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GA2 done. Selection sort added

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Claudio Maggioni 2019-03-25 15:21:57 +01:00
parent 13030cc6bc
commit 8301104864
5 changed files with 138 additions and 38 deletions
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GA2/ga2.pdf
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121
GA2/ga2.tex
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@ -32,14 +32,131 @@
\lstlistoflistings
\newpage
\section{Exercise 1}
\subsection{Mergesort}
\begin{verbatim}
[5, 6, 12, 8, 4, 10, 3, 12, 11, 1]
[5, 6, 12, 8, 4] [10, 3, 12, 11, 1]
[5, 6, 12, 8, 4]
[5, 6], [12, 8, 4]
[5, 6]
[5], [6]
[5]
[6]
[5, 6]
[12, 8, 4]
[12] [8, 4]
[12]
[8, 4]
[8], [4]
[8]
[4]
[4, 8]
[4, 8, 12]
[4, 5, 6, 8, 12]
[10, 3, 12, 11, 1]
[10, 3], [12, 11, 1]
[10], [3]
[10]
[3]
[3, 10]
[12, 11, 1]
[12], [11, 1]
[12]
[11, 1]
[11], [1]
[11]
[1]
[1, 11]
[1, 11, 12]
[1, 3, 10, 11, 12]
[1, 3, 4, 5, 6, 8, 10, 11, 12, 12]
\end{verbatim}
\subsection{Selection sort}
\begin{verbatim}
[4, 6, 12, 8, 5, 10, 3, 12, 11, 1]
[3, 6, 12, 8, 5, 10, 4, 12, 11, 1]
[1, 6, 12, 8, 5, 10, 4, 12, 11, 3]
[1, 5, 12, 8, 6, 10, 4, 12, 11, 3]
[1, 4, 12, 8, 6, 10, 5, 12, 11, 3]
[1, 3, 12, 8, 6, 10, 5, 12, 11, 4]
[1, 3, 8, 12, 6, 10, 5, 12, 11, 4]
[1, 3, 6, 12, 8, 10, 5, 12, 11, 4]
[1, 3, 5, 12, 8, 10, 6, 12, 11, 4]
[1, 3, 4, 12, 8, 10, 6, 12, 11, 5]
[1, 3, 4, 8, 12, 10, 6, 12, 11, 5]
[1, 3, 4, 6, 12, 10, 8, 12, 11, 5]
[1, 3, 4, 5, 12, 10, 8, 12, 11, 6]
[1, 3, 4, 5, 10, 12, 8, 12, 11, 6]
[1, 3, 4, 5, 8, 12, 10, 12, 11, 6]
[1, 3, 4, 5, 6, 12, 10, 12, 11, 8]
[1, 3, 4, 5, 6, 10, 12, 12, 11, 8]
[1, 3, 4, 5, 6, 8, 12, 12, 11, 10]
[1, 3, 4, 5, 6, 8, 11, 12, 12, 10]
[1, 3, 4, 5, 6, 8, 10, 12, 12, 11]
[1, 3, 4, 5, 6, 8, 10, 11, 12, 12]
[1, 3, 4, 5, 6, 8, 10, 11, 12, 12]
\end{verbatim}
\subsection{Quicksort}
\begin{verbatim}
[5, 6, 12, 8, 4, 10, 3, 12, 11, 1]
[5, 6, 3, 1, 4] 8 [12, 12, 11, 10]
[] 1 [6, 3, 4, 5]
[] 3 [5, 4, 6]
[5, 4] 6 []
[4] 5 []
[4] 5 []
[4, 5] 6 []
[] 3 [4, 5, 6]
[] 1 [3, 4, 5, 6]
[10] 11 [12, 12]
[12] 12 []
[12] 12 []
[10] 11 [12, 12]
[1, 3, 4, 5, 6] 8 [10, 11, 12, 12]
[1, 3, 4, 5, 6, 8, 10, 11, 12, 12]
\end{verbatim}
\subsection{Insertion sort}
\begin{verbatim}
[5, 6, 12, 8, 4, 10, 3, 12, 11, 1]
[5, 6, 8, 12, 4, 10, 3, 12, 11, 1]
[5, 6, 8, 4, 12, 10, 3, 12, 11, 1]
[5, 6, 4, 8, 12, 10, 3, 12, 11, 1]
[5, 4, 6, 8, 12, 10, 3, 12, 11, 1]
[4, 5, 6, 8, 12, 10, 3, 12, 11, 1]
[4, 5, 6, 8, 10, 12, 3, 12, 11, 1]
[4, 5, 6, 8, 10, 3, 12, 12, 11, 1]
[4, 5, 6, 8, 3, 10, 12, 12, 11, 1]
[4, 5, 6, 3, 8, 10, 12, 12, 11, 1]
[4, 5, 3, 6, 8, 10, 12, 12, 11, 1]
[4, 3, 5, 6, 8, 10, 12, 12, 11, 1]
[3, 4, 5, 6, 8, 10, 12, 12, 11, 1]
[3, 4, 5, 6, 8, 10, 12, 11, 12, 1]
[3, 4, 5, 6, 8, 10, 11, 12, 12, 1]
[3, 4, 5, 6, 8, 10, 11, 12, 1, 12]
[3, 4, 5, 6, 8, 10, 11, 1, 12, 12]
[3, 4, 5, 6, 8, 10, 1, 11, 12, 12]
[3, 4, 5, 6, 8, 1, 10, 11, 12, 12]
[3, 4, 5, 6, 1, 8, 10, 11, 12, 12]
[3, 4, 5, 1, 6, 8, 10, 11, 12, 12]
[3, 4, 1, 5, 6, 8, 10, 11, 12, 12]
[3, 1, 4, 5, 6, 8, 10, 11, 12, 12]
[1, 3, 4, 5, 6, 8, 10, 11, 12, 12]
\end{verbatim}
\section{Exercise 2}
\subsection{Exercise a}
The pseudocode for \textit{Sum of two} can be found in listing \ref{lst:sum2}.
The total cost of this algorithm in the worst case is the sum of the worst case
of mergesort ($O(n log(n))$) and the cost of the worst case in the partition
done afterwards (which is equivalent to not finding the sum, i.e. $2 n =
O(n)$). Therefore, the total cost is $\theta(n log(n))$.
done afterwards (which is equivalent to not finding a sum close to the median,
i.e. $2 n = O(n)$). Therefore, the total cost is $\theta(n log(n))$.
\begin{lstlisting}[caption=Sum of two in pseudocode, label={lst:sum2}]
FUNCTION SUM-OF-TWO(A, s):

3
insertion_sort.py
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@ -8,11 +8,10 @@ def insertionsort(A):
# insert the next element in the right place in the first elements
# continue until the array is done
for j in range(1,len(A)):
print(A)
print(A)
i = j - 1
# while swapping is necessary or at the end of array
while i >= 0 and A[i+1] < A[i]:
print(A)
# Swap A[i] and A[j]
A[i+1], A[i] = A[i], A[i+1]
i = i - 1

34
mergesort.py
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@ -1,34 +0,0 @@
#!/usr/bin/env python3
# vim: set ts=4 sw=4 et tw=80:
import sys
import math
def find(A,x):
for a in A:
if a == x:
return True
return False
def merge(A,B):
X = []
for a in A:
if not find(X, a):
X.append(a)
for b in B:
if not find(X, b):
X.append(b)
return X
def mergesort(A):
l = len(A)
if l < 2:
return A
else:
lh = len(A) // 2
h1 = mergesort(A[:lh])
h2 = mergesort(A[lh:])
return merge(h1,h2)
args = [int(x) for x in sys.argv[1:]]
print(mergesort(args))

18
selection.py Executable file
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@ -0,0 +1,18 @@
#!/usr/bin/env python3
import sys
def selectionsort(A):
if len(A) < 2:
return A
for i in range(len(A)):
for j in range(i + 1, len(A)):
if A[i] > A[j]:
A[i], A[j] = A[j], A[i]
print(A)
return A
if __name__ == "__main__":
args = [int(x) for x in sys.argv[1:]]
print(selectionsort(args))