return helper1(A[1:], B[1:], a)
# dot_product(A, B) returns the sum of the products of the number in 2 lists
# with the same index
# dot_product: (listof Float) (listof Float) -> Float
# requires: len(A) == len(B)
# Examples: dot_product([-1.0, 2.0], [2.0, 1.0]) => 0.0
def dot_product(A, B):
return helper1(A, B, 0)
# Tests:
check.within('Q1aT1', dot_product([0.0], [0.0]), 0.0, 0.001)
check.within('Q1aT2', dot_product([0.5, 2.0], [1.0, 0.0]), 0.5, 0.001)
# helper2(L, b) returns a list of poitive integers
# helper2: (listof Int) (listof Int) -> (listof Nat)
# effects: non_positive digits are eliminated
# Examples: helper2([1, 2, 6], []) => [1, 2, 6]
def helper2(L, b):
if L == []:
return b
elif L[0] > 0:
b = b + [L[0]]
return helper2(L[1:], b)
else:
return 0.0
return A[0]*B[0] + dot_product(A[1:], B[1:])
'''
def dot_product(A, B):
return dot_product_acc(A, B, 0.0)
# Tests:
# Test1: A and B == []
check.expect('Q1aT1', dot_product([],[]), 0.0)
# Test2: Regular Tests
check.expect('Q1aT2', dot_product([-1.0, 2.0],[2.0,1.0]), 0.0)
check.expect('Q1aT3', dot_product([1.0,2.0,3.0], [1.0,1.0,1.0]), 6.0)
check.expect('Q1aT4', dot_product([1.0,6.0,9.0,10.0],[0.0,1.0,2.0,3.0]), 54.0)
# Test3:
check.expect('Q1aT5', dot_product([-1.5, 2.5],[2.0,1.0]), -0.5)
check.within('Q1aT6', dot_product([1.5,2.0,3.0], [1.0,1.8,-1.0]), 0.00001, 2.1)
check.expect('Q1aT7', dot_product([1.1,2.0],[2.0,-2.1]), -2.0)
# Question 1 - Part b
# keep_positive_acc(lst, list_is_required) returns an list of positive Int,
# list_is_required and gets rid of the other negative element in L
# keep_positive_acc: (listof Int) (listof Int) -> (listof Nat)
# Examples:
# keep_positive_acc([1, 2],[]) => [1, 2]
# keep_positive_acc([3, -1, 2, 0, 1],[]) => [3, 2, 1]
def keep_positive_acc(lst, list_is_required):
if lst == []:
return list_is_required
else:
if lst[0] > 0:
list_is_required.append(lst[0])
self.x *= k
self.y *= k
# Test(q3b): __add__
check.expect('T1(3b1)', Vector(2, 3) + Vector(4, -1), Vector(6, 2))
check.expect('T2(3b1)', Vector(0, 0) + Vector(0, 0), Vector(0, 0))
check.expect('T3(3b1)', Vector(1, 0) + Vector(1, -1), Vector(2, -1))
check.expect('T4(3b1)', Vector(-3, -3) + Vector(-9, -9), Vector(-12, -12))
# Test(q3b): __mul__
check.expect('T1(3b2)', Vector(2, 3) * Vector(4, -1), 5)
check.expect('T2(3b2)', Vector(0, 0) * Vector(0, 0), 0)
check.expect('T3(3b2)', Vector(1, 0) * Vector(1, -1), 1)
check.expect('T4(3b2)', Vector(-3, -3) * Vector(-9, -9), 54)
# Test(q3b): self.length()
check.within('T1(3b3)', Vector(2, 3).length(), 3.6055, 0.0001)
check.within('T2(3b3)', Vector(4, -1).length(), 4.1231, 0.0001)
check.within('T3(3b3)', Vector(0, 0).length(), 0.0, 0.0001)
check.within('T4(3b3)', Vector(1, 0).length(), 1.0, 0.0001)
check.within('T5(3b3)', Vector(1, -1).length(), 1.41421, 0.0001)
check.within('T6(3b3)', Vector(-3, -3).length(), 4.24264, 0.0001)
check.within('T7(3b3)', Vector(-3, 5).length(), 5.83095, 0.0001)
# Test(q3b): self.scale(k)
u = Vector(2, 3)
check.expect('T1(3b4)', u.scale(-2), None)
check.expect('T1(3b4)(x)', u.x, -4)
check.expect('T1(3b4)(y)', u.y, -6)
a = Vector(-1, 3)
check.expect('T2(3b4)', a.scale(-1), None)
## Tests for B
check.expect("Test1", Vector(1, 1) + Vector(2, 1), Vector(3, 2))
check.expect("Test2", Vector(0, 0) + Vector(2, 1), Vector(2, 1))
check.expect("Test3", Vector(1, 2) + Vector(0, 0), Vector(1, 2))
check.expect("Test4", Vector(0, 0) + Vector(0, 0), Vector(0, 0))
check.expect("Test5", Vector(-3, -3) + Vector(2, 1), Vector(-1, -2))
check.expect("Test1", Vector(1, 1) * Vector(2, 1), 3)
check.expect("Test2", Vector(0, 0) * Vector(2, 1), 0)
check.expect("Test3", Vector(1, 2) * Vector(0, 0), 0)
check.expect("Test4", Vector(0, 0) * Vector(0, 0), 0)
check.expect("Test5", Vector(-3, -3) * Vector(2, 1), -9)
check.within("Test1", Vector(1, 2).length(), 2.23, 0.1)
check.within("Test2", Vector(-2, 4).length(), 4.47, 0.1)
check.within("Test3", Vector(-3, -1).length(), 3.16, 0.1)
check.within("Test4", Vector(2, 2).length(), 2.83, 0.1)
c = Vector(1, 2)
check.expect("Test1", c.scale(2), None)
check.expect("Test1", c, Vector(2, 4))
d = Vector(3, 4)
check.expect("Test2", d.scale(0), None)
check.expect("Test2", d, Vector(0, 0))
d = Vector(1, 0)
check.expect("Test3", d.scale(2), None)
check.expect("Test3", d, Vector(2, 0))
return cost * (1 + GST)
if prov_abbr == "SK":
return (cost * (1 + GST + SK))
if prov_abbr == "BC":
return cost * (1 + GST + BC)
if prov_abbr == "MB" or prov_abbr == "ON":
return cost * (1 + GST + MB_ON)
if (prov_abbr == "NB" or prov_abbr == "NL" or prov_abbr == "NS"
or prov_abbr == "PE"):
return cost * (1 + GST + NB_NL_NS_PE)
else:
return cost * (1 + GST)
## Test1: Literature related goods
check.within("Q2T1", after_tax(20.0, "ON", "literature"), 21.0, 0.01)
## Test2: Child related goods
check.within("Q2T2", after_tax(25.0, "AB", "child"), 26.25, 0.01)
## Test3: Food related
check.within("Q2T3", after_tax(12.25, "NS", "food"), 12.25, 0.01)
## Test4: Goods in SK
check.within("Q2T4", after_tax(50100, "SK", "car"), 55611.00, 0.01)
## Test5: Goods in BC
check.within("Q2T5", after_tax(1000000, "BC", "house"), 1120000.00, 0.01)
## Test6: Goods in MB or ON
check.within("Q2T6", after_tax(1379, "ON", "gucci"), 1158.27, 0.01)
check.within("Q2T7", after_tax(9.99, "MB", "gym membership"), 11.28, 0.01)
## Test7: Goods in NB, NL, NS, PE
check.within("Q2T8", after_tax(14.99, "NB", "movies"), 17.24, 0.01)
check.within("Q2T9", after_tax(1.99, "NL", "toothpaste"), 2.29, 0.01)
check.within("Q2T10", after_tax(999, "NS", "iphone"), 1148.85, 0.01)
# fib_rec(0) => 0
def fib_rec(n):
def fib_acc(new_n,last_fib,prev_fib):
if (new_n == n):
return last_fib
else:
return fib_acc((1+new_n),(last_fib+prev_fib),last_fib)
if (n == 0):
return 0
else:
return fib_acc(1,1,0)
# Testing fib_rec:
check.expect("Test 1", fib_rec(10), 55)
check.expect("Test 2", fib_rec(65), 17167680177565)
# fib_approx(n) consumes a natural number (n) and produces a float that is approximately the nth position of the fibonnachi sequence
# fib_approx: Nat -> Approx
# Example: fib_approx(6) => 8.0
# fib_approx(0) => 0
def fib_approx(n):
phi = (1+(math.sqrt(5)))/2
fib_final = ((phi ** n) - ((-phi) ** (-n)))/math.sqrt(5)
return fib_final
# Testing fib_approx
check.within("Test 3", fib_approx(10), 55.0, 0.0001)
check.within("Test 3", fib_approx(15), 610.0, 0.0001)
import check
## fairy_distance: float float float float -> float
## Purpose: Consumes four floats d, the starting distance between the two
## unicorns (km), v1(km/hr), the velocity of the first unicorn, v2(km/hr), the
## velocity of the second unicorn and f(km/hr), the velocity of the fairy and
## produces the float distance travelled by the fairy when the two unicorns
## meet and stop for tea with the fairy.
# Examples: fairy_distance(18.0, 2.5, 3.0, 15.0) => 49.090909 (approx)
# fairy_distance(200.0,60.0,80.0,300.0) => 428.5714286 (approx)
# fairy_distance(200.0,5.0,5.0,50.0) => 1000.0
#
def fairy_distance(d, v1, v2, f):
return(d / (v1 + v2))*f
## Testing:
print "Testing fairy_distance"
# Test 1: Example test
check.within("Question 3 Test 1", fairy_distance(18.0,2.5,3.0,15.0), \
49.09090909090909093, 0.000001)
# Test 2: Fast fairy
check.within("Question 3 Test 2", fairy_distance(200.0,60.0,80.0,300.0)\
, 428.5714286, 0.000001)
# Test 3: Slow unicorns
check.expect("Question 3 Test 3", fairy_distance(200.0,5.0,5.0,50.0),1000.0)
# Test 4: Small distance, slow fairy
check.within("Question 3 Test 4", fairy_distance(5.0,30.0,30.0,1.0)\
, 0.083333333, 0.000001)
windchill = 13.12 + 0.6125*temp - 11.37*wind**0.16 + 0.3965*temp*wind**0.16
vapour_pressure = 6.112* 10**(7.5*temp/(237.7+temp)) *(hum/100)
humidex = temp + 5/9*(vapour_pressure -10)
if temp >= 15:
if humidex - temp >= 1:
return humidex
else:
return temp
else:
if temp - windchill >= 1:
return windchill
else:
return temp
## Test1: temp higher than 15, humidex minus temp higher than 1
check.within("Q2Test1", feels_like(16, 2, 99), 20.43398, 0.0001)
## Test2: temp higher than 15, humidex minus temp less than 1
check.within("Q2Test2", feels_like(16, 2, 50), 16, 0.0001)
## Test3: temp lower than 15, windchill minus temp higher than 1
check.within("Q2Test3", feels_like(-1, 4, 30), -2.18098, 0.0001)
## Test4: temp lower than 15, windchill minus temp less than 1
check.within("Q2Test4", feels_like(-1, 2, 50), -1, 0.0001)
check.within("Q2Test5", feels_like(-9.5,1.9,91), -9.5, 0.0001)
**** a02q3.py *****************************************************************
##===============================================
## Jiadong Mai (20557203)
## CS 116 Winter 2018
## Assignment 02, Question 3
##===============================================
def participation(correct, incorrect, unanswered, threshold,
tutorials_attended):
overall_percent = 5
total_points = (2 * correct) + incorrect
total_questions = (correct + incorrect + unanswered)
questions_counted = math.ceil(total_questions * (threshold / 100))
possible_points = 2 * questions_counted
if questions_counted <= correct:
return 5.0
if questions_counted <= (correct + incorrect):
return min((((2 * correct + (questions_counted - correct)) / possible_points) \
* overall_percent) + tutorials_attended * 0.1, 5.0)
else:
return min((((2 * correct + incorrect) / possible_points) * overall_percent) \
+ tutorials_attended * 0.1 ,5.0)
# Tests for particitation:
check.expect("Q2T1", participation(30, 0, 0, 100, 0), 5.0)
check.within("Q2T2", participation(10, 15, 5, 80, 0), 3.541666, 0.0001)
check.within("Q2T3", participation(10, 15, 5, 90, 0), 3.240740, 0.0001)
check.within("Q2T4", participation(15, 5, 0, 90, 0), 4.583333, 0.0001)
check.within("Q2T5", participation(20, 5, 5, 90, 5), 4.666666, 0.0001)
check.expect("Q2T6", participation(42, 8, 0, 95, 0), 4.6875)
check.expect("Q2T7", participation(42, 8, 0, 95, 3), 4.9875)
check.expect("Q2T8", participation(42, 8, 0, 95, 4), 5.0)
check.within("Q2T9", participation(22, 3, 4, 90, 0), 4.351851, 0.0001)
check.expect("Q2T10", participation(22, 3, 4, 90, 12), 5.0)
check.expect("Q2T11", participation(0, 0, 30, 21, 4), 0.4)
elif need - correct >= incorrect:
earned = correct * 2 + incorrect * 1
else:
earned = correct * 2 + need - correct * 1
return 100 * ((earned) / total)
# Constant for tests
master1 = ['A', 'A', 'B', 'C', 'A', 'D', 'E', 'A', 'D', 'B']
master2 = ['A', 'A', 'B', 'C', 'A']
student1 = ['A', 'A', 'B', 'C', 'A', 'D', 'E', 'A', 'D', 'B']
student2 = ['A', 'A', 'B', 'C', 'D', 'E', 'A', 'E', 'B', ' ']
student3 = ['A', 'B', 'A', ' ', ' ', 'D', ' ', 'A', ' ', 'B']
student4 = ['E', 'E', ' ', ' ', ' ']
student5 = ['A', ' ', ' ', 'C', ' ']
# Tests1: contain only correct answers
check.expect("Q1T1", clicker_grade(master1, student1), 100.0)
# Tests2: contain correct and incorrect answers
check.within("Q1T2", clicker_grade(master1, student2), 78.57143, 0.00001)
# Tests3: contain all types of answers
check.within("Q1T3", clicker_grade(master1, student3), 71.42857, 0.00001)
# Tests4: contain only incorrect answers
check.expect("Q1T4", clicker_grade(['A', 'A'], ['B', 'C']), 50.0)
# Tests5: contain incorrect and unanswered answers
check.within("Q1T5", clicker_grade(master2, student4), 33.3333, 0.0001)
# Tests6: contain only unanswered answers
check.expect("Q1T6", clicker_grade(['A', 'C'], [' ', ' ']), 0.0)
# Tests7: contain only correct and unanswered answers
check.within("Q1T7", clicker_grade(master2, student5), 66.6666, 0.0001)
cost_a = 5.00*30
## cost of group b
if group_b <= 30:
cost_b = 8.00*group_b
elif group_b > 30:
cost_b = 8.00*30
## cost of group c with tax
if group_c <= 30:
cost_c = 10.00*group_c*1.13
elif group_c > 30:
cost_c = 10.00*30*1.13
## cost of adults with tax and the total cost depending on the time
if time == "Day":
adult_cost = (members*12.00*0.6 + (adults-members)*12.00) *1.13
total_cost = cost_a + cost_b + cost_c + adult_cost
return total_cost
elif time == "After_3":
adult_cost = adults*12.00*0.5*1.13
total_cost = (cost_a + cost_b + cost_c)*0.5 + adult_cost
return total_cost
# Tests
check.within("Q2T1", trip_cost(0,0,0,0,0, "Day"), 0, 0.01)
check.within("Q2T2", trip_cost(1,1,1,1,1, "Day"), 32.43, 0.01)
check.within("Q2T3", trip_cost(1,1,1,1,1, "After_3"), 18.93, 0.01)
check.within("Q2T4", trip_cost(40,55,29,33,13,"After_3"), 582.59, 0.01)
check.within("Q2T5", trip_cost(20,15,29,35,05,"Day"), 995.18, 0.01)
check.within("Q2T6", trip_cost(40,40,40,40,0, "Day"), 1271.40, 0.01)
check.within("Q2T7", trip_cost(25,15,20,30,10,"Day"), 823.56, 0.01)
check.within("Q2T8", trip_cost(10,10,10,10,5,"After_3"), 189.30, 0.01)
check.within("Q2T9", trip_cost(50,50,50,50,25, "After_3"), 703.50, 0.01)
Examples:
after_tax (20.0 , "ON", "literature") => 21.0
after_tax (20010.0 , "AB", "car") => 21010.5
'''
cost = cost + 0.05 * cost
if item == "food" or item == "literature" or item == "child":
return cost
elif prov_abbr == "AB" or prov_abbr == "NT" or prov_abbr == "NU" or prov_abbr == "YT":
return cost
elif prov_abbr == "SK":
return cost + 0.06 * cost
elif prov_abbr == "BC":
return cost + 0.07 * cost
elif prov_abbr == "QU":
return cost + 0.09975 * cost
elif prov_abbr == "NB" or prov_abbr == "NL" or prov_abbr == "NS" or prov_abbr == "PE":
return cost + 0.1 * cost
elif prov_abbr == "ON" or prov_abbr == "MB":
return cost + 0.08 * cost
##Tests
check.within("no tax item", after_tax(20.0, "ON", "literature"), 21.0, 0.0001)
check.within("Ex: AB tax", after_tax(20010.0, "AB", "car"), 21010.5, 0.0001)
check.within("Ex: SK tax", after_tax(40.0, "SK", "Clothes"), 44.52, 0.0001)
check.within("Ex: BC tax", after_tax(80.0, "BC", "Leather"), 89.88, 0.0001)
check.within("Ex: QU tax", after_tax(5700.0, "QU", "Bike"), 6582.00375, 0.0001)
check.within("Ex: NB tax", after_tax(1000.0, "NB", "Metal"), 1155.0, 0.0001)
check.within("Ex: MB tax", after_tax(570.0, "MB", "Wood"), 646.38, 0.0001)
# Example: participation(3,2,2,50,12) => 5.0
# participation(4,3,0,100,0) => 3.92857
def participation(correct, incorrect, unanswered, threshold, tutorials_attended):
all_qs = correct + incorrect + unanswered
num_of_qs = math.ceil((threshold / 100) * all_qs)
if incorrect < 0:
return participation(correct + incorrect, 0, 0, threshold, tutorials_attended)
elif unanswered < 0:
return participation(correct, incorrect + unanswered, 0, threshold, tutorials_attended)
elif num_of_qs < all_qs:
return participation(correct, incorrect, unanswered - (all_qs - num_of_qs), 100, tutorials_attended)
else:
marks_made = (correct * 2) + incorrect
marks_possible = all_qs * 2
points_deserved = ((marks_made / marks_possible) * 5.0) + (tutorials_attended * 0.1)
if points_deserved > 5.0:
return 5.0
else:
return points_deserved
# Testing participation:
check.expect("Test 1", participation(1, 0, 0, 100, 12), 5.0)
check.within("Test 2", participation(1, 3, 5, 100, 12), 2.5888, 0.0001)
check.within("Test 3", participation(5, 3, 5, 75, 12), 4.45, 0.0001)
check.within("Test 4", participation(0, 0, 5, 100, 12), 1.2, 0.0001)
check.within("Test 5", participation(0, 0, 5, 1, 12), 1.2, 0.0001)
check.within("Test 6", participation(1, 0, 0, 1, 12), 5.0, 0.0001)
import check
import math
# feels_like(temp, wind, hum) returns the temperature that you feels like
# during the day in Canada, and the humidity and the wind chill factors are
# considered
# feels_like: Float Float Nat -> Float
# requires: wind(wind_speed) >= 0
# 0 <= hum <= 100
# Example: feels_like(-9.5,1.9,91) => -9.5
def feels_like(temp, wind, hum):
windchill = 13.12 + 0.6125 * temp - 11.37 * (wind ** 0.16) +0.3965 * temp * (wind ** 0.16)
vapour_pressure = 6.112 * (10 ** ((7.5 * temp) / (237.7 + temp))) * (hum / 100)
humidex = temp + (5 / 9) * (vapour_pressure - 10)
if temp <= humidex + 1 and temp >= 15:
feeling = humidex
elif temp >= windchill + 1 and temp < 15:
feeling = windchill
else:
feeling = temp
return feeling
# Tests:
check.within("Q2T1", feels_like(-9.5, 1, 91), -9.5, 0.001)
check.within("Q2T2", feels_like(20.1, 1.9, 12), 20.1, 0.001)
check.within("Q2T3", feels_like(13.5, 100, 13), 8.817, 0.001)
check.within("Q2T4", feels_like(13.5, 1, 13), 13.5, 0.001)
check.within("Q2T5", feels_like(13.5, 19, 91), 11.750, 0.001)
