From: Neil Smith <neil.git@njae.me.uk>
Date: Thu, 4 Dec 2014 23:20:25 +0000 (+0000)
Subject: Done algorithm examples
X-Git-Url: https://git.njae.me.uk/?p=cas-master-teacher-training.git;a=commitdiff_plain;h=c83ef2510a03a1727b4ef7367edd179fab6c37a6

Done algorithm examples
---

diff --git a/algorithms.html b/algorithms.html
index f5dbe1f..57fdbae 100644
--- a/algorithms.html
+++ b/algorithms.html
@@ -280,6 +280,14 @@ Given a wordlist and a phrase, find another phrase that's an anagram.
 
 ---
 
+# Sorting with cards
+
+Classroom activity?
+
+Don't forget bogosort!
+
+---
+
 # Dealing with complex problems: some terms to know
 
 (M269 Unit 5)
@@ -298,16 +306,82 @@ Given a wordlist and a phrase, find another phrase that's an anagram.
 
 Build a soluion bottom-up from subparts
 
-## Heuristics
+---
+
+# Heuristics
 
 * Posh word for "guess"
 * Greedy algorithms
 * Backtracking
+
 ---
 
-# Sorting with cards
+# Making change
 
-Classroom activity?
+Given
+
+* some money and a set of coin denominations,
+
+find
+
+* the smallest number of coins to make that total.
+
+## Approach 1: greedy
+
+```
+Repeat:
+   Pick the biggest coin you can
+```
+
+Only works in some cases
+
+(What the best way to make 7p if you have 1p, 3p, 4p, 5p coins?)
+
+---
+
+# Making change 2: exhaustive search
+
+.float-right[![Ticket to Ride](make-change.dot.png)]
+
+Make a tree of change-making.
+
+Pick the optimal.
+
+---
+
+# Making change 3: dynamic programming
+
+Bottom-up approach
+
+Initial:
+
+0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ...
+-|-|-|-|-|-|-|-|-|-|-|-
+(0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | ...
+
+--
+----
+0* | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ...
+-|-|-|-|-|-|-|-|-|-|-|-
+(0, 0, 0) | (1, 0, 0) | (0, 1, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 1) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | ...
+
+--
+----
+0 | 1* | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ...
+-|-|-|-|-|-|-|-|-|-|-|-
+(0, 0, 0) | (1, 0, 0) | (0, 1, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 1) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | ...
+
+--
+----
+0 | 1 | 2* | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ...
+-|-|-|-|-|-|-|-|-|-|-|-
+(0, 0, 0) | (1, 0, 0) | (0, 1, 0) | (1, 1, 0) | (0, 2, 0) | (0, 0, 1) | (0, 0, 0) | (0, 1, 1) | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | ...
+
+--
+----
+0 | 1 | 2 | 3* | 4 | 5 | 6 | 7 | 8 | 9 | 10 | ...
+-|-|-|-|-|-|-|-|-|-|-|-
+(0, 0, 0) | (1, 0, 0) | (0, 1, 0) | (1, 1, 0) | (0, 2, 0) | (0, 0, 1) | (0, 0, 0) | (0, 1, 1) | (1, 1, 1) | (0, 0, 0) | (0, 0, 0) | ...
 
 ---
 
@@ -315,19 +389,21 @@ Classroom activity?
 
 ## Travelling Salesman Problem
 
-Online: http://www.math.uwaterloo.ca/tsp/games/tspOnePlayer.html
+.float-right[![Ticket to Ride](ticket-to-ride-small.jpg)]
+
+Online: 
+
+http://www.math.uwaterloo.ca/tsp/games/tspOnePlayer.html
 
 * But many implementations are Java applets, now a problem with security settings
 
 Try Android/iOS apps?
 
-## Change-finding problem
-
-Same as the Knapsack problem: M269 Unit 5 Section 3.2, especially Activity 5.9
+## Ticket to Ride boardgame
 
-Dynamic programming to find solution
+Graph algorithms
 
-## Ticket to Ride boardgame
+* Find shortest path
 
 ---
 
diff --git a/make-change.dot b/make-change.dot
new file mode 100644
index 0000000..cba93a1
--- /dev/null
+++ b/make-change.dot
@@ -0,0 +1,36 @@
+digraph G {
+	ten [label="10\n0, 0, 0"];
+	nine [label="9\n1, 0, 0"];
+	eight [label="8\n 0, 1, 0"];
+	eighta [label="8\n2, 0, 0"];
+	five [label="5\n0, 0, 1"];
+	seven [label="7\n1, 1, 0"];
+	four [label="4\n1, 0, 5"];
+	six [label="6\n0, 2, 0"];
+	three [label="3\n0, 1, 1"];
+	five [label="5\n0, 0, 1"];
+	zero [label="0\n0, 0, 2"];
+	sixa [label="6\n2, 1, 0"];
+	fivea [label="5\n1, 2, 0"];
+	two [label="2\n1, 1, 1"];
+
+	ten -> nine;
+	ten -> eight;
+	ten -> five;
+
+	nine -> eighta;
+	nine -> seven;
+	nine -> four;
+
+	seven -> sixa;
+	seven -> fivea;
+	seven -> two;
+
+	eight -> seven;
+	eight -> six;
+	eight -> three;
+
+	five -> four;
+	five -> three;
+	five -> zero;
+}
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