703287. Possible groups
Possible Groups
Slug: possible-groups2013 Difficulty: Medium Id: 703287 Topic Tags: Arrays, Data Structures, Algorithms Company Tags: Amazon
Summary
The problem is to find all possible groups of people who can attend a meeting based on the given constraints. The input consists of an array of integers representing the availability of different individuals for the meeting at specific times. The task is to identify all possible subsets of this array that add up to a target sum.
Key concepts involved include arrays, data structures, and algorithms, with a focus on solving a combinatorial problem efficiently.
Detailed Explanation
The approach to solve this problem involves using a combination of bitwise operations and recursion. We start by initializing an empty set result to store the possible groups. Then, we define a recursive function findGroups that takes three parameters: the current sum sum, the target sum targetSum, and the index index in the array.
The function works as follows:
- If the current sum is equal to the target sum, add the current group to the result set.
- If the current sum exceeds the target sum or if we have processed all elements in the array, return without adding any groups to the result.
- Otherwise, consider two cases: including and excluding the
indexth element from the current group.
For each case, recursively call findGroups with the updated sum and index. Finally, add the new groups found to the result set.
Time complexity analysis: The time complexity of this algorithm is O(2^n), where n is the size of the input array. This is because we are exploring all possible combinations of elements in the array.
Space complexity analysis: The space complexity is O(n) for storing the recursive call stack and the result set.
Optimized Solutions
Java
import java.util.*;
public class PossibleGroups {
public List<List<Integer>> findGroups(int[] availability, int targetSum) {
List<List<Integer>> result = new ArrayList<>();
findGroups(0, 0, availability, targetSum, result);
return result;
}
private void findGroups(int sum, int index, int[] availability, int targetSum, List<List<Integer>> result) {
if (sum == targetSum) {
result.add(Arrays.asList(availability).subList(index, availability.length));
} else if (sum > targetSum || index >= availability.length) {
return;
} else {
findGroups(sum + availability[index], index + 1, availability, targetSum, result);
findGroups(sum, index + 1, availability, targetSum, result);
}
}
}