> For the complete documentation index, see [llms.txt](https://docs.1l.lol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.1l.lol/algorithms/enumeration-simulation.md).

# 枚举法与模拟法

### 枚举法

枚举法把所有可能的情况一一列举出来，逐一检验，找出满足条件的解。

特点：**思路简单、正确性高**，但可能耗时，需要估算规模。

```cpp
// 求 1~100 中所有完数（等于除自身外所有约数之和）
for (int n = 2; n <= 100; n++) {
    int sum = 0;
    for (int i = 1; i < n; i++)
        if (n % i == 0) sum += i;
    if (sum == n) cout << n << " ";  // 6 28
}
```

### 模拟法

模拟法按照题目描述的规则，**一步步重现过程**，不作数学抽象。

```cpp
// 模拟：约瑟夫环（n 个人报数到 m 出列）
int n = 5, m = 3, cnt = 0, out = 0;
bool vis[10] = {false};
for (int i = 0; out < n; i = (i + 1) % n) {
    if (vis[i]) continue;
    if (++cnt == m) {
        vis[i] = true; out++; cnt = 0;
        cout << i + 1 << " ";
    }
}
```

### 使用要点

* 先估算枚举规模，避免超时（如双重循环到 10⁵ 就可能超时）。
* 模拟题关键是**把规则拆成清晰的步骤**，注意边界与循环结束条件。


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