KR-IST - Lecture 5b Game play in Java

Introduction

The implementation makes use of `negmax' evaluation but does not use alpha-beta pruning.

Step-by-step guide for writing a search program

1. Informally characterise states, goals and transitions.

2. Choose a representation for states.

3. Sketch out a method for generating successors. (Go back to step 2 if this is difficult.)

4. Write Java code to implement the successor method. (Go back to step 2 if this is difficult.)

5. Write code for the main search loop (i.e., procesing of nodes on OPEN).

6. Add everything else.

Node class

  import java.util.*;

  class Node {
     int state[] = new int[9];
     int evaluation = -1;
     Node parent = null;

     Node(int s[], Node parent) {
        for (int i = 0; i < 9; i++) state[i] = s[i];
        this.parent = parent;
     }

     public String toString() {
        String s = "";
        for (int i = 0; i < 9; i++) s = s + state[i] + " ";
        return s;
     }

Node class cont.

     int[] getStateCopy() {
        int[] s = state, copy = {s[0], s[1], s[2], s[3],
                s[4], s[5], s[6], s[7], s[8]};
        return copy;
     }

     Vector<Node> getPath(Vector<Node> v) {
        v.insertElementAt(this, 0);
        if (parent != null) v = parent.getPath(v);
        return v;
     }

     Vector<Node> getPath() { return(getPath(new Vector<Node>())); }
  }

NoughtsAndCrossesSpace class

  class NoughtsAndCrossesSpace {

     Node getRoot() {
        int state[] = {0, 0, 0, 0, 0, 0, 0, 0, 0};
        return new Node(state, null);
     }

     Vector<Node> getSuccessors(Node parent, int player) {
        Vector<Node> successors = new Vector<Node>();
        for (int r = 0; r < 3; r++) {
           for (int c = 0; c < 3; c++) {
              if (parent.state[(r * 3) + c] == 0) { /* empty cell here */
                 int state[] = parent.getStateCopy();
                 state[(r * 3) + c] = player;
                 successors.add(new Node(state, parent)); }
           }
        }
        return successors;
     }
  }

Search space

  public class NoughtsAndCrossesSearch {
     NoughtsAndCrossesSpace space = new NoughtsAndCrossesSpace();

     String name(int player) {
        String s = "_";
        if (player == 1) {
           s = "X"; }
        else if (player == -1) {
           s = "O"; }
        return s;
     }

     void pr(String s) {
        System.out.println(s);
     }

     void printState(Node node) { /* print board state */
        System.out.println("\n");
        for (int r = 0; r < 3; r++) {
           for (int c = 0; c < 3; c++) {
              int player = node.state[(r * 3) + c];
              pr(" " + name(player)); }
           pr("\n"); }
        pr("\n");
     }

Static evaluation

  /** decide whether board state s is won for player p */
  boolean wonFor(int s[], int p) {
     boolean b = (s[0] == p && s[1] == p && s[2] == p)
     || (s[3] == p && s[4] == p && s[5] == p)
     || (s[6] == p && s[7] == p && s[8] == p)
     || (s[0] == p && s[3] == p && s[6] == p)
     || (s[1] == p && s[4] == p && s[7] == p)
     || (s[2] == p && s[5] == p && s[8] == p)
     || (s[0] == p && s[4] == p && s[8] == p)
     || (s[2] == p && s[4] == p && s[6] == p);
     return b;
  }

  int winnerOf(int state[]) {
     int player = 0;
     if (wonFor(state, 1)) {
        player = 1; }
     else if (wonFor(state, -1)) {
        player = -1; }
     return player;
  }

Dynamic evaluation

  int evaluate(Node node, int player) { /* using NEGMAX */
     int value = 0;
     if (wonFor(node.state, player)) {
        value = 1; }
     else if (wonFor(node.state, -player)) {
        value = -1; }
     else {
        Vector<Node> successors = space.getSuccessors(node, -player);
        if (successors.size() == 0) { /* draw */
           value = 0; }
        else {
           for (int i = 0; i < successors.size(); i++) {
              Node successor = successors.get(i);
              successor.evaluation = evaluate(successor, -player);
              if (successor.evaluation > value) {
                 value = successor.evaluation; } }
           value = -value; } }
     return(value);
  }

Main loop

  void run() {
     int p, player = 1;
     Node node = space.getRoot();
     Vector<Node> bestNodes = new Vector<Node>();
     printState(node);
     while ((p = winnerOf(node.state)) == 0) { /* while no winner */
        Vector<Node> successors = space.getSuccessors(node, player);
        int maxValue = -Integer.MAX_VALUE;
        bestNodes.clear();
        for (int i = 0; i < successors.size(); i++) {
           Node newNode = successors.get(i);
           int value = evaluate(newNode, player);
           if (value == maxValue || player == -1) {
              bestNodes.add(newNode); } /* ensure random opponent */
           else if (value > maxValue) {
              bestNodes.clear();
              bestNodes.add(newNode);
              maxValue = value; } }

Main loop cont.

           if (successors.size() == 0) { /* game drawn */
              break; }
           else {
              pr("State after new " + name(player) + " (" + player + ")");
              int randomIndex = (int)(Math.random() * bestNodes.size());
              node = bestNodes.get(randomIndex);
              printState(node);
              player = -player; }
        }
        pr(p == 0 ? "DRAW" : "GAME WON FOR " + name(p) + "\n\n");
     }

     public static void main(String args[]) { // do the search
        new NoughtsAndCrossesSearch().run();
     }
  }

Simulated game

  Initial node: (X never errs, 0 plays randomly)
   _ _ _
   _ _ _
   _ _ _

  State after new X (1)
   _ _ _
   X _ _
   _ _ _

  State after new O (-1)
   _ _ _
   X _ _
   O _ _

Cont.

  State after new X (1)
   _ X _
   X _ _
   O _ _

  State after new O (-1)
   _ X _
   X _ _
   O O _

  State after new X (1)
   _ X _
   X _ _
   O O X

Underlying evaluations for prev move

  Evaluations
  |-- 0 for O -1 1 0 1 0 0 -1 -1 1
  |   |-- 0 for X -1 1 1 1 0 0 -1 -1 1
  |   |   |-- -1 for O -1 1 1 1 -1 0 -1 -1 1
  |   |   |   |-- 1 for X -1 1 1 1 -1 1 -1 -1 1
  |   |   |-- 0 for O -1 1 1 1 0 -1 -1 -1 1
  |   |       |-- 0 for X -1 1 1 1 1 -1 -1 -1 1
  |   |-- 0 for X -1 1 0 1 1 0 -1 -1 1
  |   |   |-- -1 for O -1 1 -1 1 1 0 -1 -1 1
  |   |   |   |-- 1 for X -1 1 -1 1 1 1 -1 -1 1
  |   |   |-- 0 for O -1 1 0 1 1 -1 -1 -1 1
  |   |       |-- 0 for X -1 1 1 1 1 -1 -1 -1 1
  |   |-- 0 for X -1 1 0 1 0 1 -1 -1 1
  |       |-- -1 for O -1 1 -1 1 0 1 -1 -1 1
  |       |   |-- 1 for X -1 1 -1 1 1 1 -1 -1 1
  |       |-- -1 for O -1 1 0 1 -1 1 -1 -1 1
  |           |-- 1 for X -1 1 1 1 -1 1 -1 -1 1

Evaluations cont.

  |-- 0 for O 0 1 -1 1 0 0 -1 -1 1
  |   |-- -1 for X 1 1 -1 1 0 0 -1 -1 1
  |   |   |-- 1 for O 1 1 -1 1 -1 0 -1 -1 1
  |   |   |-- -1 for O 1 1 -1 1 0 -1 -1 -1 1
  |   |       |-- 1 for X 1 1 -1 1 1 -1 -1 -1 1
  |   |-- 0 for X 0 1 -1 1 1 0 -1 -1 1
  |   |   |-- -1 for O -1 1 -1 1 1 0 -1 -1 1
  |   |   |   |-- 1 for X -1 1 -1 1 1 1 -1 -1 1
  |   |   |-- -1 for O 0 1 -1 1 1 -1 -1 -1 1
  |   |       |-- 1 for X 1 1 -1 1 1 -1 -1 -1 1
  |   |-- -1 for X 0 1 -1 1 0 1 -1 -1 1
  |       |-- -1 for O -1 1 -1 1 0 1 -1 -1 1
  |       |   |-- 1 for X -1 1 -1 1 1 1 -1 -1 1
  |       |-- 1 for O 0 1 -1 1 -1 1 -1 -1 1

Evaluations cont.

  |-- 0 for O 0 1 0 1 -1 0 -1 -1 1
  |   |-- -1 for X 1 1 0 1 -1 0 -1 -1 1
  |   |   |-- 1 for O 1 1 -1 1 -1 0 -1 -1 1
  |   |   |-- -1 for O 1 1 0 1 -1 -1 -1 -1 1
  |   |       |-- 1 for X 1 1 1 1 -1 -1 -1 -1 1
  |   |-- 0 for X 0 1 1 1 -1 0 -1 -1 1
  |   |   |-- -1 for O -1 1 1 1 -1 0 -1 -1 1
  |   |   |   |-- 1 for X -1 1 1 1 -1 1 -1 -1 1
  |   |   |-- -1 for O 0 1 1 1 -1 -1 -1 -1 1
  |   |       |-- 1 for X 1 1 1 1 -1 -1 -1 -1 1
  |   |-- -1 for X 0 1 0 1 -1 1 -1 -1 1
  |       |-- -1 for O -1 1 0 1 -1 1 -1 -1 1
  |       |   |-- 1 for X -1 1 1 1 -1 1 -1 -1 1
  |       |-- 1 for O 0 1 -1 1 -1 1 -1 -1 1

Evaluations cont.

  |-- 0 for O 0 1 0 1 0 -1 -1 -1 1
      |-- 0 for X 1 1 0 1 0 -1 -1 -1 1
      |   |-- -1 for O 1 1 -1 1 0 -1 -1 -1 1
      |   |   |-- 1 for X 1 1 -1 1 1 -1 -1 -1 1
      |   |-- -1 for O 1 1 0 1 -1 -1 -1 -1 1
      |       |-- 1 for X 1 1 1 1 -1 -1 -1 -1 1
      |-- 0 for X 0 1 1 1 0 -1 -1 -1 1
      |   |-- 0 for O -1 1 1 1 0 -1 -1 -1 1
      |   |   |-- 0 for X -1 1 1 1 1 -1 -1 -1 1
      |   |-- -1 for O 0 1 1 1 -1 -1 -1 -1 1
      |       |-- 1 for X 1 1 1 1 -1 -1 -1 -1 1
      |-- 0 for X 0 1 0 1 1 -1 -1 -1 1
          |-- 0 for O -1 1 0 1 1 -1 -1 -1 1
          |   |-- 0 for X -1 1 1 1 1 -1 -1 -1 1
          |-- -1 for O 0 1 -1 1 1 -1 -1 -1 1
              |-- 1 for X 1 1 -1 1 1 -1 -1 -1 1

Game continues

  State after new O (-1)
   _ X _
   X _ O
   O O X

  State after new X (1)
   _ X X
   X _ O
   O O X

   Evaluations
   |-- 0 for O -1 1 1 1 0 -1 -1 -1 1
   |   |-- 0 for X -1 1 1 1 1 -1 -1 -1 1
   |-- -1 for O 0 1 1 1 -1 -1 -1 -1 1
       |-- 1 for X 1 1 1 1 -1 -1 -1 -1 1

Game concludes

  State after new O (-1)
   _ X X
   X O O
   O O X

   Evaluations
   |-- 1 for X 1 1 1 1 -1 -1 -1 -1 1

  State after new X (1)
   X X X
   X O O
   O O X

  GAME WON FOR X

Summary

• Node class

• NoughtsAndCrossesSpace class

• Static evaluations

• Dynamic evaluation

• Tree generation

• Main loop

• main method

Questions

• Why does this program use an evaluation parameter for nodes rather than a cost parameter?

• How easy would it be to rewrite the wonFor method so as to make use of iterative constructs.

Exercises

• Modify the NoughtsAndCrossesSearch program so that it prefers wins which involve fewer moves.

• Modify the NoughtsAndCrossesSearch program so that it uses ordinary minimax evaluation.

• Modify the NoughtsAndCrossesSearch program so as to implement alpha-beta pruning.

• Modify the NoughtsAndCrossesSearch program so that it is interactive, i.e., moves by the second player are chosen by the user.