result: Double): Double = { + if (a > b) result + else iter(a + 1, op(result, f(a))) + } + iter(a, zero) + } + + def sum = reduce((x,y) => x + y, 0); + def product = reduce((x,y) => x * y, 1); + + def factorial(n: Int) = product(x => x)(1 , n); + + Console.println( + "1 + 2 + .. + 5 = " + sum(x => x)(1, 5)); + Console.println( + "1 * 2 * .. * 5 = " + product(x => x)(1, 5)); + Console.println; + + Console.println( + "1^2 + 2^2 + .. + 5^2 = " + sum(x => x*x)(1, 5)); + Console.println( + "1^2 * 2^2 * .. * 5^2 = " + product(x => x*x)(1, 5)); + Console.println; + + Console.println( + "factorial(0) = " + factorial(0)); + Console.println( + "factorial(1) = " + factorial(1)); + Console.println( + "factorial(2) = " + factorial(2)); + Console.println( + "factorial(3) = " + factorial(3)); + Console.println( + "factorial(4) = " + factorial(4)); + Console.println( + "factorial(5) = " + factorial(5)); + Console.println; +} + +//############################################################################ + +object MF { + def fib(x: Int): Int = + if (x <= 1) x + else fib(x - 2) + fib(x - 1); + + Console.println("fib(0) = " + fib(0)); + Console.println("fib(1) = " + fib(1)); + Console.println("fib(2) = " + fib(2)); + Console.println("fib(3) = " + fib(3)); + Console.println("fib(4) = " + fib(4)); + Console.println("fib(5) = " + fib(5)); + Console.println("fib(6) = " + fib(6)); + Console.println("fib(7) = " + fib(7)); + Console.println("fib(8) = " + fib(8)); + Console.println("fib(9) = " + fib(9)); +} + +//############################################################################ + +object MG { + def fib(x: Int) = { + def loop(n: Int, prev: Int, fibn: Int): Int = + if (n == x) fibn + else loop(n + 1, fibn, fibn + prev); + if (x == 0) 0 else loop(1, 0, 1) + } + + Console.println("fib(0) = " + fib(0)); + Console.println("fib(1) = " + fib(1)); + Console.println("fib(2) = " + fib(2)); + Console.println("fib(3) = " + fib(3)); + Console.println("fib(4) = " + fib(4)); + Console.println("fib(5) = " + fib(5)); + Console.println("fib(6) = " + fib(6)); + Console.println("fib(7) = " + fib(7)); + Console.println("fib(8) = " + fib(8)); + Console.println("fib(9) = " + fib(9)); +} + +//############################################################################ + +object MH { + def power(x: Double, y: Int): Double = + if (y <= 0) 1 + else if (y % 2 == 0) power(x * x, y / 2) + else x * power(x, y - 1); + + + Console.println("power(0,0) = " + power(0,0)); + Console.println("power(0,1) = " + power(0,1)); + Console.println("power(0,2) = " + power(0,2)); + Console.println("power(0,3) = " + power(0,3)); + Console.println("power(0,4) = " + power(0,4)); + Console.println("power(0,5) = " + power(0,5)); + Console.println("power(0,6) = " + power(0,6)); + Console.println("power(0,7) = " + power(0,7)); + Console.println("power(0,8) = " + power(0,8)); + Console.println; + + Console.println("power(1,0) = " + power(1,0)); + Console.println("power(1,1) = " + power(1,1)); + Console.println("power(1,2) = " + power(1,2)); + Console.println("power(1,3) = " + power(1,3)); + Console.println("power(1,4) = " + power(1,4)); + Console.println("power(1,5) = " + power(1,5)); + Console.println("power(1,6) = " + power(1,6)); + Console.println("power(1,7) = " + power(1,7)); + Console.println("power(1,8) = " + power(1,8)); + Console.println; + + Console.println("power(2,0) = " + power(2,0)); + Console.println("power(2,1) = " + power(2,1)); + Console.println("power(2,2) = " + power(2,2)); + Console.println("power(2,3) = " + power(2,3)); + Console.println("power(2,4) = " + power(2,4)); + Console.println("power(2,5) = " + power(2,5)); + Console.println("power(2,6) = " + power(2,6)); + Console.println("power(2,7) = " + power(2,7)); + Console.println("power(2,8) = " + power(2,8)); + Console.println; + + Console.println("power(3,0) = " + power(3,0)); + Console.println("power(3,1) = " + power(3,1)); + Console.println("power(3,2) = " + power(3,2)); + Console.println("power(3,3) = " + power(3,3)); + Console.println("power(3,4) = " + power(3,4)); + Console.println("power(3,5) = " + power(3,5)); + Console.println("power(3,6) = " + power(3,6)); + Console.println("power(3,7) = " + power(3,7)); + Console.println("power(3,8) = " + power(3,8)); + Console.println; + + Console.println("power(4,0) = " + power(4,0)); + Console.println("power(4,1) = " + power(4,1)); + Console.println("power(4,2) = " + power(4,2)); + Console.println("power(4,3) = " + power(4,3)); + Console.println("power(4,4) = " + power(4,4)); + Console.println("power(4,5) = " + power(4,5)); + Console.println("power(4,6) = " + power(4,6)); + Console.println("power(4,7) = " + power(4,7)); + Console.println("power(4,8) = " + power(4,8)); + Console.println; + + Console.println("power(5,0) = " + power(5,0)); + Console.println("power(5,1) = " + power(5,1)); + Console.println("power(5,2) = " + power(5,2)); + Console.println("power(5,3) = " + power(5,3)); + Console.println("power(5,4) = " + power(5,4)); + Console.println("power(5,5) = " + power(5,5)); + Console.println("power(5,6) = " + power(5,6)); + Console.println("power(5,7) = " + power(5,7)); + Console.println("power(5,8) = " + power(5,8)); + Console.println; +} + +//############################################################################ + +object Test { + def main(args: Array[String]): Unit = { + M0; + M1; + M2; + M3; + M4; + M5; + M6; + M7; + M8; + M9; + MA; + MB; + MC; + MD; + ME; + MF; + MG; + MH; + () + } +} + +//############################################################################ |