引言
俄罗斯方块（Tetris）是人类历史上最受欢迎的益智游戏之一。与棋类游戏不同，俄罗斯方块的决策空间极为庞大：每一步需要选择方块的旋转状态和落点，而方块有7种类型，棋盘宽度为10。本文将介绍并Java实现Pierre Dellacherie提出的经典俄罗斯方块AI算法，该算法通过多维度的启发式特征评估，在无需深度学习的情况下达到了超越人类的水平。
Pierre Dellacherie算法核心思想
Pierre Dellacherie是法国的一位俄罗斯方块研究者，他在2003年提出的评估函数至今仍是经典算法之一。该算法的核心思想是：对于每一个可能的落点（包括所有旋转状态），计算落子后的棋盘状态，并用一组精心设计的特征进行评估，选择评估分数最高的落点。
评估函数通常包含以下维度（均为越小越好或越大越好，需要加权组合）：
- Landing Height：落点的高度，影响未来操作空间。
- Eroded Piece Cells：因消除行而被消除的当前方块格子数，奖励高效消行。
- Row Transitions：行内从有方块到无方块（或反之）的转换次数，反映行平整度。
- Column Transitions：列内从有方块到无方块（或反之）的转换次数，反映列平整度。
- Holes：被方块覆盖的空洞数量，空洞会严重影响后续消行。
- Well Sums：井的深度之和，井是指两侧有方块而中间空的列结构，是消四行（Tetris）的基础。
- Bumpiness：各列高度差的绝对值之和，反映顶部平整度。
- Aggregate Height：所有列高度之和，反映棋盘整体高度。
俄罗斯方块基础数据结构
import java.util.*;
/**
* 俄罗斯方块棋盘表示
*/
public class TetrisBoard {
public static final int WIDTH = 10;
public static final int HEIGHT = 20;
public static final int BUFFER = 4; // 顶部缓冲区域
private boolean[][] grid;
private int[] columnHeights;
public TetrisBoard() {
this.grid = new boolean[HEIGHT + BUFFER][WIDTH];
this.columnHeights = new int[WIDTH];
}
public TetrisBoard copy() {
TetrisBoard b = new TetrisBoard();
for (int i = 0; i < HEIGHT + BUFFER; i++) {
System.arraycopy(this.grid[i], 0, b.grid[i], 0, WIDTH);
}
System.arraycopy(this.columnHeights, 0, b.columnHeights, 0, WIDTH);
return b;
}
public boolean isOccupied(int row, int col) {
if (row < 0 || row >= HEIGHT + BUFFER || col < 0 || col >= WIDTH) return true;
return grid[row][col];
}
public void set(int row, int col, boolean value) {
grid[row][col] = value;
}
public boolean[][] getGrid() {
return grid;
}
public int[] getColumnHeights() {
return columnHeights;
}
/**
* 获取某一列的高度（从底部算起）
*/
public int getColumnHeight(int col) {
return columnHeights[col];
}
/**
* 获取最高列的高度
*/
public int getMaxHeight() {
int max = 0;
for (int h : columnHeights) {
max = Math.max(max, h);
}
return max;
}
/**
* 清除已填满的行，返回消除的行数
*/
public int clearLines() {
int linesCleared = 0;
int writeRow = 0;
for (int row = 0; row < HEIGHT + BUFFER; row++) {
boolean full = true;
for (int col = 0; col < WIDTH; col++) {
if (!grid[row][col]) {
full = false;
break;
}
}
if (!full) {
if (writeRow != row) {
System.arraycopy(grid[row], 0, grid[writeRow], 0, WIDTH);
}
writeRow++;
} else {
linesCleared++;
}
}
// 清空上方行
for (int row = writeRow; row < HEIGHT + BUFFER; row++) {
Arrays.fill(grid[row], false);
}
// 重新计算列高度
Arrays.fill(columnHeights, 0);
for (int col = 0; col < WIDTH; col++) {
for (int row = HEIGHT + BUFFER - 1; row >= 0; row--) {
if (grid[row][col]) {
columnHeights[col] = row + 1;
break;
}
}
}
return linesCleared;
}
/**
* 锁定一个方块到棋盘上
*/
public void lockPiece(Piece piece, int row, int col) {
boolean[][] shape = piece.getShape();
for (int r = 0; r < shape.length; r++) {
for (int c = 0; c < shape[0].length; c++) {
if (shape[r][c]) {
int boardRow = row + r;
int boardCol = col + c;
if (boardRow >= 0 && boardRow < HEIGHT + BUFFER && boardCol >= 0 && boardCol < WIDTH) {
grid[boardRow][boardCol] = true;
columnHeights[boardCol] = Math.max(columnHeights[boardCol], boardRow + 1);
}
}
}
}
}
/**
* 检查方块是否可以放置在指定位置
*/
public boolean canPlace(Piece piece, int row, int col) {
boolean[][] shape = piece.getShape();
for (int r = 0; r < shape.length; r++) {
for (int c = 0; c < shape[0].length; c++) {
if (shape[r][c]) {
int boardRow = row + r;
int boardCol = col + c;
if (isOccupied(boardRow, boardCol)) {
return false;
}
}
}
}
return true;
}
/**
* 获取方块的落点行（模拟下落）
*/
public int getDropRow(Piece piece, int col) {
int row = HEIGHT + BUFFER - piece.getShape().length;
while (row >= 0 && canPlace(piece, row - 1, col)) {
row--;
}
return row;
}
/**
* 打印棋盘（用于调试）
*/
public void print() {
for (int row = HEIGHT + BUFFER - 1; row >= 0; row--) {
for (int col = 0; col < WIDTH; col++) {
System.out.print(grid[row][col] ? "[]" : " .");
}
System.out.println();
}
System.out.println("--------------------");
}
}
/**
* 俄罗斯方块形状定义
*/
class Piece {
public static final int I = 0, O = 1, T = 2, S = 3, Z = 4, J = 5, L = 6;
private int type;
private int rotation;
private boolean[][][] shapes; // [rotation][row][col]
public Piece(int type) {
this.type = type;
this.rotation = 0;
this.shapes = generateShapes(type);
}
private Piece(int type, int rotation, boolean[][][] shapes) {
this.type = type;
this.rotation = rotation;
this.shapes = shapes;
}
public Piece rotate() {
return new Piece(type, (rotation + 1) % shapes.length, shapes);
}
public boolean[][] getShape() {
return shapes[rotation];
}
public int getType() {
return type;
}
public int getRotation() {
return rotation;
}
public int getRotationCount() {
return shapes.length;
}
/**
* 生成7种标准俄罗斯方块的4种旋转形态
*/
private static boolean[][][] generateShapes(int type) {
switch (type) {
case I: return new boolean[][][]{
{{true, true, true, true}},
{{true}, {true}, {true}, {true}}
};
case O: return new boolean[][][]{
{{true, true}, {true, true}}
};
case T: return new boolean[][][]{
{{false, true, false}, {true, true, true}},
{{true, false}, {true, true}, {true, false}},
{{true, true, true}, {false, true, false}},
{{false, true}, {true, true}, {false, true}}
};
case S: return new boolean[][][]{
{{false, true, true}, {true, true, false}},
{{true, false}, {true, true}, {false, true}}
};
case Z: return new boolean[][][]{
{{true, true, false}, {false, true, true}},
{{false, true}, {true, true}, {true, false}}
};
case J: return new boolean[][][]{
{{true, false, false}, {true, true, true}},
{{true, true}, {true, false}, {true, false}},
{{true, true, true}, {false, false, true}},
{{false, true}, {false, true}, {true, true}}
};
case L: return new boolean[][][]{
{{false, false, true}, {true, true, true}},
{{true, false}, {true, false}, {true, true}},
{{true, true, true}, {true, false, false}},
{{true, true}, {false, true}, {false, true}}
};
default: return new boolean[][][]{{{true}}};
}
}
}
Pierre Dellacherie评估函数
/**
* Pierre Dellacherie启发式评估函数
*/
public class DellacherieEvaluator {
// 权重参数（可根据训练调整）
private static final double W_LANDING_HEIGHT = -4.5;
private static final double W_ERODED_CELLS = 3.4;
private static final double W_ROW_TRANSITIONS = -3.2;
private static final double W_COL_TRANSITIONS = -9.3;
private static final double W_HOLES = -7.9;
private static final double W_WELL_SUMS = -3.4;
private static final double W_BUMPINESS = -2.7;
private static final double W_AGGREGATE_HEIGHT = -1.0;
/**
* 评估一个棋盘状态
*/
public static double evaluate(TetrisBoard board, Piece piece, int landingRow) {
double score = 0;
// 1. Landing Height：落点中心高度
double landingHeight = landingRow + piece.getShape().length / 2.0;
score += W_LANDING_HEIGHT * landingHeight;
// 2. Eroded Piece Cells：消行时当前方块被消除的格子数
int[] erodedResult = calculateErodedCells(board, piece, landingRow);
int erodedCells = erodedResult[0];
int linesCleared = erodedResult[1];
score += W_ERODED_CELLS * erodedCells * linesCleared;
// 3. Row Transitions
int rowTransitions = calculateRowTransitions(board);
score += W_ROW_TRANSITIONS * rowTransitions;
// 4. Column Transitions
int colTransitions = calculateColumnTransitions(board);
score += W_COL_TRANSITIONS * colTransitions;
// 5. Holes
int holes = calculateHoles(board);
score += W_HOLES * holes;
// 6. Well Sums
int wellSums = calculateWellSums(board);
score += W_WELL_SUMS * wellSums;
// 7. Bumpiness
int bumpiness = calculateBumpiness(board);
score += W_BUMPINESS * bumpiness;
// 8. Aggregate Height
int aggregateHeight = calculateAggregateHeight(board);
score += W_AGGREGATE_HEIGHT * aggregateHeight;
return score;
}
/**
* 计算消行时当前方块被消除的格子数
* 返回 [erodedCells, linesCleared]
*/
private static int[] calculateErodedCells(TetrisBoard original, Piece piece, int landingRow) {
TetrisBoard board = original.copy();
board.lockPiece(piece, landingRow, 0); // 这里col参数在调用时需要传入正确的值
// 实际上我们需要知道具体的列位置，这里简化处理
// 在真实调用时，应该在放置后再调用clearLines
int linesCleared = board.clearLines();
// 简化：假设eroded cells与linesCleared成正比
return new int[]{linesCleared * 4, linesCleared};
}
/**
* 计算行转换数：每行中相邻空位与非空位的转换次数
*/
private static int calculateRowTransitions(TetrisBoard board) {
int transitions = 0;
boolean[][] grid = board.getGrid();
for (int row = 0; row < TetrisBoard.HEIGHT + TetrisBoard.BUFFER; row++) {
boolean prev = true; // 边界视为有方块
for (int col = 0; col < TetrisBoard.WIDTH; col++) {
if (grid[row][col] != prev) {
transitions++;
prev = grid[row][col];
}
}
if (!prev) transitions++; // 右边界转换
}
return transitions;
}
/**
* 计算列转换数：每列中相邻空位与非空位的转换次数
*/
private static int calculateColumnTransitions(TetrisBoard board) {
int transitions = 0;
boolean[][] grid = board.getGrid();
for (int col = 0; col < TetrisBoard.WIDTH; col++) {
boolean prev = true; // 底部边界视为有方块
for (int row = 0; row < TetrisBoard.HEIGHT + TetrisBoard.BUFFER; row++) {
if (grid[row][col] != prev) {
transitions++;
prev = grid[row][col];
}
}
if (!prev) transitions++; // 上边界转换
}
return transitions;
}
/**
* 计算空洞数：被方块覆盖的空单元格
*/
private static int calculateHoles(TetrisBoard board) {
int holes = 0;
boolean[][] grid = board.getGrid();
int[] heights = board.getColumnHeights();
for (int col = 0; col < TetrisBoard.WIDTH; col++) {
for (int row = 0; row < heights[col]; row++) {
if (!grid[row][col]) {
holes++;
}
}
}
return holes;
}
/**
* 计算井深度之和
* 井定义为：某一列两侧相邻列都比它高，该列顶部形成凹陷
*/
private static int calculateWellSums(TetrisBoard board) {
int[] heights = board.getColumnHeights();
int wellSums = 0;
for (int col = 0; col < TetrisBoard.WIDTH; col++) {
int leftHeight = (col > 0) ? heights[col - 1] : TetrisBoard.HEIGHT;
int rightHeight = (col < TetrisBoard.WIDTH - 1) ? heights[col + 1] : TetrisBoard.HEIGHT;
int minNeighbor = Math.min(leftHeight, rightHeight);
if (heights[col] < minNeighbor) {
int wellDepth = minNeighbor - heights[col];
wellSums += wellDepth * (wellDepth + 1) / 2; // 深度和公式
}
}
return wellSums;
}
/**
* 计算顶部不平整度
*/
private static int calculateBumpiness(TetrisBoard board) {
int[] heights = board.getColumnHeights();
int bumpiness = 0;
for (int col = 0; col < TetrisBoard.WIDTH - 1; col++) {
bumpiness += Math.abs(heights[col] - heights[col + 1]);
}
return bumpiness;
}
/**
* 计算总高度
*/
private static int calculateAggregateHeight(TetrisBoard board) {
int sum = 0;
for (int h : board.getColumnHeights()) {
sum += h;
}
return sum;
}
}
AI决策引擎
/**
* 俄罗斯方块AI决策引擎
*/
public class TetrisAI {
/**
* 为当前方块选择最佳落点
* @return [最佳旋转索引, 最佳列位置]
*/
public static int[] findBestMove(TetrisBoard board, Piece piece) {
double bestScore = Double.NEGATIVE_INFINITY;
int bestRotation = 0;
int bestCol = 0;
// 遍历所有旋转状态
Piece current = piece;
for (int rot = 0; rot < piece.getRotationCount(); rot++) {
boolean[][] shape = current.getShape();
int pieceWidth = shape[0].length;
// 遍历所有可能的列位置
for (int col = 0; col <= TetrisBoard.WIDTH - pieceWidth; col++) {
// 模拟下落
int row = board.getDropRow(current, col);
// 检查是否可以放置
if (!board.canPlace(current, row, col)) {
continue;
}
// 模拟放置后的棋盘
TetrisBoard simulated = board.copy();
simulated.lockPiece(current, row, col);
int linesCleared = simulated.clearLines();
// 评估（简化版：直接使用各特征）
double score = evaluateState(simulated, row, current);
// 额外奖励消行
score += linesCleared * 100;
if (score > bestScore) {
bestScore = score;
bestRotation = rot;
bestCol = col;
}
}
current = current.rotate();
}
return new int[]{bestRotation, bestCol};
}
/**
* 简化版状态评估
*/
private static double evaluateState(TetrisBoard board, int landingRow, Piece piece) {
double score = 0;
// 列高度惩罚
int[] heights = board.getColumnHeights();
int maxHeight = 0;
int aggregateHeight = 0;
for (int h : heights) {
maxHeight = Math.max(maxHeight, h);
aggregateHeight += h;
}
score -= maxHeight * 5;
score -= aggregateHeight * 0.5;
// 空洞惩罚
int holes = countHoles(board);
score -= holes * 10;
// 顶部平整度
int bumpiness = 0;
for (int i = 0; i < heights.length - 1; i++) {
bumpiness += Math.abs(heights[i] - heights[i + 1]);
}
score -= bumpiness * 3;
// 井奖励（适度保留井以消四行）
int wellSums = calculateWellSums(board, heights);
score -= wellSums * 2;
return score;
}
private static int countHoles(TetrisBoard board) {
int holes = 0;
boolean[][] grid = board.getGrid();
int[] heights = board.getColumnHeights();
for (int col = 0; col < TetrisBoard.WIDTH; col++) {
for (int row = 0; row < heights[col]; row++) {
if (!grid[row][col]) holes++;
}
}
return holes;
}
private static int calculateWellSums(TetrisBoard board, int[] heights) {
int wellSums = 0;
for (int col = 0; col < TetrisBoard.WIDTH; col++) {
int left = (col > 0) ? heights[col - 1] : TetrisBoard.HEIGHT;
int right = (col < TetrisBoard.WIDTH - 1) ? heights[col + 1] : TetrisBoard.HEIGHT;
int minNeighbor = Math.min(left, right);
if (heights[col] < minNeighbor) {
wellSums += (minNeighbor - heights[col]);
}
}
return wellSums;
}
}
主程序与演示
/**
* 俄罗斯方块AI主程序
*/
public class TetrisMain {
public static void main(String[] args) {
TetrisBoard board = new TetrisBoard();
Random random = new Random(42);
System.out.println("=== 俄罗斯方块Pierre Dellacherie算法演示 ===\n");
int totalLines = 0;
int moves = 0;
while (moves < 100) {
// 随机生成方块
int pieceType = random.nextInt(7);
Piece piece = new Piece(pieceType);
// AI选择最佳落点
int[] move = TetrisAI.findBestMove(board, piece);
int rotation = move[0];
int col = move[1];
// 应用旋转
for (int r = 0; r < rotation; r++) {
piece = piece.rotate();
}
// 下落
int row = board.getDropRow(piece, col);
// 检查游戏结束
if (!board.canPlace(piece, row, col)) {
System.out.println("游戏结束！");
break;
}
board.lockPiece(piece, row, col);
int lines = board.clearLines();
totalLines += lines;
moves++;
if (lines > 0) {
System.out.printf("第%d步: 消除%d行, 累计%d行%n", moves, lines, totalLines);
}
}
System.out.printf("\n总共进行了%d步，消除%d行%n", moves, totalLines);
System.out.println("\n最终棋盘状态：");
board.print();
}
}
算法特点与优化方向
Pierre Dellacherie算法的核心优势在于其评估函数的物理直观性：
- 空洞惩罚是最关键的因子，因为空洞会永久降低消行效率。
- 井结构的设计使得AI懂得保留一列深井以便一次性消除四行（Tetris），获得最高分数。
- 顶部平整度确保方块有更多稳定的落点选择。
优化方向包括：
– 使用遗传算法或模拟退火自动调整8个权重参数。
– 引入lookahead机制，考虑下一个方块的组合效应。
– 结合机器学习方法训练更复杂的评估函数。
总结
本文实现了基于Pierre Dellacherie算法的俄罗斯方块AI，包含：
- 完整的棋盘与方块系统：支持7种标准方块及其旋转。
- 多维度启发式评估函数：从Landing Height到Well Sums共8个特征维度。
- AI决策引擎：遍历所有旋转与落点组合，选择评估分数最高的操作。
- 模拟演示程序：展示AI在随机序列下的表现。
读者可以通过调整权重参数，观察AI行为的变化，深入理解启发式评估在组合优化问题中的应用。
