From 57a4615e0888d2e6f02e11de86e8bbc7a535791a Mon Sep 17 00:00:00 2001
From: Claudio Maggioni <claudio@maggioni.xyz>
Date: Tue, 26 Feb 2019 12:25:18 +0100
Subject: [PATCH] 2019-02-26 in class

---
 heasy.py | 30 ++++++++++++++++++++++++++++++
 min.py   | 24 ++++++++++++++++++++++++
 notes.md | 47 +++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 101 insertions(+)
 create mode 100755 heasy.py
 create mode 100755 min.py

diff --git a/heasy.py b/heasy.py
new file mode 100755
index 0000000..c5d23ee
--- /dev/null
+++ b/heasy.py
@@ -0,0 +1,30 @@
+#!/usr/bin/env python3
+
+import sys
+
+def histogram(A):
+    m = min(A)
+
+    for e in A:
+        negative = e < 0
+
+        if negative:
+            for _ in range(m,e):
+                print(" ", end="")
+            for _ in range(e,0):
+                print("#", end="")
+            print("|")
+        else:
+            for _ in range(m,0):
+                print(" ", end="")
+            print("|", end="")
+            for _ in range(0,e):
+                print("#", end="")
+            print("")
+
+def main():
+    args = [int(x) for x in sys.argv[1:]]
+    histogram(args)
+
+if __name__ == "__main__":
+    main()
diff --git a/min.py b/min.py
new file mode 100755
index 0000000..7d753af
--- /dev/null
+++ b/min.py
@@ -0,0 +1,24 @@
+#!/usr/bin/env python3
+
+import sys
+
+def minimum(a):
+    l = len(a)
+
+    if l == 0:
+        return None
+
+    m = a[0]
+    for i in range(1, l):
+        if a[i] < m:
+            m = a[i]
+
+    return m
+
+if __name__ == "__main__":
+    A = []
+    for line in sys.stdin:
+        A.append(int(line))
+
+print(minimum(A))
+
diff --git a/notes.md b/notes.md
index f2cac81..f48e18e 100644
--- a/notes.md
+++ b/notes.md
@@ -32,3 +32,50 @@ f(n) = O(g(n))
 *Definition:* if f(n) is such that f(n) = k * A(g(n)) for all _n_ sufficiently
 large and for some constant k > 0, then we say that
 
+# Complexity notations (lecture 2019-02-26)
+
+## Characterizing unknown functions
+
+pi(n) = number of primes less than n
+
+## First approximation
+
+*Upper bound:* linear function
+
+pi(n) = O(n)
+
+*Lower bound:* constant function
+
+pi(n) = omega(1)
+
+*Non-trivial tight bound*:
+
+pi(n) = theta(n/log n)
+
+## Theta notation
+Given a functio ng(n), we define the __family__ of functions theta(g(n)) such
+that given a c_1, c_2 and an n_0, for all n >= n_0 g(n) is sandwiched between
+c_1g(n) and c_2g(n)
+
+## Big omega notation
+Omega(g(n)) is a family of functions such that there exists a c and an n_0 such
+that for all n>= n_0 g(n) dominates c\*g(n)
+
+## Big "oh" notation
+O(g(n)) is a family of functions such that there exists a c and an n_0 such
+that for all n>= n_0 g(n) is dominated by c\*g(n)
+
+## Small "oh" notation
+o(g(n)) is the family of functions O(g(n)) excluding all the functions in
+theta(g(n))
+
+## Small omega notation
+omega(g(n)) is the family of functions Omega(g(n)) excluding all the functions in
+theta(g(n))
+
+## Recap
+*asymptotically* = <=> theta(g(n))
+*asymptotically* < <=> o(g(n))
+*asymptotically* > <=> omega(g(n))
+*asymptotically* <= <=> O(g(n))
+*asymptotically* >= <=> Omega(g(n))