Add new course
This commit is contained in:
AndrewTrieu
@@ -0,0 +1,121 @@
|
||||
<!doctype html>
|
||||
<html>
|
||||
<head>
|
||||
<title>Week 7 Programming Assignments (9 points)</title>
|
||||
<meta charset="utf-8">
|
||||
|
||||
</head>
|
||||
<body>
|
||||
<div>
|
||||
<h4><span>Assignment 7.1: The Quicksort</span> <span style="font-weight: normal;">(4 point)</span><br></h4>
|
||||
</div>
|
||||
<div>Familiarize yourself with the principle of Quicksort from the background material and implement Quicksort in Python.
|
||||
Create a function <strong>qsort(A: list, i: int, j: int)</strong> which has the following input parameters:</div>
|
||||
<ul>
|
||||
<ul>
|
||||
<li>\(A\): a (whole) list of integers</li>
|
||||
<li>\(i\): a start index of selected partition</li>
|
||||
<li>\(j\): a end index of selected partition</li>
|
||||
</ul>
|
||||
</ul>
|
||||
<div>The function has no return value since the sorting process is done to the original list. You can select the pivot index/value as you wish.</div>
|
||||
<br>
|
||||
<div>Limits:</div>
|
||||
<ul>
|
||||
<ul>
|
||||
<li>maximum list size is \(10^4\)</li>
|
||||
<li>all elements of the list are integers between \(1 \dots 10^4\)</li>
|
||||
</ul>
|
||||
</ul>
|
||||
<div>A code template with an example program: </div>
|
||||
<p></p>
|
||||
<div style="border:2px solid black">
|
||||
<pre>def qsort(A, i, j):
|
||||
# TODO
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
A = [9, 7, 1, 8, 5, 3, 6, 2, 4]
|
||||
print(A) # [9, 7, 1, 8, 5, 3, 6, 2, 4]
|
||||
qsort(A, 0, len(A)-1)
|
||||
print(A) # [1, 2, 3, 4, 5, 6, 7, 8, 9]
|
||||
</pre>
|
||||
</div>
|
||||
<br>
|
||||
<div>Submit your solution in CodeGrade as <strong>quicksort.py</strong>.</div>
|
||||
<br>
|
||||
<br>
|
||||
|
||||
|
||||
<div>
|
||||
<h4>Assignment 7.2: Car Sales<span style="font-weight: normal;"> (3 points)</span><br></h4>
|
||||
</div>
|
||||
<div>A car shop has cars \(A = [a_1, a_2, ..., a_n]\) (one of each) where \(a_i\) is the price of the car \(i\). Customers \(B = [b_1, b_2, ..., b_m]\) arrive to the shop.
|
||||
\(b_i\) is the price that the customer \(i\) can afford. What is the maximum amount of sales that can be made?<br></div>
|
||||
<br>
|
||||
<div>For example the shop has cars \(A = [20, 10, 15, 26]\) and there are customers \(B = [11, 25, 15, 9]\) it is possible to make \(3\) sales.</div>
|
||||
<ul>
|
||||
<ul>
|
||||
<li>The first customer (\(11\)) gets car that cost \(10\), The second customer (\(25\)) gets the car that cost \(20\), and the third customer (\(15\)) gets the car that cost \(15\).</li>
|
||||
</ul>
|
||||
</ul>
|
||||
<div>Create a function <strong>sales(A: list, B: list)</strong> in Python which returns the number of possible sales.</div>
|
||||
<br>
|
||||
<div>Limits:</div>
|
||||
<ul>
|
||||
<ul>
|
||||
<li>\(1 \leq n,m \leq 10^4\)</li>
|
||||
<li>\(1 \leq a_i, b_i \leq 10^4\)</li>
|
||||
</ul>
|
||||
</ul>
|
||||
<div>Target: the function performs in \(\Theta(n \log n)\) time.</div>
|
||||
<br>
|
||||
<div>A code template with an example program: </div>
|
||||
<p></p>
|
||||
<div style="border:2px solid black">
|
||||
<pre>def sales(cars, customers) -> int:
|
||||
# TODO
|
||||
|
||||
if __name__ == "__main__":
|
||||
print(sales([20, 10, 15], [11, 25, 15])) # 3
|
||||
print(sales([13, 7, 2, 3, 12, 4, 19], [3, 25, 16, 14])) # 4
|
||||
print(sales([24, 6, 20, 21, 12, 5], [25, 1, 24, 15])) # 3
|
||||
print(sales([14, 9, 10, 15, 18, 20], [24, 17, 9, 22, 12, 4])) # 5
|
||||
</pre>
|
||||
</div>
|
||||
<br>
|
||||
<div>Submit your solution in CodeGrade as <strong>sales.py</strong>.</div>
|
||||
<br>
|
||||
<br>
|
||||
|
||||
|
||||
<div>
|
||||
<h4>Assignment 7.3: Subsets<span style="font-weight: normal;"> (2 points)</span><br></h4>
|
||||
</div>
|
||||
<div>A given set that has numbers from \(1\) to \(N\) in increasing order (\(\{1, 2, 3, 4, \dots, N\}\)), create a function <strong>subsets(N: int)</strong> in Python which produces a list of all possible subsets.</div>
|
||||
<br>
|
||||
<div>For example when \(N = 3\) the subsets are \([1]\), \([2]\), \([1, 2]\), \([3]\), \([1, 3]\), \([2, 3]\) and \([1, 2, 3]\).</div>
|
||||
<br>
|
||||
<div>The function must return the list of subsets in specific order (see the example program below).<br></div><p></p><div>Limits: \(1 \leq N \leq 20\)<br></div><div><br></div><div>A code template with an example program:
|
||||
</div><p></p>
|
||||
<div style="border:2px solid black">
|
||||
<pre>def subsets(n: int) -> list:
|
||||
# TODO
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
print(subsets(3)) # [[1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
|
||||
|
||||
print(subsets(4)) # [[1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3],
|
||||
# [4], [1, 4], [2, 4], [1, 2, 4], [3, 4], [1, 3, 4],
|
||||
# [2, 3, 4], [1, 2, 3, 4]]
|
||||
|
||||
S = subsets(10)
|
||||
print(S[95]) # [6, 7]
|
||||
print(S[254]) # [1, 2, 3, 4, 5, 6, 7, 8]
|
||||
print(S[826]) # [1, 2, 4, 5, 6, 9, 10]
|
||||
</pre>
|
||||
</div>
|
||||
<p><br></p><p>Submit your solution in CodeGrade as <strong>subsets.py</strong></p>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,24 @@
|
||||
def qsort(A, i, j):
|
||||
if i >= j:
|
||||
return
|
||||
p = partition(A, i, j)
|
||||
qsort(A, i, p-1)
|
||||
qsort(A, p+1, j)
|
||||
|
||||
|
||||
def partition(A, i, j):
|
||||
pivot = A[j]
|
||||
p = i
|
||||
for q in range(i, j):
|
||||
if A[q] < pivot:
|
||||
A[p], A[q] = A[q], A[p]
|
||||
p += 1
|
||||
A[p], A[j] = A[j], A[p]
|
||||
return p
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
A = [9, 7, 1, 8, 5, 3, 6, 2, 4]
|
||||
print(A) # [9, 7, 1, 8, 5, 3, 6, 2, 4]
|
||||
qsort(A, 0, len(A)-1)
|
||||
print(A) # [1, 2, 3, 4, 5, 6, 7, 8, 9]
|
||||
@@ -0,0 +1,18 @@
|
||||
def sales(cars, customers) -> int:
|
||||
cars.sort()
|
||||
customers.sort()
|
||||
sales = 0
|
||||
for customer in customers:
|
||||
for car in cars:
|
||||
if car <= customer:
|
||||
sales += 1
|
||||
cars.remove(car)
|
||||
break
|
||||
return sales
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
print(sales([20, 10, 15], [11, 25, 15])) # 3
|
||||
print(sales([13, 7, 2, 3, 12, 4, 19], [3, 25, 16, 14])) # 4
|
||||
print(sales([24, 6, 20, 21, 12, 5], [25, 1, 24, 15])) # 3
|
||||
print(sales([14, 9, 10, 15, 18, 20], [24, 17, 9, 22, 12, 4])) # 5
|
||||
@@ -0,0 +1,26 @@
|
||||
def subsets(a: int) -> list:
|
||||
s = [i for i in range(1, a+1)]
|
||||
return [x for x in get_sets(s) if x]
|
||||
|
||||
|
||||
def get_sets(s):
|
||||
size = 2**len(s)
|
||||
for cnt in range(0, size):
|
||||
final = []
|
||||
for i in range(0, len(s)):
|
||||
if ((cnt & (1 << i)) > 0):
|
||||
final.append(s[i])
|
||||
yield final
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
print(subsets(3)) # [[1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
|
||||
|
||||
print(subsets(4)) # [[1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3],
|
||||
# [4], [1, 4], [2, 4], [1, 2, 4], [3, 4], [1, 3, 4],
|
||||
# [2, 3, 4], [1, 2, 3, 4]]
|
||||
|
||||
S = subsets(10)
|
||||
print(S[95]) # [6, 7]
|
||||
print(S[254]) # [1, 2, 3, 4, 5, 6, 7, 8]
|
||||
print(S[826]) # [1, 2, 4, 5, 6, 9, 10]
|
||||
Reference in New Issue
Block a user