Given an array, find all subsets in the array

Intuition

Use DFS to iterate over all subsets and record them.

Approach

A subset can be represented as a binary number of n digits. Each digit is either 0 or 1. We can use DFS to iterate over all possible such format of binary numbers.

Complexity

Time complexity: iterate all binary numbers of length n once.
$$O(2^n)$$
Space complexity:
$$O(2^n)$$

Code

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class Solution {
public:
    void dfs(const vector<int>& nums, int index, vector<vector<int>>& result,
             vector<int>& s) {
        if (index == nums.size()) {
            result.push_back(s);
            return;
        }
        // digit is 1
        s.push_back(nums[index]);
        dfs(nums, index + 1, result, s);
        s.pop_back();
        // digit is 0
        dfs(nums, index + 1, result, s);
    }

    vector<vector<int>> subsets(vector<int>& nums) {
        vector<vector<int>> result;
        vector<int> s;
        dfs(nums, 0, result, s);
        return result;
    }
};

Reference

Leetcode

78. Subsets

Find all subsets given an array

Intuition

Approach

Complexity

Code

Reference