子集生成算法-优快云博客

本文链接：https://blog.youkuaiyun.com/smallfish_yy/article/details/18356265

本文介绍了一种使用深度优先搜索(DFS)策略生成给定整数集合所有可能子集的算法。该算法首先对输入数组进行排序，然后递归地选择每个元素与已有的子集组合，确保生成的子集有序且不包含重复项。

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Given a set of distinct integers, S, return all possible subsets.

Note:

Elements in a subset must be in non-descending order.
The solution set must not contain duplicate subsets.

For example,
If S = [1,2,3], a solution is:

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

Analysis: DFS. Sort the array at the beginning. Each time, select the first element in the array, which is the smallest number in the array and the biggest number compared to all of the numbers in res, and insert itself and its combinations with all of the existing sets in res into res.

public class Solution {
    public void subsets(int[] S, ArrayList<ArrayList<Integer>> res) {
        if(S.length == 0) {
            res.add(new ArrayList<Integer>());      // empty set
            return;
        }
        
        int size = res.size();
        for(int i=0; i<size; i++) {
            ArrayList<Integer> tem = new ArrayList<Integer>(res.get(i));
            tem.add(S[0]);
            res.add(tem);
        }
        int[] nextS = Arrays.copyOfRange(S, 1, S.length);
        ArrayList<Integer> loc = new ArrayList<Integer>();
        loc.add(S[0]);
        res.add(loc);
        subsets(nextS, res);
    }
    
    public ArrayList<ArrayList<Integer>> subsets(int[] S) {
        ArrayList<ArrayList<Integer>> res = new ArrayList<ArrayList<Integer>>();
        Arrays.sort(S);
        subsets(S, res);
        return res;
    }
}

Subsets I