获得笛卡尔积的算法 [英] Algorithm to get Cartesian product

问题描述

我有一个像 [0,2,3,0,1] 这样的数组作为输入，我需要找到 { 0} x {0,1,2} x {0,1,2,3} x {0} x {0,1} ，更确切地说，我需要输出如下。

I have an array like [0,2,3,0,1] as input , and I need to find Cartesian product of {0}x{0,1,2}x{0,1,2,3}x{0}x{0,1}, more precisely I need to have output as following.

输入：

[0, 2, 3, 0, 1]

输出：

[0, 0, 0, 0, 0]
[0, 0, 0, 0, 1]
[0, 0, 1, 0, 0]
[0, 0, 1, 0, 1]
[0, 0, 2, 0, 0]
[0, 0, 2, 0, 1]
[0, 0, 3, 0, 0]
[0, 0, 3, 0, 1]
[0, 1, 0, 0, 0]
[0, 1, 0, 0, 1]
[0, 1, 1, 0, 0]
[0, 1, 1, 0, 1]
[0, 1, 2, 0, 0]
[0, 1, 2, 0, 1]
[0, 1, 3, 0, 0]
[0, 1, 3, 0, 1]
[0, 2, 0, 0, 0]
[0, 2, 0, 0, 1]
[0, 2, 1, 0, 0]
[0, 2, 1, 0, 1]
[0, 2, 2, 0, 0]
[0, 2, 2, 0, 1]
[0, 2, 3, 0, 0]
[0, 2, 3, 0, 1]

我需要一个通用算法。任何的想法 ？我想用C ++编写。
谢谢

I need a general algorithm. Any idea ? I would like to write it in c++. Thanks

推荐答案

一个硬代码解决方案是：

A hard code solution would be:

for (int a1 : {0}) {
  for (int a2 : {0,1,2}) {
    for (int a3 : {0,1,2,3}) {
      for (int a4 : {0}) {
        for (int a5 : {0,1}) {
            do_job(a1, a2, a3, a4, a5);
        }
      }
    }
  }
}

您可以使用以下通用方法（将所有 a 放入向量）：

You may use the following for a generic way (putting all as into vector):

bool increase(const std::vector<std::size_t>& v, std::vector<std::size_t>& it)
{
    for (std::size_t i = 0, size = it.size(); i != size; ++i) {
        const std::size_t index = size - 1 - i;
        ++it[index];
        if (it[index] > v[index]) {
            it[index] = 0;
        } else {
            return true;
        }
    }
    return false;
}

void iterate(const std::vector<std::size_t>& v)
{
    std::vector<std::size_t> it(v.size(), 0);

    do {
        do_job(it);
    } while (increase(v, it));
}

实时演示

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