当前位置： 面试刷题>> 生命游戏(经典算法150题)
### 题目描述补充
**生命游戏（Conway's Game of Life）** 是一种零玩家游戏，由数学家约翰·何顿·康威在1970年发明。在这个游戏中，一个二维网格上的每个格子居住着一个细胞，细胞可以是活的（用1表示）或死的（用0表示）。每个细胞与其相邻的八个格子（包括水平、垂直和对角线方向）相互作用。根据以下规则，细胞的状态会在每个时间步更新：
1. **出生**：如果一个死细胞恰好有三个活邻居，则在下一个时间步，该细胞变为活细胞（出生）。
2. **存活**：如果一个活细胞有两个或三个活邻居，则在下一个时间步，该细胞保持活状态（存活）。
3. **死亡**：如果一个活细胞有少于两个或多于三个活邻居，则在下一个时间步，该细胞变为死细胞（死亡）。
游戏从一个初始状态开始，然后按照上述规则不断迭代，直到网格达到一个稳定状态（即，没有细胞的状态会在下一个时间步改变）。
### 示例代码
以下是使用PHP、Python和JavaScript编写的生命游戏示例代码。
#### PHP 示例
```php
function countNeighbors($grid, $x, $y, $width, $height) {
$count = 0;
for ($dx = -1; $dx <= 1; $dx++) {
for ($dy = -1; $dy <= 1; $dy++) {
if ($dx == 0 && $dy == 0) continue;
$nx = $x + $dx;
$ny = $y + $dy;
if ($nx >= 0 && $nx < $width && $ny >= 0 && $ny < $height && $grid[$ny][$nx] == 1) {
$count++;
}
}
}
return $count;
}
function nextGeneration($grid, $width, $height) {
$next = array_fill(0, $height, array_fill(0, $width, 0));
for ($y = 0; $y < $height; $y++) {
for ($x = 0; $x < $width; $x++) {
$neighbors = countNeighbors($grid, $x, $y, $width, $height);
if ($grid[$y][$x] == 1 && ($neighbors == 2 || $neighbors == 3)) {
$next[$y][$x] = 1; // Survive
} elseif ($grid[$y][$x] == 0 && $neighbors == 3) {
$next[$y][$x] = 1; // Born
}
}
}
return $next;
}
// 示例初始网格
$grid = [
[0, 1, 0],
[0, 0, 1],
[1, 1, 1]
];
// 迭代更新网格
$nextGen = nextGeneration($grid, 3, 3);
print_r($nextGen);
```
#### Python 示例
```python
def count_neighbors(grid, x, y, width, height):
count = 0
for dx in [-1, 0, 1]:
for dy in [-1, 0, 1]:
if dx == 0 and dy == 0:
continue
nx, ny = x + dx, y + dy
if 0 <= nx < width and 0 <= ny < height and grid[ny][nx] == 1:
count += 1
return count
def next_generation(grid, width, height):
next_grid = [[0] * width for _ in range(height)]
for y in range(height):
for x in range(width):
neighbors = count_neighbors(grid, x, y, width, height)
if grid[y][x] == 1 and (neighbors == 2 or neighbors == 3):
next_grid[y][x] = 1 # Survive
elif grid[y][x] == 0 and neighbors == 3:
next_grid[y][x] = 1 # Born
return next_grid
# 示例初始网格
grid = [
[0, 1, 0],
[0, 0, 1],
[1, 1, 1]
]
# 迭代更新网格
next_gen = next_generation(grid, 3, 3)
for row in next_gen:
print(row)
```
#### JavaScript 示例
```javascript
function countNeighbors(grid, x, y, width, height) {
let count = 0;
for (let dx = -1; dx <= 1; dx++) {
for (let dy = -1; dy <= 1; dy++) {
if (dx === 0 && dy === 0) continue;
const nx = x + dx;
const ny = y + dy;
if (nx >= 0 && nx < width && ny >= 0 && ny < height && grid[ny][nx] === 1) {
count++;
}
}
}
return count;
}
function nextGeneration(grid, width, height) {
const next = Array.from({ length: height }, () => Array(width).fill(0));
for (let y = 0; y < height; y++) {
for (let x = 0; x < width; x++) {
const neighbors = countNeighbors(grid, x, y, width, height);
if (grid[y][x] === 1 && (neighbors === 2 || neighbors === 3)) {
next[y][x] = 1; // Survive
} else if (grid[y][x] === 0 && neighbors === 3) {
next[y][x] = 1; // Born
}
}
}
return next;
}
// 示例初始网格
const grid = [
[0, 1, 0],
[0, 0, 1],
[1, 1, 1]
];
// 迭代更新网格
const nextGen = nextGeneration(grid, 3, 3);
console.log(nextGen);
```
这些示例代码展示了如何根据生命游戏的规则来更新网格的状态。你可以在自己的环境中运行这些代码，并观察网格如何随时间变化。