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author | paltherr <paltherr@epfl.ch> | 2003-03-21 10:12:37 +0000 |
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committer | paltherr <paltherr@epfl.ch> | 2003-03-21 10:12:37 +0000 |
commit | 5e7f6d941d16569f430fd4e078b32329c028ae21 (patch) | |
tree | 3299ae08c20cebcbdf0c93e22473c0a78581b5d2 /test/files/run | |
parent | 6a7bec093bbf8da427657fa84783dcc21c59fcc0 (diff) | |
download | scala-5e7f6d941d16569f430fd4e078b32329c028ae21.tar.gz scala-5e7f6d941d16569f430fd4e078b32329c028ae21.tar.bz2 scala-5e7f6d941d16569f430fd4e078b32329c028ae21.zip |
- Added exercices
Diffstat (limited to 'test/files/run')
-rw-r--r-- | test/files/run/Course-2002-07.check | 35 | ||||
-rw-r--r-- | test/files/run/Course-2002-07.scala | 255 |
2 files changed, 290 insertions, 0 deletions
diff --git a/test/files/run/Course-2002-07.check b/test/files/run/Course-2002-07.check index d2e92a6463..bb69b26734 100644 --- a/test/files/run/Course-2002-07.check +++ b/test/files/run/Course-2002-07.check @@ -100,3 +100,38 @@ g'(x) = 2 * x * 1 + x * (2 * 1 + x * 0) + 3 * 1 + x * 0 g (3) = 27 g'(3) = 15 +ta(x) = x + 3 +tb(x) = x + 3 +tc(x) = x + 3 +td(x) = x + 3 +te(x) = 2 * x + 3 +tf(x) = 2 * x + 3 +tg(x) = 6 * x +th(x) = x^6 + +f4(x) = x^4 + 7 * x^3 + 20 * x^2 + 23 * x + 5 +f3(x) = 4 * x^3 + 21 * x^2 + 40 * x + 23 +f2(x) = 12 * x^2 + 42 * x + 40 +f1(x) = 24 * x + 42 +f0(x) = 24 + +f4(0) = 5 ok +f4(1) = 56 ok +f4(2) = 203 ok +f4(3) = 524 ok +f4(4) = 1121 ok + +f3(0) = 23 ok +f3(1) = 88 ok +f3(2) = 219 ok +f3(3) = 440 ok + +f2(0) = 40 ok +f2(1) = 94 ok +f2(2) = 172 ok + +f1(0) = 42 ok +f1(1) = 66 ok + +f0(0) = 24 ok + diff --git a/test/files/run/Course-2002-07.scala b/test/files/run/Course-2002-07.scala index aebef8b429..3d1f21b209 100644 --- a/test/files/run/Course-2002-07.scala +++ b/test/files/run/Course-2002-07.scala @@ -449,6 +449,260 @@ module MA { //############################################################################ +module Utils { + + private def power0(x: int, y: int): int = + if (y == 1) x else if (y % 2 == 0) power0(x*x,y/2) else x*power0(x, y-1); + + def power(x: int, y: int): int = Pair(x,y) match { + case Pair(0,0) => error("power(0,0)") + case Pair(0,_) => 0 + case Pair(1,_) => 1 + case Pair(_,0) => 1 + case Pair(_,1) => x + case Pair(_,2) => x*x + case Pair(_,_) => if (y < 0) 1/power0(x,y) else power0(x,y) + } + + def lookup(entries: List[Pair[String,int]], key: String):int = entries match{ + case List() => error("no value for " + key) + case Pair(k,v) :: _ if (k == key) => v + case _ :: rest => lookup(rest, key) + } + + def compare(xs: List[String], ys: List[String]): int = Pair(xs,ys) match{ + case Pair(List(), List()) => 0 + case Pair(List(), _ ) => -1 + case Pair(_ , List()) => +1 + case Pair(x::xs , y::ys ) => { + val diff = x.compareTo(y); + if (diff != 0) diff else compare(xs,ys) + } + } + +} + +module MB { + + import Utils._; + + + trait Expr { + + private def count: int = match { + case Lit(n) => n + case Mul(Lit(n),_) => n + case _ => 1 + } + + private def term: Expr = match { + case Lit(_) => Lit(1) + case Mul(Lit(_),r) => r + case _ => this + } + + private def vars: List[String] = match { + case Var(n) => List(n) + case Mul(l,r) => l.vars ::: r.vars + case Pow(l,n) => { val vs = l.vars; List.range(0,n).flatMap(i => vs) } + case _ => List() + } + + private def +< (that: Expr): boolean = (this +<? that) < 0; + private def +<= (that: Expr): boolean = (this +<? that) <= 0; + private def +<? (that: Expr): int = Pair(this,that) match { + case Pair(Add(_,_), _ ) => 0 + case Pair(_ , Add(_,_)) => 0 + case Pair(_ , _ ) => compare(this.vars,that.vars) + } + + def + (that: Expr): Expr = if (that +<= this) Pair(this,that) match { + case Pair(_ , Lit(0) ) => this + case Pair(Lit(l) , Lit(r) ) => Lit(l + r) + case Pair(_ , Add(rl,rr)) => (this + rl) + rr + case Pair(Add(ll,lr), _ ) if (lr +<= that) => ll + (that + lr) + case Pair(_ , _ ) => { + val l = this.term; + val r = that.term; + if (l equ r) Lit(this.count + that.count) * r else Add(this, that) + } + } else that + this; + + private def *< (that: Expr): boolean = (this *<? that) < 0; + private def *<= (that: Expr): boolean = (this *<? that) <= 0; + private def *<? (that: Expr): int = Pair(this,that) match { + case Pair(Mul(_,_), _ ) => 0 + case Pair(_ , Mul(_,_)) => 0 + case Pair(Add(_,_), Add(_,_)) => 0 + case Pair(Add(_,_), _ ) => -1 + case Pair(_ , Add(_,_)) => +1 + case Pair(Lit(_) , Lit(_) ) => 0 + case Pair(Lit(_) , _ ) => -1 + case Pair(_ , Lit(_) ) => +1 + case Pair(Var(l) , Var(r) ) => l.compareTo(r) + case Pair(Var(_) , Pow(r,_)) => if (this *<= r) -1 else +1 + case Pair(Pow(l,_), Var(_) ) => if (l *< that) -1 else +1 + case Pair(Pow(l,_), Pow(r,_)) => l *<? r + } + + def * (that: Expr): Expr = if (this *<= that) Pair(this,that) match { + case Pair(Lit(0) , _ ) => this + case Pair(Lit(1) , _ ) => that + case Pair(Mul(ll,lr), r ) => ll * (lr * r) + case Pair(Add(ll,lr), r ) => ll * r + lr * r + case Pair(Lit(l) , Lit(r) ) => Lit(l * r) + case Pair(Var(_) , Var(_) ) if (this equ that) => Pow(this,2) + case Pair(Var(_) , Pow(r,n) ) if (this equ r) => Pow(this,n + 1) + case Pair(Pow(ll,lr), Pow(rl,rr)) if (ll equ rl) => Pow(ll,lr + rr) + case Pair(l , Mul(rl,rr)) if (rl *<= l) => (rl * l) * rr + case Pair(_ , _ ) => Mul(this,that) + } else that * this; + + def ^ (that: int): Expr = Pair(this,that) match { + case Pair(_ ,1) => this + case Pair(Lit(i) ,n) => Lit(power(i,n)) + case Pair(Var(_) ,n) => Pow(this,n) + case Pair(Add(_,_),n) => this * (this ^ (n - 1)) + case Pair(Mul(l,r),n) => (l ^ n) * (r ^ n) + case Pair(Pow(e,m),n) => Pow(e,m + n) + } + + def derive(v: Var): Expr = match { + case Lit(_) => Lit(0) + case Var(name) => if (name == v.name) Lit(1) else Lit(0) + case Add(e1, e2) => (e1 derive v) + (e2 derive v) + case Mul(e1, e2) => e1 * (e2 derive v) + e2 * (e1 derive v) + case Pow(e1, i2) => Lit(i2) * (e1 derive v) * (e1 ^ (i2 - 1)) + } + + def evaluate(vars: List[Pair[String,int]]): int = match { + case Lit(cst) => cst + case Var (name) => lookup(vars, name) + case Add (l, r) => l.evaluate(vars) + r.evaluate(vars) + case Mul (l, r) => l.evaluate(vars) * r.evaluate(vars) + case Pow(l, r) => power(l.evaluate(vars), r) + } + + def equ(that: Expr): boolean = Pair(this,that) match { + case Pair(Lit(l) ,Lit(r)) => l == r + case Pair(Var(l) ,Var(r)) => l == r + case Pair(Add(ll,lr),Add(rl,rr)) => (ll equ rl) && (lr equ rr) + case Pair(Mul(ll,lr),Mul(rl,rr)) => (ll equ rl) && (lr equ rr) + case Pair(Pow(ll,lr),Pow(rl,rr)) => (ll equ rl) && (lr == rr) + case _ => false + } + + } + + case class Lit(x: int) extends Expr { + override def toString() = x.toString() + } + + case class Var(name: String) extends Expr { + override def toString() = name; + } + + case class Add(e1: Expr, e2: Expr) extends Expr { + override def toString() = e1.toString() + " + " + e2.toString(); // !!! .toString + } + + case class Mul(e1: Expr, e2: Expr) extends Expr { + override def toString() = { + def factorToString(e: Expr) = e match { + case Add(_, _) => "(" + e.toString() + ")" + case _ => e.toString() + } + factorToString(e1) + " * " + factorToString(e2); + } + } + + case class Pow(e1: Expr, i2: int) extends Expr { + override def toString() = { + def factorToString(e: Expr) = e match { + case Add(_, _) => "(" + e.toString() + ")" + case Mul(_, _) => "(" + e.toString() + ")" + case _ => e.toString() + } + factorToString(e1) + "^" + i2; + } + } + + def test = { + val _1 = Lit(1); + val _2 = Lit(2); + val _3 = Lit(3); + val _4 = Lit(4); + val _5 = Lit(5); + + val x = Var("x"); + + val ta = (_1 + (_2 + x)); + val tb = (_1 + (x + _2)); + val tc = ((_1 + x) + _2); + val td = ((x + _1) + _2); + val te = ((x + _1) + (x + _2)); + val tf = ((_1 + x) + (_2 + x)); + val tg = x + x + (x * _2) + x + x; + val th = x * x * (x ^ 2) * x * x; + + System.out.println("ta(x) = " + ta); + System.out.println("tb(x) = " + tb); + System.out.println("tc(x) = " + tc); + System.out.println("td(x) = " + td); + System.out.println("te(x) = " + te); + System.out.println("tf(x) = " + tf); + System.out.println("tg(x) = " + tg); + System.out.println("th(x) = " + th); + System.out.println(); + + val f4 = (x+ _3)*(_2+x)*x*(x+ _1) + (x+ _5)*(x*(x+ _2)+x+ _1) + (x^2) + x; + val f3 = f4.derive(x); + val f2 = f3.derive(x); + val f1 = f2.derive(x); + val f0 = f1.derive(x); + + System.out.println("f4(x) = " + f4); + System.out.println("f3(x) = " + f3); + System.out.println("f2(x) = " + f2); + System.out.println("f1(x) = " + f1); + System.out.println("f0(x) = " + f0); + System.out.println(); + + def check(n: String, f: Expr, x: int, e: int) = { + val a: int = f.evaluate(List(Pair("x",x))); + val s: String = if (a == e) "ok" else "KO(" + e + ")"; + System.out.println(n + "(" + x + ") = " + a + " " + s); + } + + check("f4", f4, 0, 5); + check("f4", f4, 1, 56); + check("f4", f4, 2, 203); + check("f4", f4, 3, 524); + check("f4", f4, 4, 1121); + System.out.println(); + + check("f3", f3, 0, 23); + check("f3", f3, 1, 88); + check("f3", f3, 2, 219); + check("f3", f3, 3, 440); + System.out.println(); + + check("f2", f2, 0, 40); + check("f2", f2, 1, 94); + check("f2", f2, 2, 172); + System.out.println(); + + check("f1", f1, 0, 42); + check("f1", f1, 1, 66); + System.out.println(); + + check("f0", f0, 0, 24); + System.out.println(); + } +} + +//############################################################################ + module Test { def main(args: Array[String]): unit = { M0.test; @@ -462,6 +716,7 @@ module Test { M8.test; M9.test; MA.test; + MB.test; () } } |