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#SetsU = {0,1,2,3,4,5,6,7,8,9}P = {1,2,3,4}Q = {4,5,6}R = {3,4,6,8,9}def set2bits(xs,us) :bs=[]for x in us :if x in xs :bs.append(1)else:bs.append(0)assert len(us) == len(bs)return bsdef union(set1,set2) :finalSet = set()bitList1 = set2bits(set1, U)bitList2 = set2bits(set2, U)for i in range(len(U)) :if(bitList1[i] or bitList2[i]) :finalSet.add(i)return finalSetdef intersection(set1,set2) :finalSet = set()bitList1 = set2bits(set1, U)bitList2 = set2bits(set2, U)for i in range(len(U)) :if(bitList1[i] and bitList2[i]) :finalSet.add(i)return finalSetdef compliment(set1) :finalSet = set()bitList = set2bits(set1, U)for i in range(len(U)) :if(not bitList[i]) :finalSet.add(i)return finalSetdef implication(a,b):return union(compliment(a), b)################################################################################################################# Problems 1-6 ###################################################################################################################################p \/ (q /\ r) = (p \/ q) /\ (p \/ r)def prob1():return union(P, intersection(Q,R)) == intersection(union(P,Q), union(P,R))#p /\ (q \/ r) = (p /\ q) \/ (p /\ r)def prob2():return intersection(P, union(Q,R)) == union(intersection(P,Q), intersection(P,R))#~(p /\ q) = ~p \/ ~qdef prob3():return compliment(intersection(P,R)) == union(compliment(P), compliment(R))#~(p \/ q) = ~p /\ ~qdef prob4():return compliment(union(P,Q)) == intersection(compliment(P), compliment(Q))#(p=>q) = (~q => ~p)def prob5():return implication(P,Q) == implication(compliment(Q), compliment(P))#(p => q) /\ (q => r) => (p => r)def prob6():return implication(intersection(implication(P,Q), implication(Q,R)), implication(P,R))print("Problem 1: ", prob1())print("Problem 2: ", prob2())print("Problem 3: ", prob3())print("Problem 4: ", prob4())print("Problem 5: ", prob5())print("Problem 6: ", prob6())'''Problem 1: TrueProblem 2: TrueProblem 3: TrueProblem 4: TrueProblem 5: TrueProblem 6: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}'''
"""Assignment 6The goal is to make a graph ofwho bit who and who was bitten.There should be 10 nodes and 15 edges.3 arrows of biting each other and3 arrows of someone biting themselves.Networkx can not do self bitingarrows, but it is in the code."""from graphviz import Digraph as DDotGraphfrom graphviz import Graph as UDotGraphimport networkx as nxfrom networkx.algorithms.dag import transitive_closureimport graphviz as gvimport matplotlib.pyplot as pltimport numpy as npfrom numpy.linalg import matrix_power"""class DGraph:def __init__(self):self.d = dict()def clear(self):self.d = dict()def add_node(self,n):if not self.d.get(n):self.d[n] = set()def add_edge(self,e):f,t=eself.add_node(f)self.add_node(t)vs=self.d.get(f)if not vs:self.d[f] = {t}else:vs.add(t)def add_edges_from(self,es):for e in es:self.add_edge(e)def edges(self):for f in self.d:for t in self.d[f]:yield (f,t)def number_of_nodes(self):return len(self.d)def __repr__(self):return self.d.__repr__()def show(self):dot = gv.Digraph()for e in self.edges():#print(e)f, t = edot.edge(str(f), str(t), label='')#print(dot.source)show(dot)# displays graph with graphvizdef show(dot, show=True, file_name='graph.gv'):dot.render(file_name, view=show)def showGraph(g,label="",directed=True):if directed:dot = gv.Digraph()else:dot = gv.Graph()for e in g.edges():print(e)f, t = edot.edge(str(f), str(t), label=label)print(dot.source)show(dot)def bit():G = DGraph()G.add_edge(("Blade","Samara"))G.add_edge(("Shadow","Wolfe"))G.add_edge(("Raven", "Austin"))G.add_edge(("Blade", "Alice"))G.add_edge(("Alice","Brandon"))G.add_edge(("Blade", "Wolfe"))G.add_edge(("Samara", "Robin"))G.add_edge(("Samara", "Raven"))G.add_edge(("Samara", "Hamed"))G.add_edge(("Wolfe", "Blade"))G.add_edge(("Hamed", "Samara"))G.add_edge(("Wolfe", "Shadow"))G.add_edge(("Brandon", "Brandon"))G.add_edge(("Hamed", "Hamed"))G.add_edge(("Austin", "Austin"))showGraph(G, label="bit")bit()def bitten():G=DGraph()G.add_edge(("Samara","Blade"))G.add_edge(("Wolfe","Shadow"))G.add_edge(("Austin", "Raven"))G.add_edge(("Alice","Blade"))G.add_edge(("Brandon", "Alice"))G.add_edge(("Wolfe", "Blade" ))G.add_edge(("Robin", "Samara"))G.add_edge(("Raven", "Samara"))G.add_edge(("Hamed", "Samara"))G.add_edge(("Blade", "Wolfe"))G.add_edge(("Samara", "Hamed"))G.add_edge(("Shadow", "Wolfe"))G.add_edge(("Brandon", "Brandon"))G.add_edge(("Hamed", "Hamed"))G.add_edge(("Austin", "Austin"))showGraph(G, label="bitten by")#bitten()family = ["Blade", "Samara", "Shadow", "Wolfe", "Raven", "Alice"]"""#Do transitive closure call out and the#matrix power operation should be the sameD = nx.DiGraph()#D.add_nodes_from("SamaraBladeWolfeShadowAliceRavenBrandonRobinHamedAustin")D.add_edge("Blade","Samara")D.add_edge("Shadow","Wolfe")D.add_edge("Raven", "Austin")D.add_edge("Blade", "Alice")D.add_edge("Alice","Brandon")D.add_edge("Blade", "Wolfe")D.add_edge("Samara", "Robin")D.add_edge("Samara", "Raven")D.add_edge("Samara", "Hamed")D.add_edge("Wolfe", "Blade")D.add_edge("Hamed", "Samara")D.add_edge("Wolfe", "Shadow")D.add_edge("Brandon", "Brandon")D.add_edge("Hamed", "Hamed")D.add_edge("Austin", "Austin")T = transitive_closure(D)for e in D.edges(): print(e)for n in D.nodes(): print(n)def show(H):nx.draw(H, with_labels=True, font_weight='bold')plt.show()#Use nx.to_numpy_matrix instead of nx.adjacency_matrix# M = nx.adjacency_matrix(D)# MT = nx.adjacency_matrix(T)M = nx.to_numpy_matrix(D)MT = nx.to_numpy_matrix(T)M2 = M@Mdef mPower(M, k): #M is numpy matrixassert k >= 1P = Mfor _ in range(k):P = P @ Mreturn Pdef tc(M):#compute transitive closurepassD1 = nx.DiGraph(M)D2 = nx.DiGraph(M2)print('Matrix for Original\n', M)N = nx.to_numpy_array(D,dtype=int)print('np_array for Original\n', N)print('\nMatrix for Transitive Closure\n', MT)N2 = nx.to_numpy_array(T,dtype=int)print('np_array for Transitive Closure\n', N2)show(D) #can use D, T, and numpy matrix power operationshow(T)show(T)
def to_roman_numeral(num):lookup = [(1000, 'M'),(900, 'CM'),(500, 'D'),(400, 'CD'),(100, 'C'),(90, 'XC'),(50, 'L'),(40, 'XL'),(10, 'X'),(9, 'IX'),(5, 'V'),(4, 'IV'),(1, 'I'),]res = ''for (n, roman) in lookup:(d, num) = divmod(num, n)res += roman * dreturn resto_roman_numeral(3) # 'III'to_roman_numeral(11) # 'XI'to_roman_numeral(1998) # 'MCMXCVIII'
# question3.pyfrom itertools import productV='∀'E='∃'def tt(f,n) :xss=product((0,1),repeat=n)print('function:',f.__name__)for xs in xss : print(*xs,':',int(f(*xs)))print('')# this is the logic for part A (p\/q\/r) /\ (p\/q\/~r) /\ (p\/~q\/r) /\ (p\/~q\/~r) /\ (~p\/q\/r) /\ (~p\/q\/~r) /\ (~p\/~q\/r) /\ (~p\/~q\/~r)def parta(p,q,r) :a=(p or q or r) and (p or q or not r) and (p or not q or r)and (p or not q or not r)b=(not p or q or r ) and (not p or q or not r) and (not p or not q or r) and (not p or not q or not r)c= a and breturn cdef partb(p,q,r) :a=(p or q and r) and (p or not q or not r) and (p or not q or not r)and (p or q or not r)b=(not p or q or r ) and (not p or q or not r) and (not p or not q or r) and (not p or not q or not r)c= a and breturn cprint("part A:")tt(parta,3)print("part B:")tt(partb,3)
mydict = {'carl':40, 'alan':2, 'bob':1, 'danny':0}# How to sort a dict by value Python 3>sort = {key:value for key, value in sorted(mydict.items(), key=lambda kv: (kv[1], kv[0]))}print(sort)# How to sort a dict by key Python 3>sort = {key:mydict[key] for key in sorted(mydict.keys())}print(sort)
list_1 = [1,2,3,4,5,6,7,8,9]cubed = map(lambda x: pow(x,3), list_1)print(list(cubed))#Results#[1, 8, 27, 64, 125, 216, 343, 512, 729]