GA2 done. Selection sort added

GA2/ga2.tex

@@ -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. $2 n =
+done afterwards (which is equivalent to not finding a sum close to the median,
-O(n)$). Therefore, the total cost is $\theta(n log(n))$.
+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):

insertion_sort.py

@@ -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

mergesort.py

@@ -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))

selection.py

@@ -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))
+