13 files changed, 0 insertions, 274 deletions
diff --git a/ws2015/EiP/blaetter/01/Basistypen.md b/ws2015/EiP/blaetter/01/Basistypen.md
deleted file mode 100644
index 0074be2..0000000
--- a/ws2015/EiP/blaetter/01/Basistypen.md
+++ /dev/null
@@ -1,14 +0,0 @@
-# Aufgabe H1-2 -- Basistypen II
-a)
-    `(double)3.0`
-b)
-    `(double)1.3333333333333333`
-c)
-    `(double)1.6666666666666665`
-d)
-    `(double)1.75`
-e)
-    `(string)"7.27"`
-f)
-    `(string)"374.2"`
diff --git a/ws2015/EiP/blaetter/01/GreatEscape.java b/ws2015/EiP/blaetter/01/GreatEscape.java
deleted file mode 100644
index 35fa406..0000000
--- a/ws2015/EiP/blaetter/01/GreatEscape.java
+++ /dev/null
@@ -1,11 +0,0 @@
-public class GreatEscape
-{
-    public static void main (String[] args)
-    {
-        System.out.println("       \\__/ \\__/");
-        System.out.println("       (\"\") (\"\")");
-        System.out.println("  .-----\\/   \\/-----.");
-        System.out.println(" /|_____|     |_____|\\");
-        System.out.println("\" | \\  ||     ||  / | \"");
-    }
-}
diff --git a/ws2015/EiP/blaetter/01/manifest b/ws2015/EiP/blaetter/01/manifest
deleted file mode 100644
index 775d7e2..0000000
--- a/ws2015/EiP/blaetter/01/manifest
+++ /dev/null
@@ -1,2 +0,0 @@
-GreatEscape.java
-Basistypen.pdf
-\ No newline at end of file
diff --git a/ws2015/EiP/blaetter/02/Arithmetik.java b/ws2015/EiP/blaetter/02/Arithmetik.java
deleted file mode 100644
index 90335a4..0000000
--- a/ws2015/EiP/blaetter/02/Arithmetik.java
+++ /dev/null
@@ -1,33 +0,0 @@
-import java.util.Scanner;
-class Arithmetik
-{
-    public static void main (String[] args)
-    {
-        Scanner scanner = new Scanner(System.in);
-        System.out.print("Vorname: ");
-        String vorname = scanner.nextLine();
-        System.out.print("Nachname: ");
-        String nachname = scanner.nextLine();
-        System.out.print("x_1 = ");
-        int x1 = scanner.nextInt();
-        System.out.print("x_2 = ");
-        int x2 = scanner.nextInt();
-        
-        System.out.print("Hallo " + vorname.substring(0,1) + ". " + nachname + "! ");
-        if (x1 < x2)
-            {
-                System.out.println("Der Mittelwert von " + x1 + " und " + x2 + " ist übrigens " + ((x1 + x2) / 2.0) + "!");
-            }
-        else if (x1 > 0 && x2 > 0)
-            {
-                System.out.println("Der Kehrwert von " + x1 + " ist ungefähr " + 1.0/x1 + "!");
-            }
-        else
-            {
-                System.out.println(x1 + x2);
-            }
-    }
-}
diff --git a/ws2015/EiP/blaetter/02/H2-1.md b/ws2015/EiP/blaetter/02/H2-1.md
deleted file mode 100644
index e2fa908..0000000
--- a/ws2015/EiP/blaetter/02/H2-1.md
+++ /dev/null
@@ -1,18 +0,0 @@
-# Speicherbild
-Wir notieren eine Referenz mit Variablennamen `x` auf ein Objekt, dessen Repräsentation als String `...` ist, wie folgt:
-~~~ {.java}
-x -> ...
-~~~
-~~~ {.java}
-Int x = 9
-Prof prof1 -> Prof[name="Chris",teaching=9]
-Prof prof2 -> Prof[name="Dora",teaching=9]
-Student student1 -> Student[name="Alois",matrikel=1234]
-Student student2 -> Student[name="Bine",matrikel=4567]
-Student student3 -> Student[name="Alois",matrikel=1234]
-~~~
-`student1` und `student3` zeigen auf unterschiedliche Speicherbereiche.
diff --git a/ws2015/EiP/blaetter/02/H2-2.md b/ws2015/EiP/blaetter/02/H2-2.md
deleted file mode 100644
index 430d28e..0000000
--- a/ws2015/EiP/blaetter/02/H2-2.md
+++ /dev/null
@@ -1,13 +0,0 @@
-# Variablen
-2 -- `int x`
-  ~ Instanzvariable -- Lebenspanne identisch mit der des Objekts, Sichtbar (und nicht überschattet) in 9, und 13
-4 -- `int x`
-  ~ Parameter -- Lebenspanne bis 6, Sichtbar in 5
-12 -- `int y`
-  ~ Parameter -- Lebenspanne bis 17, Sichtbar in 13--16
-14 -- `int x`
-  ~ Lokale Variable -- Lebenspanne bis 17, Sichtbar in 15--16
diff --git a/ws2015/EiP/blaetter/02/H2-3.java b/ws2015/EiP/blaetter/02/H2-3.java
deleted file mode 120000
index 34aea7f..0000000
--- a/ws2015/EiP/blaetter/02/H2-3.java
+++ /dev/null
@@ -1 +0,0 @@
-Arithmetik.java
-\ No newline at end of file
diff --git a/ws2015/EiP/blaetter/02/manifest b/ws2015/EiP/blaetter/02/manifest
deleted file mode 100644
index 9cec2d1..0000000
--- a/ws2015/EiP/blaetter/02/manifest
+++ /dev/null
@@ -1,3 +0,0 @@
-H2-1.pdf
-H2-2.pdf
-H2-3.java
-\ No newline at end of file
diff --git a/ws2015/EiP/blaetter/02/test.sh b/ws2015/EiP/blaetter/02/test.sh
deleted file mode 100644
index 5647e13..0000000
--- a/ws2015/EiP/blaetter/02/test.sh
+++ /dev/null
@@ -1,20 +0,0 @@
-#!/usr/bin/env zsh
-runTest() {
-    ret=$(echo $1 | java Arithmetik | tail -c +32) 
-    if [[ $ret != $2 ]]; then
-        echo "Input:"
-        echo $1
-        echo "Should return:"
-        echo $2
-        echo "But returns:"
-        echo $ret
-        exit 1
-    fi
-}
-gup --update Arithmetik.class || exit 1
-runTest "Christian\nElegans\n2\n7" "Hallo C. Elegans! Der Mittelwert von 2 und 7 ist übrigens 4.5!"
-runTest "Gustav\nEnauer\n70\n15" "Hallo G. Enauer! Der Kehrwert von 70 ist ungefähr 0.014285714285714!"
-runTest "Karla\nEhr-Wert\n7\n3" "Hallo K. Ehr-Wert! Der Kehrwert von 7 ist ungefähr 0.143!"
diff --git a/ws2015/EiP/blaetter/03/H3-1.md b/ws2015/EiP/blaetter/03/H3-1.md
deleted file mode 100644
index bb3d2ca..0000000
--- a/ws2015/EiP/blaetter/03/H3-1.md
+++ /dev/null
@@ -1,39 +0,0 @@
---
-header-includes:
-        - \usepackage{bussproofs}
-        - \renewcommand{\implies}{\rightarrow}
-        - \EnableBpAbbreviations
---
-# Hoare-Tripel II
-d)
-\begin{prooftree}
-\AXC{$\forall \phi \ldotp \phi \implies \phi$}
-\UIC{$(0 < n + 1 \land n < m) \implies (0 < n + 1 \land n < m)$}
-\RightLabel{Umformung}
-\UIC{$(0 < n + 1 \land n < m) \implies (0 < n + 1 \land n \leq m - 1)$}
-\RightLabel{Umformung}
-\UIC{$(0 < n + 1 \land n < m) \implies (0 < n + 1 \land n + 1 \leq m)$}
-\RightLabel{Zuweisung}
-\UIC{$ \{ 0 < n + 1 \land n < m \} $ \texttt{n = n + 1} $ \{ 0 < n \land n \leq m \} $}
-\end{prooftree}
-e) Nimm als Gegenbeispiel:
-~~~
-a = -1
-b = 0
-~~~
-f) Seit $\phi$ die Nachfolgerfunktion auf $\mathbb{N}$.
-\begin{prooftree}
-\AXC{$\forall n \in \mathbb{N} \ldotp \phi(n) > n$}
-\UIC{$1 > 0$}
-\UIC{$((x + 1) + y > x + y)$}
-\UIC{$(z = x + y) \implies ((x + 1) + y > z)$}
-\UIC{$ \{ z = x + y \} $ \texttt{ x = x + 1} $ \{ x + y > z \} $}
-\UIC{$ \{ z = x + y \land z \equiv 0 \mod 2 \} $ \texttt{x = x + 1} $ \{ x + y > z \} $ \quad $ \{ z = x + y \land z \equiv 1 \mod 2 \} $ \texttt{x = x + 1} $ \{ x + y > z \} $}
-\UIC{$ \{ z = x + y \} $ \texttt{if (z \% 2 == 0) x = x + 1; else y = y + 1;} $ \{ x + y > z \} $}
-\end{prooftree}
diff --git a/ws2015/EiP/blaetter/03/H3-2.md b/ws2015/EiP/blaetter/03/H3-2.md
deleted file mode 100644
index 62d8fc2..0000000
--- a/ws2015/EiP/blaetter/03/H3-2.md
+++ /dev/null
@@ -1,84 +0,0 @@
---
-header-includes:
-        - \usepackage{bussproofs}
-        - \renewcommand{\implies}{\rightarrow}
-        - \EnableBpAbbreviations
---
-# Hoare-Logik: While-Schleife II
-| Schleifendurchlauf | \texttt{n} | \texttt{a} | \texttt{b} | \texttt{c} |
-|--------------------+------------+------------+------------+------------|
-|                  0 |          5 |          0 |          0 |          1 |
-|                  1 |          5 |          1 |          1 |          7 |
-|                  2 |          5 |          8 |          2 |         19 |
-|                  3 |          5 |         27 |          3 |         37 |
-|                  4 |          5 |         64 |          4 |         61 |
-|                  5 |          5 |        125 |          5 |         91 |
-Wir bezeichnen mit $P'$:
-~~~
-a = a + c
-b = b + 1
-c = c + 6*b
-~~~
-Wir bezeichnen mit $J$:
-~~~
-a = 0
-b = 0
-c = 1
-~~~
-und setzen $J'$ derart, dass $\{\} J \{J'\}$ gültig ist.
-Wir bezeichnen zudem mit $\bar P$:
-~~~
-while (b != n) {
-  a = a + c
-  b = b + 1
-  c = c + 6*b
-}
-~~~
-Es sei zudem $I = (c = (b + 1)^3 - b^3)$.
-\begin{prooftree}
-\AXC{$ 1 = (0 + 1)^3 - 0 $}
-\UIC{$ (a, b, c) = (0, 0, 1) \implies c = ( b + 1 )^3 - b^3$}
-\UIC{$J' \implies I$}
-\end{prooftree}
-\begin{prooftree}
-\AXC{$0 = 0$}
-\RightLabel{Algebraische Umformung}
-\UIC{$(b + 1)^3 - b^3 + 6 \cdot (b + 1) = (b + 2)^3 - (b + 1)^3$}
-\UIC{$c = ( b + 1 )^3 - b^3 \implies c + 6 \cdot (b + 1) = (b + 2)^3 - (b + 1)^3$}
-\UIC{$\{c = ( b + 1 )^3 - b^3 \land b \neq n \}$ $P'$ $\{ c = (b + 1)^3 - b^3 \}$}
-\UIC{$\{ I \land b \}$ $P'$ $ \{ I \} $}
-\end{prooftree}
-\begin{prooftree}
-\AXC{$J' \implies I$}
-\AXC{$\{I \land b\}$ $P'$ $\{ I \}$}
-\AXC{$I \land b = n \implies a = n^3$}
-\TIC{$ \{ n > 0 \land J' \} $ $ \bar P $ $ \{ a = n^3 \} $}
-\end{prooftree}
-Es bleibt zu zeigen, dass $a(n) = n^3$.
-Es gilt wegen $P'$ und $J$:
-\begin{align*}
-c(0) &= 1 \\
-c(k) &= c(k - 1) + 6 \cdot k \\
-     &= 1 + \sum_{i = 0}^{k} 6i \\
-a(0) &= 0 \\
-a(k) &= a(k - 1) + c(k - 1) \\
-         &= a(k - 1) + 1 + \sum_{i = 0}^{k - 1} 6i \\
-         &= \sum_{j = 0}^{k} \left ( 1 + \sum_{i = 0}^{j - 1} 6i \right ) \\
-         &= k + \sum_{j = 0}^{k} \sum_{i = 0}^{j - 1} 6i \\
-         &= k + \sum_{j = 0}^{k} \left ( 3j (j - 1) \right ) \\
-         &= k + \left ( k^3 - k \right ) \\
-         &= k^3
-\end{align*}
diff --git a/ws2015/EiP/blaetter/03/H3-3.md b/ws2015/EiP/blaetter/03/H3-3.md
deleted file mode 100644
index ca9fbd8..0000000
--- a/ws2015/EiP/blaetter/03/H3-3.md
+++ /dev/null
@@ -1,33 +0,0 @@
-# Code Verständnis
-| Zeile | Zuweisung |
-|-------+-----------|
-|   010 | x = 42    |
-|   030 | y = 36    |
-|   070 | z = 1     |
-|   080 | z = 2     |
-|   090 | z = 3     |
-|   100 | y = 39    |
-|   120 | z = 6     |
-|   070 | z = 1     |
-|   080 | z = 2     |
-|   090 | z = 3     |
-|   100 | y = 42    |
-|   120 | z = 6     |
-|   230 | x = 53    |
-|   240 | z = 0     |
-|   250 | x = 57    |
-|   260 | y = 36    |
-|   270 | z = 1     |
-|   240 | z = 1     |
-|   250 | x = 61    |
-|   260 | y = 37    |
-|   270 | z = 2     |
-|   240 | z = 2     |
-|   250 | x = 65    |
-|   260 | y = 39    |
-|   270 | z = 3     |
-|   240 | z = 3     |
-|   250 | x = 69    |
-|   260 | y = 42    |
-|   270 | z = 4     |
diff --git a/ws2015/EiP/blaetter/03/manifest b/ws2015/EiP/blaetter/03/manifest
deleted file mode 100644
index ff79ea4..0000000
--- a/ws2015/EiP/blaetter/03/manifest
+++ /dev/null
@@ -1,3 +0,0 @@
-H3-1.pdf
-H3-2.pdf
-H3-3.pdf
-\ No newline at end of file

diff --git a/ws2015/EiP/blaetter/01/Basistypen.md b/ws2015/EiP/blaetter/01/Basistypen.md deleted file mode 100644 index 0074be2..0000000 --- a/ws2015/EiP/blaetter/01/Basistypen.md +++ /dev/null
@@ -1,14 +0,0 @@
1	# Aufgabe H1-2 -- Basistypen II
2
3	a)
4	`(double)3.0`
5	b)
6	`(double)1.3333333333333333`
7	c)
8	`(double)1.6666666666666665`
9	d)
10	`(double)1.75`
11	e)
12	`(string)"7.27"`
13	f)
14	`(string)"374.2"`


diff --git a/ws2015/EiP/blaetter/01/GreatEscape.java b/ws2015/EiP/blaetter/01/GreatEscape.java deleted file mode 100644 index 35fa406..0000000 --- a/ws2015/EiP/blaetter/01/GreatEscape.java +++ /dev/null
@@ -1,11 +0,0 @@
1	public class GreatEscape
2	{
3	public static void main (String[] args)
4	{
5	System.out.println(" \\__/ \\__/");
6	System.out.println(" (\"\") (\"\")");
7	System.out.println(" .-----\\/ \\/-----.");
8	System.out.println(" /\|_____\| \|_____\|\\");
9	System.out.println("\" \| \\ \|\| \|\| / \| \"");
10	}
11	}


diff --git a/ws2015/EiP/blaetter/01/manifest b/ws2015/EiP/blaetter/01/manifest deleted file mode 100644 index 775d7e2..0000000 --- a/ws2015/EiP/blaetter/01/manifest +++ /dev/null
@@ -1,2 +0,0 @@
1	GreatEscape.java
2	Basistypen.pdf \ No newline at end of file


diff --git a/ws2015/EiP/blaetter/02/Arithmetik.java b/ws2015/EiP/blaetter/02/Arithmetik.java deleted file mode 100644 index 90335a4..0000000 --- a/ws2015/EiP/blaetter/02/Arithmetik.java +++ /dev/null
@@ -1,33 +0,0 @@
1	import java.util.Scanner;
2
3	class Arithmetik
4	{
5	public static void main (String[] args)
6	{
7	Scanner scanner = new Scanner(System.in);
8
9	System.out.print("Vorname: ");
10	String vorname = scanner.nextLine();
11	System.out.print("Nachname: ");
12	String nachname = scanner.nextLine();
13	System.out.print("x_1 = ");
14	int x1 = scanner.nextInt();
15	System.out.print("x_2 = ");
16	int x2 = scanner.nextInt();
17
18	System.out.print("Hallo " + vorname.substring(0,1) + ". " + nachname + "! ");
19
20	if (x1 < x2)
21	{
22	System.out.println("Der Mittelwert von " + x1 + " und " + x2 + " ist übrigens " + ((x1 + x2) / 2.0) + "!");
23	}
24	else if (x1 > 0 && x2 > 0)
25	{
26	System.out.println("Der Kehrwert von " + x1 + " ist ungefähr " + 1.0/x1 + "!");
27	}
28	else
29	{
30	System.out.println(x1 + x2);
31	}
32	}
33	}


diff --git a/ws2015/EiP/blaetter/02/H2-1.md b/ws2015/EiP/blaetter/02/H2-1.md deleted file mode 100644 index e2fa908..0000000 --- a/ws2015/EiP/blaetter/02/H2-1.md +++ /dev/null
@@ -1,18 +0,0 @@
1	# Speicherbild
2
3	Wir notieren eine Referenz mit Variablennamen `x` auf ein Objekt, dessen Repräsentation als String `...` ist, wie folgt:
4
5	~~~ {.java}
6	x -> ...
7	~~~
8
9	~~~ {.java}
10	Int x = 9
11	Prof prof1 -> Prof[name="Chris",teaching=9]
12	Prof prof2 -> Prof[name="Dora",teaching=9]
13	Student student1 -> Student[name="Alois",matrikel=1234]
14	Student student2 -> Student[name="Bine",matrikel=4567]
15	Student student3 -> Student[name="Alois",matrikel=1234]
16	~~~
17
18	`student1` und `student3` zeigen auf unterschiedliche Speicherbereiche.


diff --git a/ws2015/EiP/blaetter/02/H2-2.md b/ws2015/EiP/blaetter/02/H2-2.md deleted file mode 100644 index 430d28e..0000000 --- a/ws2015/EiP/blaetter/02/H2-2.md +++ /dev/null
@@ -1,13 +0,0 @@
1	# Variablen
2
3	2 -- `int x`
4	~ Instanzvariable -- Lebenspanne identisch mit der des Objekts, Sichtbar (und nicht überschattet) in 9, und 13
5
6	4 -- `int x`
7	~ Parameter -- Lebenspanne bis 6, Sichtbar in 5
8
9	12 -- `int y`
10	~ Parameter -- Lebenspanne bis 17, Sichtbar in 13--16
11
12	14 -- `int x`
13	~ Lokale Variable -- Lebenspanne bis 17, Sichtbar in 15--16


diff --git a/ws2015/EiP/blaetter/02/H2-3.java b/ws2015/EiP/blaetter/02/H2-3.java deleted file mode 120000 index 34aea7f..0000000 --- a/ws2015/EiP/blaetter/02/H2-3.java +++ /dev/null
@@ -1 +0,0 @@
1	Arithmetik.java \ No newline at end of file


diff --git a/ws2015/EiP/blaetter/02/manifest b/ws2015/EiP/blaetter/02/manifest deleted file mode 100644 index 9cec2d1..0000000 --- a/ws2015/EiP/blaetter/02/manifest +++ /dev/null
@@ -1,3 +0,0 @@
1	H2-1.pdf
2	H2-2.pdf
3	H2-3.java \ No newline at end of file


diff --git a/ws2015/EiP/blaetter/02/test.sh b/ws2015/EiP/blaetter/02/test.sh deleted file mode 100644 index 5647e13..0000000 --- a/ws2015/EiP/blaetter/02/test.sh +++ /dev/null
@@ -1,20 +0,0 @@
1	#!/usr/bin/env zsh
2
3	runTest() {
4	ret=$(echo $1 \| java Arithmetik \| tail -c +32)
5	if [[ $ret != $2 ]]; then
6	echo "Input:"
7	echo $1
8	echo "Should return:"
9	echo $2
10	echo "But returns:"
11	echo $ret
12	exit 1
13	fi
14	}
15
16	gup --update Arithmetik.class \|\| exit 1
17
18	runTest "Christian\nElegans\n2\n7" "Hallo C. Elegans! Der Mittelwert von 2 und 7 ist übrigens 4.5!"
19	runTest "Gustav\nEnauer\n70\n15" "Hallo G. Enauer! Der Kehrwert von 70 ist ungefähr 0.014285714285714!"
20	runTest "Karla\nEhr-Wert\n7\n3" "Hallo K. Ehr-Wert! Der Kehrwert von 7 ist ungefähr 0.143!"


diff --git a/ws2015/EiP/blaetter/03/H3-1.md b/ws2015/EiP/blaetter/03/H3-1.md deleted file mode 100644 index bb3d2ca..0000000 --- a/ws2015/EiP/blaetter/03/H3-1.md +++ /dev/null
@@ -1,39 +0,0 @@
1	---
2	header-includes:
3	- \usepackage{bussproofs}
4	- \renewcommand{\implies}{\rightarrow}
5	- \EnableBpAbbreviations
6	---
7	# Hoare-Tripel II
8
9	d)
10
11	\begin{prooftree}
12	\AXC{$\forall \phi \ldotp \phi \implies \phi$}
13	\UIC{$(0 < n + 1 \land n < m) \implies (0 < n + 1 \land n < m)$}
14	\RightLabel{Umformung}
15	\UIC{$(0 < n + 1 \land n < m) \implies (0 < n + 1 \land n \leq m - 1)$}
16	\RightLabel{Umformung}
17	\UIC{$(0 < n + 1 \land n < m) \implies (0 < n + 1 \land n + 1 \leq m)$}
18	\RightLabel{Zuweisung}
19	\UIC{$ \{ 0 < n + 1 \land n < m \} $ \texttt{n = n + 1} $ \{ 0 < n \land n \leq m \} $}
20	\end{prooftree}
21
22	e) Nimm als Gegenbeispiel:
23
24	~~~
25	a = -1
26	b = 0
27	~~~
28
29	f) Seit $\phi$ die Nachfolgerfunktion auf $\mathbb{N}$.
30
31	\begin{prooftree}
32	\AXC{$\forall n \in \mathbb{N} \ldotp \phi(n) > n$}
33	\UIC{$1 > 0$}
34	\UIC{$((x + 1) + y > x + y)$}
35	\UIC{$(z = x + y) \implies ((x + 1) + y > z)$}
36	\UIC{$ \{ z = x + y \} $ \texttt{ x = x + 1} $ \{ x + y > z \} $}
37	\UIC{$ \{ z = x + y \land z \equiv 0 \mod 2 \} $ \texttt{x = x + 1} $ \{ x + y > z \} $ \quad $ \{ z = x + y \land z \equiv 1 \mod 2 \} $ \texttt{x = x + 1} $ \{ x + y > z \} $}
38	\UIC{$ \{ z = x + y \} $ \texttt{if (z \% 2 == 0) x = x + 1; else y = y + 1;} $ \{ x + y > z \} $}
39	\end{prooftree}


diff --git a/ws2015/EiP/blaetter/03/H3-2.md b/ws2015/EiP/blaetter/03/H3-2.md deleted file mode 100644 index 62d8fc2..0000000 --- a/ws2015/EiP/blaetter/03/H3-2.md +++ /dev/null
@@ -1,84 +0,0 @@
1	---
2	header-includes:
3	- \usepackage{bussproofs}
4	- \renewcommand{\implies}{\rightarrow}
5	- \EnableBpAbbreviations
6	---
7	# Hoare-Logik: While-Schleife II
8
9	\| Schleifendurchlauf \| \texttt{n} \| \texttt{a} \| \texttt{b} \| \texttt{c} \|
10	\|--------------------+------------+------------+------------+------------\|
11	\| 0 \| 5 \| 0 \| 0 \| 1 \|
12	\| 1 \| 5 \| 1 \| 1 \| 7 \|
13	\| 2 \| 5 \| 8 \| 2 \| 19 \|
14	\| 3 \| 5 \| 27 \| 3 \| 37 \|
15	\| 4 \| 5 \| 64 \| 4 \| 61 \|
16	\| 5 \| 5 \| 125 \| 5 \| 91 \|
17
18	Wir bezeichnen mit $P'$:
19
20	~~~
21	a = a + c
22	b = b + 1
23	c = c + 6*b
24	~~~
25
26	Wir bezeichnen mit $J$:
27
28	~~~
29	a = 0
30	b = 0
31	c = 1
32	~~~
33
34	und setzen $J'$ derart, dass $\{\} J \{J'\}$ gültig ist.
35
36	Wir bezeichnen zudem mit $\bar P$:
37
38	~~~
39	while (b != n) {
40	a = a + c
41	b = b + 1
42	c = c + 6*b
43	}
44	~~~
45
46	Es sei zudem $I = (c = (b + 1)^3 - b^3)$.
47
48	\begin{prooftree}
49	\AXC{$ 1 = (0 + 1)^3 - 0 $}
50	\UIC{$ (a, b, c) = (0, 0, 1) \implies c = ( b + 1 )^3 - b^3$}
51	\UIC{$J' \implies I$}
52	\end{prooftree}
53
54	\begin{prooftree}
55	\AXC{$0 = 0$}
56	\RightLabel{Algebraische Umformung}
57	\UIC{$(b + 1)^3 - b^3 + 6 \cdot (b + 1) = (b + 2)^3 - (b + 1)^3$}
58	\UIC{$c = ( b + 1 )^3 - b^3 \implies c + 6 \cdot (b + 1) = (b + 2)^3 - (b + 1)^3$}
59	\UIC{$\{c = ( b + 1 )^3 - b^3 \land b \neq n \}$ $P'$ $\{ c = (b + 1)^3 - b^3 \}$}
60	\UIC{$\{ I \land b \}$ $P'$ $ \{ I \} $}
61	\end{prooftree}
62
63	\begin{prooftree}
64	\AXC{$J' \implies I$}
65	\AXC{$\{I \land b\}$ $P'$ $\{ I \}$}
66	\AXC{$I \land b = n \implies a = n^3$}
67	\TIC{$ \{ n > 0 \land J' \} $ $ \bar P $ $ \{ a = n^3 \} $}
68	\end{prooftree}
69
70	Es bleibt zu zeigen, dass $a(n) = n^3$.
71	Es gilt wegen $P'$ und $J$:
72	\begin{align*}
73	c(0) &= 1 \\
74	c(k) &= c(k - 1) + 6 \cdot k \\
75	&= 1 + \sum_{i = 0}^{k} 6i \\
76	a(0) &= 0 \\
77	a(k) &= a(k - 1) + c(k - 1) \\
78	&= a(k - 1) + 1 + \sum_{i = 0}^{k - 1} 6i \\
79	&= \sum_{j = 0}^{k} \left ( 1 + \sum_{i = 0}^{j - 1} 6i \right ) \\
80	&= k + \sum_{j = 0}^{k} \sum_{i = 0}^{j - 1} 6i \\
81	&= k + \sum_{j = 0}^{k} \left ( 3j (j - 1) \right ) \\
82	&= k + \left ( k^3 - k \right ) \\
83	&= k^3
84	\end{align*}


diff --git a/ws2015/EiP/blaetter/03/H3-3.md b/ws2015/EiP/blaetter/03/H3-3.md deleted file mode 100644 index ca9fbd8..0000000 --- a/ws2015/EiP/blaetter/03/H3-3.md +++ /dev/null
@@ -1,33 +0,0 @@
1	# Code Verständnis
2
3	\| Zeile \| Zuweisung \|
4	\|-------+-----------\|
5	\| 010 \| x = 42 \|
6	\| 030 \| y = 36 \|
7	\| 070 \| z = 1 \|
8	\| 080 \| z = 2 \|
9	\| 090 \| z = 3 \|
10	\| 100 \| y = 39 \|
11	\| 120 \| z = 6 \|
12	\| 070 \| z = 1 \|
13	\| 080 \| z = 2 \|
14	\| 090 \| z = 3 \|
15	\| 100 \| y = 42 \|
16	\| 120 \| z = 6 \|
17	\| 230 \| x = 53 \|
18	\| 240 \| z = 0 \|
19	\| 250 \| x = 57 \|
20	\| 260 \| y = 36 \|
21	\| 270 \| z = 1 \|
22	\| 240 \| z = 1 \|
23	\| 250 \| x = 61 \|
24	\| 260 \| y = 37 \|
25	\| 270 \| z = 2 \|
26	\| 240 \| z = 2 \|
27	\| 250 \| x = 65 \|
28	\| 260 \| y = 39 \|
29	\| 270 \| z = 3 \|
30	\| 240 \| z = 3 \|
31	\| 250 \| x = 69 \|
32	\| 260 \| y = 42 \|
33	\| 270 \| z = 4 \|


diff --git a/ws2015/EiP/blaetter/03/manifest b/ws2015/EiP/blaetter/03/manifest deleted file mode 100644 index ff79ea4..0000000 --- a/ws2015/EiP/blaetter/03/manifest +++ /dev/null
@@ -1,3 +0,0 @@
1	H3-1.pdf
2	H3-2.pdf
3	H3-3.pdf \ No newline at end of file