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Zobrist Hashing è una funzione di hashing ampiamente utilizzata nei giochi da tavolo a 2 giocatori. È la funzione di hashing più comune utilizzata nella tabella di trasposizione. Le tabelle di trasposizione memorizzano fondamentalmente i valori valutati dei precedenti stati della scheda in modo che, se si verificano nuovamente, recuperiamo semplicemente il valore memorizzato dalla tabella di trasposizione. Tratteremo le tabelle di recepimento in un articolo successivo. In questo articolo prenderemo l'esempio della scacchiera e implementeremo una funzione di hashing per questo.
Pseudocodice:
// A matrix with random numbers initialized once Table[#ofBoardCells][#ofPieces] // Returns Zobrist hash function for current conf- // iguration of board. function findhash(board): hash = 0 for each cell on the board : if cell is not empty : piece = board[cell] hash ^= table[cell][piece] return hash
Spiegazione:
L'idea alla base di Zobrist Hashing è che per un dato stato della scacchiera, se c'è un pezzo su una determinata cella, utilizziamo il numero casuale di quel pezzo dalla cella corrispondente nella tabella.
Se nel numero casuale sono presenti più bit, minore è la possibilità di una collisione di hash. Pertanto i numeri a 64 bit vengono comunemente utilizzati come standard ed è altamente improbabile che si verifichi una collisione di hash con numeri così grandi. La tabella deve essere inizializzata una sola volta durante l'esecuzione del programma.
Anche il motivo per cui Zobrist Hashing è ampiamente utilizzato nei giochi da tavolo è perché quando un giocatore effettua una mossa non è necessario ricalcolare da zero il valore dell'hash. A causa della natura dell'operazione XOR possiamo semplicemente utilizzare poche operazioni XOR per ricalcolare il valore hash.
Attuazione:
Cercheremo di trovare un valore hash per la configurazione della scheda data.
// A program to illustrate Zobrist Hashing Algorithm #include
// A Java program to illustrate Zobrist Hashing Algorithm import java.util.*; public class GFG { public static List<List<List<Integer>>> ZobristTable = new ArrayList<>(); // mt19937 mt(01234567); public static void initialise() { for (int i = 0; i < 8; i++) { ZobristTable.add(new ArrayList<>()); for (int j = 0; j < 8; j++) { ZobristTable.get(i).add(new ArrayList<>()); for (int k = 0; k < 12; k++) { ZobristTable.get(i).get(j).add(0); } } } } // Generates a Random number from 0 to 2^64-1 public static long randomLong() { long min = 0L; long max = (long) Math.pow(2 64); Random rnd = new Random(); return rnd.nextLong() * (max - min) + min; } // This function associates each piece with a number public static int indexOf(char piece) { if (piece=='P') return 0; if (piece=='N') return 1; if (piece=='B') return 2; if (piece=='R') return 3; if (piece=='Q') return 4; if (piece=='K') return 5; if (piece=='p') return 6; if (piece=='n') return 7; if (piece=='b') return 8; if (piece=='r') return 9; if (piece=='q') return 10; if (piece=='k') return 11; else return -1; } // Initializes the table public static void initTable() { for (int i = 0; i < 8; i++) { for (int j = 0; j < 8; j++) { for (int k = 0; k < 12; k++) { Random rnd = new Random(); ZobristTable.get(i).get(j).set(k (int) randomLong()); } } } } // Computes the hash value of a given board public static int computeHash(List<List<Character>> board) { int h = 0; for (int i = 0; i < 8; i++) { for (int j = 0; j < 8; j++) { if (board.get(i).get(j) != '-') { int piece = indexOf(board.get(i).get(j)); h ^= ZobristTable.get(i).get(j).get(piece); } } } return h; } public static void main(String[] args) { // Main Function // Uppercase letters are white pieces // Lowercase letters are black pieces List<List<Character>> board = new ArrayList<>(); board.add(new ArrayList<>(Arrays.asList('-' '-' '-' 'K' '-' '-' '-' '-'))); board.add(new ArrayList<>(Arrays.asList('-' 'R' '-' '-' '-' '-' 'Q' '-'))); board.add(new ArrayList<>(Arrays.asList('-' '-' '-' 'K' '-' '-' '-' '-'))); board.add(new ArrayList<>(Arrays.asList('-' '-' '-' '-' '-' '-' '-' '-'))); board.add(new ArrayList<>(Arrays.asList('-' 'P' '-' '-' '-' '-' 'p' '-'))); board.add(new ArrayList<>(Arrays.asList('-' '-' '-' '-' '-' 'p' '-' '-'))); board.add(new ArrayList<>(Arrays.asList('-' '-' '-' '-' '-' '-' '-' '-'))); board.add(new ArrayList<>(Arrays.asList('p' '-' '-' '-' 'b' '-' '-' 'q'))); board.add(new ArrayList<>(Arrays.asList('-' '-' '-' '-' 'n' '-' '-' 'k'))); initialise(); initTable(); int hashValue = computeHash(board); System.out.println('The hash value is : ' + hashValue); // Move the white king to the left char piece = board.get(0).get(3); board.get(0).set(3 '-'); hashValue ^= ZobristTable.get(0).get(3).get(indexOf(piece)); board.get(0).set(2 piece); hashValue ^= ZobristTable.get(0).get(2).get(indexOf(piece)); System.out.println('The new hash value is : ' + hashValue); // Undo the white king move piece = board.get(0).get(2); board.get(0).set(2 '-'); hashValue ^= ZobristTable.get(0).get(2).get(indexOf(piece)); board.get(0).set(3 piece); hashValue ^= ZobristTable.get(0).get(3).get(indexOf(piece)); System.out.println('The new hash value is : ' + hashValue); } } // This code is contributed by Vaibhav
# A program to illustrate Zobrist Hashing Algorithm # python code implementation import random # mt19937 mt(01234567); # Generates a Random number from 0 to 2^64-1 def randomInt(): min = 0 max = pow(2 64) return random.randint(min max) # This function associates each piece with # a number def indexOf(piece): if (piece=='P'): return 0 elif (piece=='N'): return 1 elif (piece=='B'): return 2 elif (piece=='R'): return 3 elif (piece=='Q'): return 4 elif (piece=='K'): return 5 elif (piece=='p'): return 6 elif (piece=='n'): return 7 elif (piece=='b'): return 8 elif (piece=='r'): return 9 elif (piece=='q'): return 10 elif (piece=='k'): return 11 else: return -1 # Initializes the table def initTable(): # 8x8x12 array ZobristTable = [[[randomInt() for k in range(12)] for j in range(8)] for i in range(8)] return ZobristTable # Computes the hash value of a given board def computeHash(board ZobristTable): h = 0 for i in range(8): for j in range(8): if (board[i][j] != '-'): piece = indexOf(board[i][j]) h ^= ZobristTable[i][j][piece] return h # Main Function # Uppercase letters are white pieces # Lowercase letters are black pieces board = [ '---K----' '-R----Q-' '--------' '-P----p-' '-----p--' '--------' 'p---b--q' '----n--k' ] ZobristTable = initTable() hashValue = computeHash(board ZobristTable) print('The hash value is : ' + str(hashValue)) #Move the white king to the left piece = board[0][3] board[0] = list(board[0]) board[0][3] = '-' board[0] = ''.join(board[0]) hashValue ^= ZobristTable[0][3][indexOf(piece)] board[0] = list(board[0]) board[0][2] = piece board[0] = ''.join(board[0]) hashValue ^= ZobristTable[0][2][indexOf(piece)] print('The new hash value is : ' + str(hashValue)) # Undo the white king move piece = board[0][2] board[0] = list(board[0]) board[0][2] = '-' board[0] = ''.join(board[0]) hashValue ^= ZobristTable[0][2][indexOf(piece)] board[0] = list(board[0]) board[0][3] = piece board[0] = ''.join(board[0]) hashValue ^= ZobristTable[0][3][indexOf(piece)] print('The old hash value is : ' + str(hashValue))
using System; using System.Collections; using System.Collections.Generic; using System.Linq; // C# program for the above approach // A program to illustrate Zobrist Hashing Algorithm // javascript code implementation class HelloWorld { public static List<List<List<int>>> ZobristTable = new List<List<List<int>>>(); // mt19937 mt(01234567); public static void initialise(){ for(int i = 0; i < 8; i++){ ZobristTable.Add(new List<List<int>>()); for(int j = 0; j < 8; j++){ ZobristTable[i].Add(new List<int>()); for(int k = 0; k < 12; k++){ ZobristTable[i][j].Add(0); } } } } // Generates a Random number from 0 to 2^64-1 public static int randomInt() { int min = 0; int max = (int)Math.Pow(2 64); Random rnd = new Random(); return rnd.Next() * (max - min) + min; } // This function associates each piece with // a number public static int indexOf(char piece) { if (piece=='P') return 0; if (piece=='N') return 1; if (piece=='B') return 2; if (piece=='R') return 3; if (piece=='Q') return 4; if (piece=='K') return 5; if (piece=='p') return 6; if (piece=='n') return 7; if (piece=='b') return 8; if (piece=='r') return 9; if (piece=='q') return 10; if (piece=='k') return 11; else return -1; } // Initializes the table public static void initTable() { for (int i = 0; i<8; i++){ for(int j = 0; j < 8; j++){ for(int k = 0; k < 12; k++){ Random rnd = new Random(); ZobristTable[i][j][k] = rnd.Next(); } } } } // Computes the hash value of a given board public static int computeHash(List<List<char>> board) { int h = 0; for (int i = 0; i<8; i++) { for (int j = 0; j<8; j++) { if (board[i][j]!='-') { int piece = indexOf(board[i][j]); h ^= ZobristTable[i][j][piece]; } } } return h; } static void Main() { // Main Function // Uppercase letters are white pieces // Lowercase letters are black pieces List<List<char>> board = new List<List<char>>(); board.Add(new List<char>(){'-' '-' '-' 'K' '-' '-' '-' '-'}); board.Add(new List<char>(){'-' 'R' '-' '-' '-' '-' 'Q' '-'}); board.Add(new List<char>(){'-' '-' '-' 'K' '-' '-' '-' '-'}); board.Add(new List<char>(){'-' '-' '-' '-' '-' '-' '-' '-'}); board.Add(new List<char>(){'-' 'P' '-' '-' '-' '-' 'p' '-'}); board.Add(new List<char>(){'-' '-' '-' '-' '-' 'p' '-' '-' }); board.Add(new List<char>(){'-' '-' '-' '-' '-' '-' '-' '-'}); board.Add(new List<char>(){'p' '-' '-' '-' 'b' '-' '-' 'q'}); board.Add(new List<char>(){'-' '-' '-' '-' 'n' '-' '-' 'k'}); initialise(); initTable(); int hashValue = computeHash(board); Console.WriteLine('The hash value is : ' + hashValue); //Move the white king to the left char piece = board[0][3]; board[0][3] = '-'; hashValue ^= ZobristTable[0][3][indexOf(piece)]; board[0][2] = piece; hashValue ^= ZobristTable[0][2][indexOf(piece)]; Console.WriteLine('The new hash value is : ' + hashValue); // Undo the white king move piece = board[0][2]; board[0][2] = '-'; hashValue ^= ZobristTable[0][2][indexOf(piece)]; board[0][3] = piece; hashValue ^= ZobristTable[0][3][indexOf(piece)]; Console.WriteLine('The old hash value is : ' + hashValue); } } // The code is contributed by Nidhi goel.
// A program to illustrate Zobrist Hashing Algorithm // javascript code implementation let ZobristTable = new Array(8); for(let i = 0; i < 8; i++){ ZobristTable[i] = new Array(8); } for(let i = 0; i < 8; i++){ for(let j = 0; j < 8; j++){ ZobristTable[i][j] = new Array(12); } } // mt19937 mt(01234567); // Generates a Random number from 0 to 2^64-1 function randomInt() { let min = 0; let max = Math.pow(2 64); return Math.floor(Math.random() * (max - min) + min); } // This function associates each piece with // a number function indexOf(piece) { if (piece=='P') return 0; if (piece=='N') return 1; if (piece=='B') return 2; if (piece=='R') return 3; if (piece=='Q') return 4; if (piece=='K') return 5; if (piece=='p') return 6; if (piece=='n') return 7; if (piece=='b') return 8; if (piece=='r') return 9; if (piece=='q') return 10; if (piece=='k') return 11; else return -1; } // Initializes the table function initTable() { for (let i = 0; i<8; i++) for (let j = 0; j<8; j++) for (let k = 0; k<12; k++){ ZobristTable[i][j][k] = randomInt(); } } // Computes the hash value of a given board function computeHash(board) { let h = 0; for (let i = 0; i<8; i++) { for (let j = 0; j<8; j++) { if (board[i][j]!='-') { let piece = indexOf(board[i][j]); h ^= ZobristTable[i][j][piece]; } } } return h; } // Main Function // Uppercase letters are white pieces // Lowercase letters are black pieces let board = [ '---K----' '-R----Q-' '--------' '-P----p-' '-----p--' '--------' 'p---b--q' '----n--k' ]; initTable(); let hashValue = computeHash(board); console.log('The hash value is : ' + hashValue); //Move the white king to the left let piece = board[0][3]; board[0] = board[0].split(''); board[0][3] = '-'; board[0] = board[0].join(''); hashValue ^= ZobristTable[0][3][indexOf(piece)]; board[0] = board[0].split(''); board[0][2] = piece; board[0] = board[0].join(''); hashValue ^= ZobristTable[0][2][indexOf(piece)]; console.log('The new hash value is : ' + hashValue); // Undo the white king move piece = board[0][2]; board[0] = board[0].split(''); board[0][2] = '-'; board[0] = board[0].join(''); hashValue ^= ZobristTable[0][2][indexOf(piece)]; board[0][3] = piece; hashValue ^= ZobristTable[0][3][indexOf(piece)]; console.log('The old hash value is : ' + hashValue); // The code is contributed by Nidhi goel.
Produzione :
The hash value is : 14226429382419125366 The new hash value is : 15124945578233295113 The old hash value is : 14226429382419125366