我这个才是最容易记住的思路。。。

从n个元素里面取出m个组合等于 （先从组合里面取出一个元素e，再从n-1个元素里面取出m-1个元素）加上（排除元素e,从n-1个元素里面直接取出m个元素）

也就是 C(m,n)=C(m-1,n-1)+C(m,n-1)

多清晰的递归思路


package test;

import java.util.*;
import java.util.stream.Collectors;

public class MyDp {

        public static void main(String[] args) {

                Object[] elements = { "a", "b", "c", "d" };
                List<List<Object>> combinations = new ArrayList<>();
                // 求 C(n,1)+C(n,2)+C(n,3)+...+C(n,m-1)+C(n,m) 这里n=m
                for (int i = 1; i <= elements.length; i++) {
                        combinations.addAll(combinations(Arrays.asList(elements), elements.length, i));
                }
                
                for(List<Object> eSet : combinations) {
                        System.out.println(Arrays.deepToString(eSet.toArray()));
                }
        }

        //从n个组合里面取出m个元素
        private static List<List<Object>> combinations(List<Object> elements, int n, int m) {

                List<List<Object>> ret = new ArrayList<>();
                //如果从n个元素里面取出一个元素，每个元素都是一个单独的组合,结果返回
                if (m == 1) {
                        for (Object e : elements) {
                                List<Object> elementSet = new ArrayList<>();
                                elementSet.add(e);
                                ret.add(elementSet);
                        }
                        return ret;
                }
                // 如果从n个元素里面取出m>1个元素，利用递归思路 C(m,n)=C(m-1,n-1)+C(m,n-1)              
                List<Object> tElements = new ArrayList<>(elements);
                for (Object e : elements) {
                        tElements.remove(e); //元素删除
                        ret = combinations(tElements, n - 1, m - 1); // 包含e元素
                        for (List<Object> eSet : ret) {
                                eSet.add(e);
                        }
                        ret.addAll(combinations(tElements, n - 1, m));// 不包含e元素
                        tElements.add(e); //元素回填
                }
                return ret;
        }
}
--
修改:iStudy FROM 58.37.127.*
FROM 58.37.127.*