Subsets I I Algorithm
The Subsets I I Algorithm is a technique used in computer science and mathematics for generating all the possible subsets of a given set. This algorithm is particularly useful in solving combinatorial problems, where the goal is to find all possible combinations of elements in a set. The Subsets I I Algorithm is based on a recursive approach, which essentially breaks down the problem into smaller subproblems, and then solves these subproblems to arrive at the final solution. This method is also known as backtracking, as it involves exploring all possible paths in the solution space and backtracking whenever a dead end is reached.
The algorithm begins by initializing an empty set, which represents the initial state of the solution. It then iterates through each element in the input set, adding the element to the current subset, and recursively generating all subsets containing that element. Once all possible subsets containing the current element have been generated, the algorithm backtracks by removing the element from the current subset and proceeding to the next element in the input set. This process continues until all elements in the input set have been considered. The result is a collection of all possible subsets of the input set, including the empty set and the set itself. This algorithm is efficient and scalable, making it suitable for solving large-scale combinatorial problems with numerous elements.
class Solution {
public:
vector<vector<int>> subsetsWithDup(vector<int>& S) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
vector<vector<int>> subsets;
vector<int> integers;
if (S.empty()) return subsets;
sort(S.begin(), S.end());
DFS(integers, 0, S, subsets);
return move(subsets);
}
void DFS(vector<int>& integers, int start, vector<int>& S, vector<vector<int>>& subsets) {
if (start == S.size()) {
subsets.push_back(integers);
return;
}
int end = start;
while (end + 1 < S.size() && S[start] == S[end+1])
end += 1;
DFS(integers, end + 1, S, subsets);
for (int i = start; i <= end; i++) {
integers.push_back(S[i]);
DFS(integers, end + 1, S, subsets);
}
for (int i = start; i <= end; i++)
integers.pop_back();
}
};
