5. Subset sum problem <= Partition problem
问题描述：
Subset sum problem：given a set (or multiset) of integers T=(t1,t2,⋯,tn), is there a non-empty subset whose sum is k。
Partition problem: partition problem (or number partitioning) is the task of deciding whether a given multiset W of positive integers can be partitioned into two subsets W1 and W2 such that the sum of the numbers in W1 equals the sum of the numbers in W2.
转化过程：
而且，新添加的两个元素肯定不会同时在W1或W2里，否则二者所在的子集的元素和必定大于二者之和3A>2A。
2A−k所在的子集的其它元素就是一个满足子集和问题的子集。
7. Partition problem <= Knapsack problem
问题描述：
Partition problem： partition problem (or number partitioning) is the task of deciding whether a given multiset W of positive integers can be partitioned into two subsets W1 and W2 such that the sum of the numbers in W1 equals the sum of the numbers in W2, i.e.
Knapsack problem：Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. 即给定一个物品集合U={u1,u2,⋯,un}，且每个物品item有大小s(u)和价值w(u)，正整数B（容量）和正数K（价值），是否存在子集U′⊂U使得
转化过程：
P的输入转换为Q的输入：
- 划分问题中的每个数For each t∈W ==> 构造背包问题中一个物品item u 且大小s(u)=价值w(u)=t, 然后对背包容量 B,最小价值K添加如下条件，即等于和的一半
那么有
体积符合要求、总价值符合要求，所以是背包问题的解。
Q的输出转换为P的输出：
因为此时的U'正好等于U的一半，所以划分问题也有解。