13 files changed, 274 insertions, 0 deletions

diff --git a/ws2015/eip/blaetter/01/Basistypen.md b/ws2015/eip/blaetter/01/Basistypen.md
new file mode 100644
index 0000000..0074be2
--- /dev/null
+++ b/ws2015/eip/blaetter/01/Basistypen.md
@@ -0,0 +1,14 @@
+# 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
new file mode 100644
index 0000000..35fa406
--- /dev/null
+++ b/ws2015/eip/blaetter/01/GreatEscape.java
@@ -0,0 +1,11 @@
+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
new file mode 100644
index 0000000..775d7e2
--- /dev/null
+++ b/ws2015/eip/blaetter/01/manifest
@@ -0,0 +1,2 @@
+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
new file mode 100644
index 0000000..90335a4
--- /dev/null
+++ b/ws2015/eip/blaetter/02/Arithmetik.java
@@ -0,0 +1,33 @@
+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
new file mode 100644
index 0000000..e2fa908
--- /dev/null
+++ b/ws2015/eip/blaetter/02/H2-1.md
@@ -0,0 +1,18 @@
+# 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
new file mode 100644
index 0000000..430d28e
--- /dev/null
+++ b/ws2015/eip/blaetter/02/H2-2.md
@@ -0,0 +1,13 @@
+# 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
new file mode 120000
index 0000000..34aea7f
--- /dev/null
+++ b/ws2015/eip/blaetter/02/H2-3.java
@@ -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
new file mode 100644
index 0000000..9cec2d1
--- /dev/null
+++ b/ws2015/eip/blaetter/02/manifest
@@ -0,0 +1,3 @@
+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
new file mode 100644
index 0000000..5647e13
--- /dev/null
+++ b/ws2015/eip/blaetter/02/test.sh
@@ -0,0 +1,20 @@
+#!/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 $ret
+        exit 1
+    fi
+}
+
+gup --update Arithmetik.class || exit 1
+
+runTest "Christian\nElegans\n2\n7" "Hallo C. Elegans! Der Mittelwert von 2 und 7 ist übrigens 4.5!"
+runTest "Gustav\nEnauer\n70\n15" "Hallo G. Enauer! Der Kehrwert von 70 ist ungefähr 0.014285714285714!"
+runTest "Karla\nEhr-Wert\n7\n3" "Hallo K. Ehr-Wert! Der Kehrwert von 7 ist ungefähr 0.143!"
diff --git a/ws2015/eip/blaetter/03/H3-1.md b/ws2015/eip/blaetter/03/H3-1.md
new file mode 100644
index 0000000..bb3d2ca
--- /dev/null
+++ b/ws2015/eip/blaetter/03/H3-1.md
@@ -0,0 +1,39 @@
+---
+header-includes:
+        - \usepackage{bussproofs}
+        - \renewcommand{\implies}{\rightarrow}
+        - \EnableBpAbbreviations
+---
+# Hoare-Tripel II
+
+d)
+
+\begin{prooftree}
+\AXC{$\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
new file mode 100644
index 0000000..62d8fc2
--- /dev/null
+++ b/ws2015/eip/blaetter/03/H3-2.md
@@ -0,0 +1,84 @@
+---
+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
new file mode 100644
index 0000000..ca9fbd8
--- /dev/null
+++ b/ws2015/eip/blaetter/03/H3-3.md
@@ -0,0 +1,33 @@
+# 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
new file mode 100644
index 0000000..ff79ea4
--- /dev/null
+++ b/ws2015/eip/blaetter/03/manifest
@@ -0,0 +1,3 @@
+H3-1.pdf
+H3-2.pdf
+H3-3.pdf
\ No newline at end of file