078. Subsets

Description

Given a set of distinct integers, nums, return all possible subsets (the power set).

Note: The solution set must not contain duplicate subsets.

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

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

Solving Ideas

• 首先，给定 n 个元素的集合，其子集元素个数为 2^n;
• 其次，集合中每个元素是/否在某个子集中可以用 1/0 比特来表示；
• 借助Bit Manipulation的特性，检验 0 到 2^n-1 的每一个二进制位，即可实现。

Solutions

class Solution {public:    vector<vector<int>> subsets(vector<int>& nums) {        sort(nums.begin(), nums.end());        vector<vector<int>> res(pow(2, nums.size()), vector<int>());        for (int i = 0; i < nums.size(); i++) {            for (int j = 0; j < pow(2, nums.size()); j++) {                if ( (j >> i) & 1 ) {                    res[j].push_back(nums[i]);                }            }        }        return res;    }};

Complexity

Time Space O(n * 2^n) O(1)