我并不完全相信此处需要进行归纳。

I'm not entirely convinced that induction is necessary here.

这是我的两分钱：

假设您有一个数字 S 和整数 k 的序列，并且您已经知道存在一个子集总和为 k 的数字。现在，从序列中删除一个数字（称为 i ），然后在剩余的内容上使用黑框（使用相同的 k 像以前一样。）

Suppose you have a sequence of numbers S, and integer k, and you already know that there exists a subset of numbers whose sum is k. Now, remove a number from your sequence (call it i), and use your black box on what remains (using the same k as before).

• 如果算法在新序列上返回是，那么对 i 和 S 的任何子集，其总和为 k ？


• 如果算法在新序列上返回否，那么这将告诉您有关 i 和 S $的任何子集的信息c $ c>的总和为 k ？

• If the algorithm returns YES on the new sequence, what does that tell you about i and any subset of S whose sum is k?
• If the algorithm returns NO on the new sequence, what does that tell you about i and any subset of S whose sum is k?