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Expand Up @@ -135,6 +135,7 @@ The official book of the course, <cite><a href="https://comp-think.github.io/">C
- slides: [HTML](https://comp-think.github.io/2024-2025/slides/11%20-%20Organising%20information%20-%20trees.html)
- Python: [tree_instructions.py](https://comp-think.github.io/python/tree_instructions.py)
- exercises: [1](https://github.com/comp-think/2024-2025/issues/33), [2](https://github.com/comp-think/2024-2025/issues/34)
- solutions: [1](https://comp-think.github.io/keys/11/exercise-1), [2](https://comp-think.github.io/keys/11/exercise-2)
<hr />
17. [6/12/24, *lab*] Laboratory: 5th Lesson
- book chapter: [HTML](https://comp-think.github.io/laboratory/chapter/05)
Expand All @@ -144,7 +145,9 @@ The official book of the course, <cite><a href="https://comp-think.github.io/">C
<hr />
19. [11/12/24, *the*] Backtracking algorithms
- book chapter: [PDF](https://comp-think.github.io/book/12.pdf), [Google Docs](https://comp-think.github.io/book/12)
- slides: [HTML](https://comp-think.github.io/2024-2025/slides/12%20-%20Backtracking%20algorithms.html)
- Python: [peg_solitaire.py](https://comp-think.github.io/python/peg_solitaire.py)
- exercises: [1](https://github.com/comp-think/2024-2025/issues/35), [2](https://github.com/comp-think/2024-2025/issues/36)
<hr />
20. [13/12/24, *the*] Organising information: graphs
- book chapter: [PDF](https://comp-think.github.io/book/13.pdf), [Google Docs](https://comp-think.github.io/book/13)
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<section id="title" class="title_slide" role="doc-cover">
<h1>Backtracking algorithms</h1>
<div class="author">
<p><a href="https://www.unibo.it/sitoweb/silvio.peroni/en">Silvio Peroni</a></p>
<p class="contact">
<i class="fa fa-envelope" aria-hidden="true"></i> <a href="mailto:[email protected]">[email protected]</a>
<i class="ai ai-orcid" aria-hidden="true"></i> <a href="https://orcid.org/0000-0003-0530-4305">0000-0003-0530-4305</a>
<i class="fa fa-twitter" aria-hidden="true"></i> <a href="https://twitter.com/essepuntato">@essepuntato</a>
</p>
<p class="sst mtl"><a href="https://www.unibo.it/en/teaching/course-unit-catalogue/course-unit/2024/467045">Computational Thinking and Programming (A.Y. 2024/2025)</a></p>
<p class="ssst"><a href="https://corsi.unibo.it/2cycle/DigitalHumanitiesKnowledge">Second Cycle Degree in Digital Humanities and Digital Knowledge</a></p>
<p class="ssst"><a href="http://www.unibo.it/en">Alma Mater Studiorum - Università di Bologna</a></p>
<p class="license"><a rel="license" href="http://creativecommons.org/licenses/by/4.0/"></a> <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a></p>
</div>
</section>

<section>
<h2>Communication 1</h2>
<div class="st">
<p>A non-mandatory workshop will be held on 17 December, from 09:00-12:00 in Aula Affreschi</p>
<p>Please, bring your computer</p>
<p><span class="fragment highlight-red">You have to organise in groups of 3-4 people</span> (link to register your group will follow on Discord)</p>
<p>The task to address will be presented the day of the workshop</p>
<p>Max. score: 4 (in addition to 32 points you can take with the written examination)</p>
</div>
</section>

<section>
<h2>Any question about the previous lecture?</h2>
</section>

<section>
<h2 class="bbt">Historic hero: AlphaGo</h2>
<img class="wm fr mlm" src="img/go.jpg" />
<p>It is an artificial intelligence developed by Google DeepMind for playing to Go</p>
<p class="fragment">Before 2015: several software have been developed to play to Go automatically, but all of them showed their limits when tested with human expert players of the game - in fact, no Go software was able to beat a human master</p>
<p class="fragment">In 2015: Google declared to have developed the best artificial intelligence for playing to Go, and asked to test it in international matches against the strongest Go players</p>
</section>

<section>
<h2>AlphaGo vs. Fan Hui</h2>
<img class="wm fr mlm" src="img/fanhui.jpg" />
<p>Match in October 2015, best of five games</p>
<p class="fragment">Fan Hui was the champion of the European Go Championship in 2013, 2014 and 2015 (professional 2 dan player)</p>
<p class="fragment">Result: 5 - 0</p>
</section>

<section>
<h2>AlphaGo vs. Lee Sedol</h2>
<img class="wm fr mlm" src="img/leesedol.jpg" />
<p>Match in March 2016, best of five games</p>
<p class="fragment">In 2016, Lee Sedol was ranked second in international titles (professional 9 dan player, max rank)</p>
<p class="fragment">Result: 4 - 1</p>
</section>

<section>
<h2>AlphaGo vs. Ke Jie</h2>
<img class="wm fr mlm" src="img/kejie.png" />
<p>Match in May 2017, best of three games</p>
<p class="fragment">In 2017, Ke Jie was ranked number one in the world (professional 9 dan player, max rank)</p>
<p class="fragment">Result: 3 - 0</p>
</section>

<section>
<h2>AlphaGo Zero vs. AlphaGo</h2>
<img class="wm fr mlm" src="img/alphago.png" />
<p>Match in October 2017, best of one hundred games</p>
<p class="fragment">AlphaGo Zero has been trained without using any existing human knowledge – i.e. the matches between human champions that have been archived in the past, that have been actually used for training AlphaGo</p>
<p class="fragment">Result: 100 - 0</p>
</section>

<section>
<h2>Backtracking</h2>
<p>Algorithms for finding a solution to abstract strategy board games are based on a tree (node = possible move)</p>
<p class="fragment">Backtracking algorithms find a solution by <span class="fragment highlight-red">identifying possible candidates incrementally</span>, and <span class="fragment highlight-red">abandons partial candidates</span> if they won't provide a solution</p>
<ol class="st">
<li class="fragment"><p><strong>[leaf-win]</strong> if current node is a leaf and it is a solution then return it, otherwise</p></li>
<li class="fragment"><p><strong>[leaf-lose]</strong> if current node is a leaf but it is not a solution, then return no solution back the parent node, otherwise</p></li>
<li class="fragment"><p><strong>[recursive-step]</strong> apply recursively the whole approach for each child of the current node, until one of these recursive executions returns a solution - if no solution, return no solution back the parent node</p></li>
</ol>
</section>

<section>
<h2>Peg solitaire</h2>
<p>It is a board game for one person only which involves the movement of some pegs on board containing holes</p>
<p class="tc"><img class="wl" src="img/peg.png" /></p>
<p class="fragment">Starting situation: the entire board is filled up with pegs except the central position which is empty</p>
<p class="fragment">Goal: whole board is full of holes except the central position which must contain a peg</p>
</section>

<section>
<h2>Moves</h2>
<p>Valid move: moving orthogonally a peg over an adjacent peg into a hole two position away, removing the jumped peg from the board</p>
<p class="tc"><img class="wl" src="img/move.png" /></p>
<p class="fragment">Computational problem: find a sequence of moves that allows one to solve the peg solitaire</p>
</section>

<section>
<h2>Descriptive solution</h2>
<ol>
<li><p><strong>[leaf-win]</strong> if last move brought to only one peg in the board in central position, then a solution has been found and return it, otherwise</li>
<li class="fragment"><p><strong>[leaf-lose]</strong> if last move brought to a situation where no additional moves are possible, then recreate previous status of the board and return no solutions, otherwise</p></li>
<li class="fragment"><p><strong>[recursive-step]</strong> apply recursively the algorithm for each possible valid move executable according to the current status of the board, until one of these recursive executions of the algorithm returns a solution – if none of them provide a solution, recreate the previous status of the board and return no solutions</p></li>
</ol>
</section>

<section>
<section data-transition="slide-in fade-out">
<h2>Algorithm: execution</h2>
<p class="tc"><img class="hl" src="img/move-tree-01.png" /></p>
</section>
<section data-transition="fade-in">
<h2>Algorithm: execution</h2>
<p class="tc"><img class="hl" src="img/move-tree-02.png" /></p>
</section>
<section data-transition="fade-in">
<h2>Algorithm: execution</h2>
<p class="tc"><img class="hl" src="img/move-tree-03.png" /></p>
</section>
<section data-transition="fade-in">
<h2>Algorithm: execution</h2>
<p class="tc"><img class="hl" src="img/move-tree-04.png" /></p>
</section>
<section data-transition="fade-in">
<h2>Algorithm: execution</h2>
<p class="tc"><img class="hl" src="img/move-tree-05.png" /></p>
</section>
</section>

<section>
<h2>6x6 square board</h2>
<p>This board is the smallest square board on which the complement problem can be solved</p>
<p>Complement problem: obtaining the complement of a given an initial configuration of a board by replacing every peg by a hole and vice versa</p>
<p class="tc"><img class="wl" src="img/6x6-square-board.png" /></p>
</section>

<section>
<h2>How to represent the board</h2>
<pre class="tc"> (1,0) (4,0) &nbsp;
(0,1) (1,1) (2,1) (3,1) (4,1) (5,1)
(1,2) (4,2)
(1,3) (4,3)
(0,4) (1,4) (2,4) (3,4) (4,4) (5,4)
(1,5) (4,5) ​</pre>
<p class="fragment">Two sets of tuples:</p>
<ul>
<li class="fragment"><p><code>pegs</code>: the set of the positions occupied by pegs - starting situation: all position but <code>(5,1)</code></p></li>
<li class="fragment"><p><code>holes</code>: the set of the positions with no pegs - starting situation: only <code>(5,1)</code></p></li>
</ul>
</section>

<section>
<h2>Ancillary functions</h2>
<p><code>def valid_moves(pegs, holes)</code>: it returns a list of tree nodes, where each node represent a possible move that one can execute according to the current status of the board (defined by the two input sets <code>pegs</code> and <code>holes</code>)</p>
<p class="fragment"><code>def apply_move(node, pegs, holes)</code>: execute the move defined by the input node, and change the status of the board accordingly</p>
<p class="fragment"><code>def undo_move(node, pegs, holes)</code>: undo the move defined by the input node, and change the status of the board accordingly</p>
</section>

<section>
<h2>The algorithm</h2>
<pre><code class="python">def solve(pegs, holes, last_move):
result = None
if len(pegs) == 1 and (5, 1) in pegs: # leaf-win base case
result = last_move
else:
last_move.children = valid_moves(pegs, holes)
if len(last_move.children) == 0: # leaf-lose base case
undo_move(last_move, pegs, holes) # backtracking
else: # recursive step
possible_moves = deque(last_move.children)
while result is None and len(possible_moves) > 0:
current_move = possible_moves.pop()
apply_move(current_move, pegs, holes)
result = solve(pegs, holes, current_move)
if result is None:
undo_move(last_move, pegs, holes) # backtracking
return result</code></pre>
<p class="fragment">First execution:<br/><code class="st">solve(initial_pegs, initial_holes, Node("start"))</code></p>
</section>

<section class="title_slide">
<h2>
END
<span class="subtitle">Backtracking algorithms</span>
</h2>
<div class="author">
<p><a href="https://www.unibo.it/sitoweb/silvio.peroni/en">Silvio Peroni</a></p>
<p class="contact">
<i class="fa fa-envelope" aria-hidden="true"></i> <a href="mailto:[email protected]">[email protected]</a>
<i class="ai ai-orcid" aria-hidden="true"></i> <a href="https://orcid.org/0000-0003-0530-4305">0000-0003-0530-4305</a>
<i class="fa fa-twitter" aria-hidden="true"></i> <a href="https://twitter.com/essepuntato">@essepuntato</a>
</p>
<p class="sst mtl"><a href="https://www.unibo.it/en/teaching/course-unit-catalogue/course-unit/2024/467045">Computational Thinking and Programming (A.Y. 2024/2025)</a></p>
<p class="ssst"><a href="https://corsi.unibo.it/2cycle/DigitalHumanitiesKnowledge">Second Cycle Degree in Digital Humanities and Digital Knowledge</a></p>
<p class="ssst"><a href="http://www.unibo.it/en">Alma Mater Studiorum - Università di Bologna</a></p>
</div>
</section>
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