From 864d111326187ac0971f2ee4fd4d3110b28f5e1d Mon Sep 17 00:00:00 2001
From: Claudio Maggioni <claudio@maggioni.xyz>
Date: Tue, 5 Mar 2019 13:23:46 +0100
Subject: [PATCH] 2019-03-05 in class

---
 histogram.py      | 33 +++++++++++++++------------------
 insertion_sort.py | 10 +++++-----
 mergesort.py      | 34 ++++++++++++++++++++++++++++++++++
 notes.md          |  5 +++++
 4 files changed, 59 insertions(+), 23 deletions(-)
 create mode 100644 mergesort.py

diff --git a/histogram.py b/histogram.py
index 2a671f8..74c3367 100755
--- a/histogram.py
+++ b/histogram.py
@@ -1,30 +1,27 @@
 #!/usr/bin/env python3
+# vim: set sw=4 ts=4 et tw=80:
 
 import sys
 
 def histogram(data):
-    height_max = max(data)
-    height_min = min(min(data), 0)
-    current_line = height_max
+    top = max(max(data), 0)
+    bottom = min(min(data), 0)
+    i = top
 
-    while current_line >= height_min:
+    while i >= bottom:
         to_print = ""
 
-        if current_line == 0:
-            print("-" * len(data))
-        else:
-            for elem in data:
-                if current_line > 0 and elem >= current_line:
-                    to_print += "#"
-                elif current_line > 0:
-                    to_print += " "
-                elif current_line < 0 and elem <= current_line:
-                    to_print += "#"
-                else:
-                    to_print += " "
-            print(to_print)
+        for elem in data:
+            if i == 0:
+                to_print += "-"
+            elif (i > 0 and elem >= i) or \
+                 (i < 0 and elem <= i):
+                to_print += "#"
+            else:
+                to_print += " "
+        print(to_print)
 
-        current_line = current_line - 1
+        i = i - 1
 
 def main():
     args = [int(x) for x in sys.argv[1:]]
diff --git a/insertion_sort.py b/insertion_sort.py
index f369757..28afbac 100755
--- a/insertion_sort.py
+++ b/insertion_sort.py
@@ -1,4 +1,5 @@
 #!/usr/bin/env python3
+# vim: set ts=4 sw=4 et tw=80:
 
 import sys
 
@@ -10,11 +11,10 @@ def insertionsort(A):
         print(A)
         print(A)
         i = j - 1
-        tomove = A[j]
-        while i >= 0 and tomove < A[i]:
-            if A[i] > A[i+1]:
-                # Swap A[i] and A[j]
-                A[i+1], A[i] = A[i], A[i+1]
+        # while swapping is necessary or at the end of array
+        while i >= 0 and A[i+1] < A[i]:
+            # Swap A[i] and A[j]
+            A[i+1], A[i] = A[i], A[i+1]
             i = i - 1
     return A
 
diff --git a/mergesort.py b/mergesort.py
new file mode 100644
index 0000000..a1b6a32
--- /dev/null
+++ b/mergesort.py
@@ -0,0 +1,34 @@
+#!/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))
diff --git a/notes.md b/notes.md
index 12b98ac..65667a9 100644
--- a/notes.md
+++ b/notes.md
@@ -94,3 +94,8 @@ Proof sort of by induction.
 
 An algorithm is correct if given an input the output satisfies the conditions
 stated. The algorithm must terminate.
+
+### The loop invariant
+
+Invariant condition able to make a loop equivalent to a straight path in an
+execution graph.