Computing Science (CMPUT) 496

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1 Computing Science (CMPUT) 496 Search, Knowledge, and Simulations Martin Müller Department of Computing Science University of Alberta Winter 2017

2 Part I Intro - Problem Solving for humans and computers

3 496 Today - Jan 12 Topics: Eyes and Life in Go Basic data structures and algorithms for Go Programs Tools for Go programming: GoGui, attaching Go programs, GTP text interface Why talk about Go in the Problem-solving topic? I am doing this early for two reasons: You need it for Assignment 1 For many of the (general purpose) algorithms throughout the course, we will use Go as example

4 About Python Code for Go and Assignment 1 I start using Python 3 code as example today So far, examples are only on slides Source code not released yet I want to do a final check for quality and consistency this weekend You will get the code for our Go1 program I will announce it when ready Plays random moves, but does not fill one point eyes This is also the code you will modify for Assignment 1 (Random NoGo Player)

playing, and even very strong stones keep dying Games would last VERY long, and result

5 What are Eyes and Why are they Useful? End of last class, we saw a problem with a true random player It keeps playing and playing, and even very strong stones keep dying Games would last VERY long, and result would have no meaning Solution: remove some of the most stupid moves, to make sure the game ends in reasonable time We remove so-called eye-filling moves

6 Eyes and Capturing An eye is a point that is surrounded by one color For the opponent: (illegal) suicide to play there... (A, B, C in top picture)...unless that point is the last liberty of the surrounding stones (bottom picture) - then it becomes a (legal) capture

Two Eyes are Safe Here, Black has one block surrounding two eyes A and B White cannot attack, both A and B are suicide Black is safe as long as Black leaves

7 Two Eyes are Safe Here, Black has one block surrounding two eyes A and B White cannot attack, both A and B are suicide Black is safe as long as Black leaves the eyes alone Remember you can always pass, no need to hurt your own stones Black should NEVER play A or B If Black fills second-last eye then White can capture

8 What is an Eye? Simple definition used here There are other kinds of eyes (later) 1 Single empty point 2 All neighbors occupied by stones of the same color 3 All these stones are connected Examples: eye in corner, edge of board, and center

Detecting Eyes Locally Most simple eyes can be detected locally Only look at neighbors and diagonals Corner, edge: need all (1 or 2) diagonals to connect Center: need at

9 Detecting Eyes Locally Most simple eyes can be detected locally Only look at neighbors and diagonals Corner, edge: need all (1 or 2) diagonals to connect Center: need at least 3 of 4 diagonals In principle, can connect along some longer path Pretty rare, ignore in program for now Example: A7 eye Stones A6 and B7 connected over a long path

10 Simple Eyes - Summary Random player keeps playing senselessly......unless we stop it from filling its eyes An eye is an empty point, surrounded by a connected block of stones A simple local definition of eye is good enough for now Very fast to check in program, only look at 8 neighbors and diagonals (at most) Having two (or more) eyes makes a block safe from capture Next topic: implementing Go board and rules

11 Implementing a Go Board and Go Rules Representing the board Updating the board after a move Recognize capture Checking for legal moves Recognize suicide and repetition (simple ko)

12 Why Bother with an Efficient Board Representation? Most game programs are based on search and simulation Billions of moves played and taken back during a game Playing strength strongly depends on amount of search So, make it as fast as possible Our first Python codes may be times slower than state of the art Mostly, that is due to algorithms and data structures, not Python...

13 Representing State of a Point Three possible states: empty, black or white We could use the new-ish Python 3 enumeration type https: //docs.python.org/3/library/enum.html class BoardColor(Enum): EMPTY = 0 BLACK = 1 WHITE = 2 In current program we just use integer codes for colors EMPTY = 0 BLACK = 1 WHITE = 2

14 Representing the Go Board - 2d Array MAXSIZE = 7 board = [[EMPTY for x in range(maxsize)] for y in range(maxsize)] print(board) board[3][4] = BLACK print(board) Most direct representation: 2-dimensional array Store a point on the board at coordinates [x][y] in array

15 Drawbacks of Two-dimensional Array Overhead from 2-d address calculation Need two variables (x, y) to represent a single point Often need two computations, for x, y separately Complex checking for boundary cases if x > 0 and y > 0 and x <= MAXSIZE and y <= MAXSIZE if statements introduce conditional branches and slow down execution

16 Go Board as One-dimensional Array Solution: use a simple 1-dimensional array From (x,y) to single index p = x + y * MAXSIZE Back from p to x, y by integer division and modulo operators x = p % MAXSIZE y = p // MAXSIZE Can also precompute the calculations Lookup tables, e.g. x = xcoord[p] Frequent operations use simple offset, constant time Go to neighbors and diagonals Check if on border, or has neighbor Many more..

17 Drawbacks of Simple One-dimensional Array Edges of board still needs special case treatment (lots of if statements) Index 6 and 7 are not neighbors... There is no neighbor upwards from 4... Similar for bottom edge

18 Solution: Add Padding Image source: gnugo/gnugo_15.html Solution: add extra padding Above board Below board Between rows For these points, store a new code "off the board" BORDER = 3 Many special edge cases can be avoided by only checking the content of the point

19 Summary and Comments for Board Representation Standard way for Go uses 1-d board with extra padding Other special purpose representations are possible: Bitsets, one set per color List of stones Cover board with small patterns, e.g. 3 3 squares Will use this as simple features later Optional - to learn more: see e.g. Board+Representation for detailed discussions for chess Next: Playing and Undoing moves

20 Playing and Undoing Moves play(p, color) Put stone of given color on point p Simplest case: just need board[p] = color Major complication: recognize captures and remove captured stones Closely related: check if move on p is legal, before playing it...

21 Capturing Stones How to find which opponent stones are captured? Black move A captures one stone Black move B does not capture anything... To decide whether B is a capture, we must look at the neighbors of the whole block We must find the liberty at C to decide it s no capture Update board: for stone in capturedby(p, color) board[stone] = EMPTY

Capturing Stones Algorithm How to find which opponent stones are

similar to floodfill in graphics Look at all stones connected to

22 Capturing Stones Algorithm How to find which opponent stones are captured? Look at all neighbors nb of p which are stones of opponent Check if nb is part of a block that loses its last liberty Algorithm is similar to floodfill in graphics Look at all stones connected to nb If any stone has a liberty (other than p), stop: no capture If no stone in the block has another liberty, then all are captured

23 Checking If Move is Legal islegal(p, color): 1 board[p] == EMPTY 2 not issuicide(p, color) 3 not repetition(p, color)

24 Checking Suicide Very similar to checking capture for the other color Main difference: the move can connect several blocks, and none of them may have another liberty See examples: Black A is suicide, Black B is not because liberty at C

move: set kopoint = NULL When checking islegal(p, color): if

25 Checking Repetition For now, only check for simple ko After capture of a single stone s: set kopoint = s After any other move: set kopoint = NULL When checking islegal(p, color): if p == kopoint and p would capture a single stone : p is illegal

26 Software Demo GoGui Attaching different Go programs Tools that come with GoGui GTP text commands

27 Summary and Outlook Discussed most of the basics of implementing Go Still to come: scoring at the end, taking back moves during search Discussed useful tools and GTP text interface

1010 Moves A move in Go is the action of a player to place his stone on a vacant intersection of the board.

1010 Moves A move in Go is the action of a player to place his stone on a vacant intersection of the board. Chapter 2 Basic Concepts 1000 Basic Concepts As for the rules, what was explained in the last chapter was concise enough. You will be able to start playing a game and learn more as you experience many