From f3e1c473173020d25f56f0319ba5637473547416 Mon Sep 17 00:00:00 2001
From: trollhase <valentingehrke@gmx.de>
Date: Thu, 3 Oct 2013 05:36:40 +0200
Subject: [PATCH] colortest, deriver

---
 colortest.py          | 244 ++++++++++++++++++++++++++++++
 deriver.py            | 342 ++++++++++++++++++++++++++++++++++++++++++
 fizzbuzz-oneline.py   |   2 +-
 pso.py                |   7 +-
 sorting_algorithms.py |  32 +++-
 5 files changed, 615 insertions(+), 12 deletions(-)
 create mode 100644 colortest.py
 create mode 100644 deriver.py

diff --git a/colortest.py b/colortest.py
new file mode 100644
index 0000000..b5a177a
--- /dev/null
+++ b/colortest.py
@@ -0,0 +1,244 @@
+import pygame
+from pygame.locals import *
+from random import random,randint
+from math import sqrt
+
+screen = None
+color = (128,128,128)
+color_vel = (0,0,0)
+running = True
+
+class Vector(tuple):
+	def __add__(self,other):
+		if len(self) != len(other):
+			raise Exception("Can't add vectors of different size: %d %d" % (len(self), len(other)))
+		return Vector([ self[i]+other[i] for i in range(len(self)) ])
+
+	def __sub__(self,other):
+		if len(self) != len(other):
+			raise Exception("Can't subtract vectors of different size")
+		return Vector([ self[i]-other[i] for i in range(len(self)) ])
+
+	def __mul__(self,factor):
+		return Vector([ self[i]*factor for i in range(len(self)) ])
+
+	def __div__(self,factor):
+		return self.__mul__(1.0/factor)
+
+	def __rmul__(self,factor):
+		return self.__mul__(factor)
+
+	def __rdiv__(self,factor):
+		raise NotImplemented
+
+	def __iadd__(self,other):
+		return self.__add__(other)
+
+	def __isub__(self,other):
+		return self.__sub__(other)
+
+	def __neg__(self):
+		return self.__mul__(-1.0)
+
+	def __setitem__(self,k,v):
+		raise Exception("Not available") # immutable
+
+	def distance(self, other):
+		if len(self) != len(other):
+			raise Exception("Can't calculate distance between vectors of different size")
+		return sqrt(sum([ (self[i]-other[i])**2 for i in range(len(self)) ]))
+
+	def length(self):
+		return self.distance( Vector( (0,0) ) )
+
+
+class Tick(object):
+	def __init__(self, tickrange):
+		self.tickrange = tickrange
+		self.m_tick = 0
+
+	def tick(self):
+		self.m_tick = (self.m_tick+1)%self.tickrange
+		return self.m_tick == 0
+
+class Mode(object):
+	def __init__(self, screensize):
+		self.screensize = screensize
+
+	def update(self):
+		pass
+
+	def draw(self,screen):
+		pass
+
+def minmax(vmin,vmax):
+	return lambda v: min(vmax,max(vmin,v))
+
+class TransitionMode(Mode):
+	t = 0.3
+	a = 30
+	def __init__(self, screensize):
+		Mode.__init__(self,screensize)
+		self.color = Vector( (127,127,127) )
+		self.color_vel = Vector( 2*self.a*random()+self.a for i in range(3) )
+		self.utick = Tick(10)
+
+	def update(self):
+		if self.utick.tick():
+			randvec = Vector( (2*self.a*random()-self.a) for i in range(3) )
+			self.color_vel = (1-self.t)*self.color_vel+self.t*randvec
+		self.color = Vector( map(minmax(0,255), self.color+self.color_vel) )
+
+	def draw(self,screen):
+		screen.fill( self.color )
+
+class LelMode(Mode):
+	color = [(255,0,0),(0,255,0)]
+	size = 10
+	def __init__(self,screensize):
+		Mode.__init__(self,screensize)
+		self.offset = 0
+		self.tick = 0
+
+	def update(self):
+		self.offset = (self.offset+1)%2
+
+	def draw(self,screen):
+		w,h = screen.get_size()
+		for x in range(w):
+			color = self.color[ (x//self.size + self.offset)%2]
+			pygame.draw.line(screen, color, (x,0), (x,h) )
+
+class BallMode(Mode):
+	def __init__(self,screensize):
+		Mode.__init__(self,screensize)
+		self.ball = [200,200]
+		self.radius = 70
+		self.velocity = [10,10]
+
+	def update(self):
+		w, h = self.screensize
+		if self.ball[0] + self.radius >= w:
+			self.velocity[0] = -abs(self.velocity[0])
+		elif self.ball[0] - self.radius < 0:
+			self.velocity[0] = abs(self.velocity[0])
+		elif self.ball[1] + self.radius >= h:
+			self.velocity[1] = -abs(self.velocity[1])
+		elif self.ball[1] - self.radius < 0:
+			self.velocity[1] = abs(self.velocity[1])
+
+		for i in range(2):
+			self.ball[i] += self.velocity[i]
+
+	def draw(self,screen):
+		screen.fill( (0,0,0) )
+		pygame.draw.circle(screen, (255,0,0), tuple(self.ball), self.radius)
+
+
+class Particle:
+	def __init__(self,color, pos, vel):
+		self.color = color
+		self.pos = Vector(pos)
+		self.vel = Vector(vel)
+
+	def updateVel(self,gravity,max_v=20):
+		gravity = Vector(gravity)
+
+		#Update velocity
+		self.vel = 0.95*self.vel+0.01*random()*(gravity-self.pos)+0.1*random()*Vector( randint(-70,70) for i in range(2) )
+
+		#Limit speed
+		l = self.vel.length()
+		self.vel *= max_v/l
+
+	def updatePos(self):
+		self.pos = self.pos + self.vel
+
+	def draw(self,screen):
+		w,h = 1280,800
+		if self.pos[0] > 0 and self.pos[0] < w and self.pos[1] > 0 and self.pos[1] < h:
+			pos = tuple(map(int,self.pos))
+			velpos = tuple(map(int,self.pos+self.vel))
+			pygame.draw.circle(screen, self.color, pos, 5)
+			pygame.draw.line(screen, (255,255,255), pos, velpos, 1 )
+
+	@staticmethod
+	def generate(xmax,ymax):
+		return Particle( tuple( randint(100,255) for i in range(3) ), ( randint(0,xmax), randint(0,ymax) ), tuple( randint(-50,50) for i in range(2) ) )
+
+class SwarmMode(Mode):
+	swarmsize = 60
+	def __init__(self,screensize):
+		Mode.__init__(self,screensize)
+		self.particles = list( Particle.generate(1280,800) for i in range(self.swarmsize) )
+		self.generateGravity()
+		self.gtick = Tick(150)
+		self.utick = Tick(2)
+	
+	def generateGravity(self):
+		#self.gravity = tuple( randint(0,m) for m in [1280,800] )
+		self.gravity = Vector( (1280,800) )/2
+
+	def update(self):
+		if self.gtick.tick():
+			self.generateGravity()
+
+		v = self.utick.tick()
+
+		#king = self.particles[0]
+		#if v: king.updateVel(self.gravity, max_v=3)
+		#king.updatePos()
+
+		for p in self.particles:
+			if v: p.updateVel(self.gravity)
+			p.updatePos()
+
+	def draw(self,screen):
+		screen.fill( (0,0,0) )
+		for p in self.particles:
+			p.draw(screen)
+
+class Game(object):
+	def __init__(self, modes=[SwarmMode,TransitionMode,LelMode,BallMode]):
+		self.modes = modes
+		pygame.init()
+		self.screen = pygame.display.set_mode( (1280,800), pygame.FULLSCREEN )
+		pygame.mouse.set_visible(False)
+		self.setmode(0)
+		self.running = True
+
+	def update(self):
+		self.mode.update()
+		
+	def setmode(self,i):
+		self.modeindex = i
+		self.mode = self.modes[i%len(self.modes)](self.screen.get_size())
+
+	def nextmode(self):
+		self.setmode( self.modeindex+1 )
+
+	def draw(self):
+		self.mode.draw(self.screen)
+		pygame.display.flip()
+
+	def getevents(self):
+		for event in pygame.event.get():
+			if event.type == QUIT:
+				self.running = False
+			elif event.type == KEYDOWN:
+				if event.key == K_ESCAPE:
+					pygame.event.post(pygame.event.Event(QUIT))
+				elif event.key == K_SPACE:
+					self.nextmode()
+
+	def run(self):
+		clock = pygame.time.Clock()
+		while self.running:
+			clock.tick(30)
+			self.getevents()
+			self.update()
+			self.draw()
+
+
+if __name__ == '__main__':
+	Game().run()
\ No newline at end of file
diff --git a/deriver.py b/deriver.py
new file mode 100644
index 0000000..125a0ab
--- /dev/null
+++ b/deriver.py
@@ -0,0 +1,342 @@
+#!/usr/bin/env python
+
+#DeriverTest
+
+import re
+
+LEFT = 1
+RIGHT = 2
+
+def is_between(v,mi,ma):
+	mi = ord(mi)
+	ma = ord(ma)
+	v = ord(v)
+	return mi <= v and ma >= v
+
+def is_alpha(v):
+	return is_between(v,'a','z')
+
+def is_numeric(v):
+	return is_between(v,'0','9')
+
+class Operator2(object):
+	priority = 0
+	symbol = None
+	priority_side = LEFT
+	def __init__(self,left,right):
+		self.left = left
+		self.right = right
+
+	def __repr__(self):
+		return "(" + repr(self.left) + ") "+self.symbol+" (" + repr(self.right) + ")"
+
+	def insert(self,id_dict,idv=None):
+		return self.__class__(self.left.insert(id_dict,idv),self.right.insert(id_dict,idv))
+
+	def __eq__(self,other):
+		return self.__class__ == other.__class__ and self.left == other.left and self.right == other.right
+
+	def is_constant(self,idv=None):
+		return self.left.is_constant(idv) and self.right.is_constant(idv)
+
+	def calc(self):
+		a = self.left.calc().value
+		b = self.right.calc().value
+
+		return Numeric(self._calc(a,b))
+
+	def _calc(self):
+		raise "Error symbol %s not implemented" % self.symbol
+
+class Addition(Operator2):
+	priority = 3
+	symbol = "+"
+
+	def _calc(self,a,b):
+		return a + b
+
+class Subtraction(Operator2):
+	priority = 3
+	symbol = "-"
+
+	def _calc(self,a,b):
+		return a - b
+
+class Multiplication(Operator2):
+	priority = 2
+	symbol = "*"
+
+	def _calc(self,a,b):
+		return a * b
+
+class Division(Operator2):
+	priority = 2
+	symbol = "/"
+
+	def _calc(self,a,b):
+		return a/b
+
+class Power(Operator2):
+	priority = 1
+	symbol = "^"
+
+	def _calc(self,a,b):
+		return a**b
+
+class Numeric(object):
+	def __init__(self,value):
+		self.value = value
+
+	def __repr__(self):
+		return str(self.value)
+
+	def __eq__(self,other):
+		return self.__class__ == other.__class__ and self.value == other.value
+
+	def insert(self,id_dict,idv=None):
+		return self.__class__(self.value)
+
+	def is_constant(self,idv=None):
+		return True
+
+	def calc(self):
+		return self
+
+class Var(object):
+	def __init__(self,idv):
+		self.idv = idv
+
+	def insert(self,id_dict,idv=None):
+		raise Exception("That shits not real")
+
+	def is_constant(self,idv=None):
+		if idv is None:
+			return False
+		return idv != self.idv
+
+	def __repr__(self):
+		return self.idv
+
+	def calc(self):
+		raise "Can't calculate a variable"
+
+class Parser:
+	operators2 = dict( (cls.symbol,cls) for cls in Operator2.__subclasses__() )
+	@classmethod
+	def parse(cls, term):
+		if len(term) == 0:
+			raise Exception("shit's empty")
+
+		if len(term) == 1 and is_alpha(term):
+			return Var(term)
+
+		try:
+			numeric_value = float(term)
+			return Numeric(numeric_value) #return Numeric if term is numeric
+		except ValueError:
+			pass
+
+		brackets_counter = 0
+		operator_match = (-1,None)
+
+		for index,char in enumerate(term):
+			if char == "(":
+				brackets_counter+=1
+			elif char == ")":
+				brackets_counter-=1
+				if brackets_counter < 0:
+					raise Exception("Bracket error")
+			elif char in cls.operators2 and brackets_counter == 0:
+				operator_found = cls.operators2[char]
+				if operator_match[0] < 0 or operator_found.priority > operator_match[1].priority:
+					operator_match = (index,operator_found)
+
+		if operator_match[0] >= 0:
+			return operator_match[1]( Parser.parse( term[:operator_match[0]] ), Parser.parse( term[operator_match[0]+1:] ) )
+
+		if term[0] == "(" and term[-1] == ")":
+			return Parser.parse(term[1:-1])
+
+		raise Exception("WTF is this shit %s" % term)
+
+class IdMark:
+	def __init__(self,idv,constant=False):
+		self.idv = idv
+		self.constant = constant
+
+	def insert(self,id_dict,idv):
+		return id_dict[self.idv]
+
+	def __repr__(self):
+		if self.constant:
+			return "IDC[%s]" % self.idv
+		else:
+			return "ID[%s]" % self.idv
+
+class DeriveVarIdMark:
+	def insert(self,id_dict,idv):
+		return Var(idv)
+
+	def __repr__(self):
+		return "X[]"
+
+class DerivationMark:
+	def __init__(self,content):
+		self.content = content
+
+	def insert(self,id_dict,idv):
+		return Deriver.derive(self.content.insert(id_dict,idv),idv)
+
+class DRule:
+	def __init__(self,pattern,skeleton):
+		self.pattern = pattern
+		self.skeleton = skeleton
+
+	def test(self,term,idv):
+		queue = [(self.pattern,term)]
+		id_dict = {}
+		while len(queue) != 0:
+			vpattern,vterm = queue[0]
+			queue = queue[1:]
+
+			if vpattern.__class__ == IdMark: 
+				if vpattern.constant and not vterm.is_constant(idv):
+					return None
+				elif vpattern.idv in id_dict:
+					if id_dict[vpattern.idv] != vterm:
+						return None
+				else:
+					id_dict[vpattern.idv] = vterm
+			elif vpattern.__class__ == DeriveVarIdMark:
+				if not (vterm.__class__ == Var and vterm.idv == idv):
+					return None
+			elif vpattern.__class__ == vterm.__class__:
+				queue.append( (vpattern.left,vterm.left) )
+				queue.append( (vpattern.right,vterm.right) )
+			else:
+				return None
+
+		return id_dict
+
+class Deriver:
+	rules = [
+		DRule( #dc/dx = 0 / c const
+			IdMark("c",constant=True),
+			Numeric(0)
+		),
+		DRule( #d/dx (a+b) = da/dx + db/dx
+			Addition(IdMark("x"),IdMark("y")),
+			Addition(DerivationMark(IdMark("x")),DerivationMark(IdMark("y")))
+		),
+		DRule( #d/dx (a-b) = da/dx - db/dx
+			Subtraction(IdMark("a"),IdMark("b")),
+			Subtraction(DerivationMark(IdMark("a")),DerivationMark(IdMark("b")))
+		),
+		DRule( #d/dx (c*a) = c * da/dx
+			Multiplication(IdMark("c",constant=True),IdMark("x")),
+			Multiplication(IdMark("c"), DerivationMark(IdMark("x")) )
+		),
+		DRule( #dx/dx = 1
+			DeriveVarIdMark(),
+			Numeric(1)
+		),
+		DRule( #d/dx (x^c) = c * x ^ (c-1)
+			Power( DeriveVarIdMark(), IdMark("c") ),
+			Multiplication( 
+				IdMark("c"), 
+				Power(
+					DeriveVarIdMark(),
+					Subtraction(
+						IdMark("c"),
+						Numeric(1)
+					)
+				)
+			)
+		),
+		DRule( #d/dx (a*b) = a * db/dx + b * da/dx
+			Multiplication( IdMark("a"), IdMark("b") ),
+			Addition(
+				Multiplication(
+					IdMark("a"),
+					DerivationMark( IdMark("b") )
+				),
+				Multiplication(
+					IdMark("b"),
+					DerivationMark( IdMark("a") )
+				)
+			)
+		),
+		DRule( #d/dx (a/b) = (da/dx * b - a * db/dx)/b^2
+			Division(
+				IdMark("a"),
+				IdMark("b")
+			),
+			Division(
+				Subtraction(
+					Multiplication(
+						DerivationMark( IdMark("a") ),
+						IdMark("b")
+					),
+					Multiplication(
+						IdMark("a"),
+						DerivationMark( IdMark("b") )
+					)
+				),
+				Power(
+					IdMark("b"),
+					Numeric(2)
+				)
+			)
+		)
+	]
+
+	@classmethod
+	def derive(cls,term,idv):
+		for rule in cls.rules:
+			id_dict = rule.test(term,idv)
+			if id_dict is not None:
+				return rule.skeleton.insert(id_dict,idv)
+
+		raise Exception("Couldn't derive %s" % term)
+
+class SRule:
+	def __init__(self,pattern,applier):
+		self.pattern = pattern
+		self.applier = applier
+
+class Simplifier:
+	@staticmethod
+	def simplify(term):
+		if term.is_constant():
+			return term.calc()
+		elif isinstance(term,Operator2):
+			print term.__class__.__name__
+
+			sleft = Simplifier.simplify(term.left)
+			sright = Simplifier.simplify(term.right)
+			term = term.__class__(sleft,sright)
+
+			if term.left.is_constant():
+				tleft = term.left.calc()
+			else:
+				tleft = term.left
+
+			if term.right.is_constant():
+				tright = Simplifier.simplify(term.right.calc())
+			else:
+				tright = term.right
+
+			return term.__class__(tleft,tright)
+		else:
+			return term
+
+sterm = raw_input("Input term (deriving by x): ")
+
+term = Parser.parse(sterm)
+print "Deriving %s" % term
+dterm = Deriver.derive(term,"x")
+print "DTerm: %s" % dterm
+sterm = Simplifier.simplify(dterm)
+print "Result: %s" % sterm
+
+
diff --git a/fizzbuzz-oneline.py b/fizzbuzz-oneline.py
index 3059f11..3e077d9 100644
--- a/fizzbuzz-oneline.py
+++ b/fizzbuzz-oneline.py
@@ -1 +1 @@
-print reduce(lambda x,y:x+"\n"+y, [ (((str(i),"Fizz")[i%3==0],"Buzz")[i%5==0],"FizzBuzz")[i%15==0] for i in range(1,101) ], "")[1:]
\ No newline at end of file
+print reduce(lambda x,y:x+"\n"+y, map(lambda i: (((str(i),"Fizz")[i%3==0],"Buzz")[i%5==0],"FizzBuzz")[i%15==0], range(1,101) ), "")[1:]
\ No newline at end of file
diff --git a/pso.py b/pso.py
index 5da195e..6d989c2 100644
--- a/pso.py
+++ b/pso.py
@@ -119,16 +119,17 @@ class Swarm:
 
 
 	def __centerOfSwarm(self):
-		return reduce(lambda a,b: a+b, [ p.position for p in self.particles ], Vector([0,0]) )/len(self.particles)
+		return reduce(lambda a,b: a+b, [ p.bestposition for p in self.particles ], Vector([0,0]) )/len(self.particles)
 
 	def __swarmSize(self):
 		center = self.__centerOfSwarm()
-		return max([ p.position.distance(center) for p in self.particles ])
+		return max([ p.bestposition.distance(center) for p in self.particles ])
 
 if __name__ == '__main__':
 	swarm = Swarm( 20, ParticleCreator([(-2000.0,2000.0),(-2000.0,2000.0)]), Fitness(), 1, 0.4, 0.2 )
 	
-	iterations = swarm.runUntilSwarmSize(1)
+	iterations = 10000
+	swarm.stepN(iterations)
 
 	print "%d iterations" % iterations
 
diff --git a/sorting_algorithms.py b/sorting_algorithms.py
index 92d218f..6e558b0 100644
--- a/sorting_algorithms.py
+++ b/sorting_algorithms.py
@@ -1,8 +1,9 @@
 
 from random import randint
 from time import clock
+from sys import argv
 
-class SortAlgorithm:
+class SortAlgorithm(object):
 	def __init__(self):
 		self.swaps = 0
 		self.vgls = 0
@@ -40,7 +41,7 @@ class InsertSort(SortAlgorithm):
 		for i in range(1,len(a)):
 			t = a[i]
 			j = i-1
-			while j >= 0 and self.vgl(a[i] > t):
+			while j >= 0 and self.vgl(a[j] > t):
 				self.set(a,j,a[j+1])
 				j-=1
 			#a[j+1] = t
@@ -65,7 +66,7 @@ class QuickSort(SortAlgorithm):
 
 		while i < j:
 			while self.vgl(a[i] <= pivot) and i < right: i+=1
-			while self.vgl(a[i] >= pivot) and j > left: j-=1
+			while self.vgl(a[j] >= pivot) and j > left: j-=1
 
 			if i < j:
 				self.swap(a,i,j)
@@ -78,7 +79,7 @@ class QuickSort(SortAlgorithm):
 class HeapSort(SortAlgorithm):
 	def sort(self,a):
 		self.heapsort(a)
-		return a
+		return list(reversed(a))
 
 	def heapify(self, data, i, w):
 		#indexes = filter(lambda v: v < w, [i,2*(i+1)-1,2*(i+1)])
@@ -182,18 +183,33 @@ class SortTester:
 			print "Testing %s..." % algorithm.__name__
 			inst = algorithm()
 			c = data[:]
-			inst.sort(c)
+			s = inst.sort(c)
+			if not SortedTest().test(s):
+				raise Exception(algorithm.__name__+" failed to sort")
 			results[algorithm] = (inst.vgls,inst.swaps)
 
 		return results
 
+class SortedTest:
+	def test(self, a):
+		v = a[0]
+		for n in a[1:]:
+			if v > n:
+				return False
+			v = n
+		return True
+
 def main():
-	result = SortTester([BubbleSort,InsertSort,QuickSort,HeapSort,MergeSort,ShellSort,SelectSort]).test(size=1000)
+	try:
+		size = int( argv[1])
+	except Exception:
+		size= 1000
+	result = SortTester(list( SortAlgorithm.__subclasses__() )).test(size=size)
 	for cls, r in result.items():
-		print "%-12s: %d compares, %d swaps" % (cls.__name__, r[0],r[1])
+		print "%-12s: %10d, %d compares, %d swaps" % (cls.__name__, r[0]+r[1], r[0],r[1])
 
 def test():
-	print ShellSort().sort([randint(0,500) for i in range(0,100)])
+	print HeapSort().sort([randint(0,500) for i in range(0,100)])
 
 if __name__ == '__main__':
 	main()