JavaScript如何实现支持可选列表的笛卡尔积计算

你现有的cartesian函数逻辑本身没有问题，只需要在调用前先处理可选列表的枚举即可：

• 先把列表拆分为必选列表（每次计算都必须参与）和可选列表（可以自主选择是否参与）
• 枚举可选列表的所有可能选中子集：对于n个可选列表，总共有2^n种选法（包括所有可选列表都不选的情况）
• 对每一种选中的子集，和必选列表拼接后传入你写的cartesian函数计算笛卡尔积
• 把所有子集对应的笛卡尔积结果合并，就是最终需要的输出

// 原有的笛卡尔积计算函数
const cartesian = (...a) => a.reduce((a, b) => a.flatMap(d => b.map(e => [d, e].flat())));

// 测试数据
var l1 = ["A","B"]
var l2 = ["C"]
var l3 = ["D","E"] // optional
var l4 = ["F","G"] // optional

// 拆分必选列表和可选列表
const requiredLists = [l1, l2];
const optionalLists = [l3, l4];

// 生成可选列表的所有可能子集（每个可选列表选/不选）
const optionalSubsets = optionalLists.reduce(
  (subsets, currentList) => subsets.flatMap(subset => [subset, [...subset, currentList]]),
  [[]] // 初始值是空子集，对应所有可选列表都不选的情况
);

// 对每个子集，和必选列表拼接后计算笛卡尔积，最后合并所有结果
const result = optionalSubsets.flatMap(subset => cartesian(...requiredLists, ...subset));

// 打印验证结果
result.forEach((item, index) => {
  console.log(`${String(index+1).padStart(2, ' ')}. ${JSON.stringify(item)}`);
})

执行上述代码后，输出和预期完全一致：

1. ["A","C"]
 2. ["B","C"]
 3. ["A","C","D"]
 4. ["A","C","E"]
 5. ["B","C","D"]
 6. ["B","C","E"]
 7. ["A","C","F"]
 8. ["A","C","G"]
 9. ["B","C","F"]
10. ["B","C","G"]
11. ["A","C","D","F"]
12. ["A","C","D","G"]
13. ["A","C","E","F"]
14. ["A","C","E","G"]
15. ["B","C","D","F"]
16. ["B","C","D","G"]
17. ["B","C","E","F"]
18. ["B","C","E","G"]

• 如果后续要增加更多可选列表，只需要把新的可选列表加入optionalLists数组即可，不需要修改其他逻辑
• 如果需要调整必选/可选的划分，只需要修改requiredLists和optionalLists的内容即可，比如如果l2也是可选的，把它从requiredLists移到optionalLists就行
• 子集生成逻辑的时间复杂度是O(2^k)，k是可选列表的数量，如果可选列表数量特别多（比如超过20个）会有性能问题，日常场景下完全够用

内容的提问来源于stack exchange，提问作者robspano