878962. Union of Two Sets
Union of Two Sets
Summary
The problem "Union of Two Sets" is about combining two sets into a single set containing all unique elements from both sets. This problem involves basic algorithmic concepts, including data structures and mathematical operations.
Detailed Explanation
To solve this problem, we can use the concept of union operation in set theory. The union of two sets A and B (denoted by A ∪ B) is a set that contains all elements from both sets, without duplicates. We can achieve this using a hash-based approach or sorting the arrays.
Here's a step-by-step breakdown of the solution:
- Initialize an empty set or array to store the union.
- Iterate through the first array and add each element to the set/array if it is not already present.
- Repeat step 2 for the second array.
- Return the resulting set/array, which contains all unique elements from both arrays.
Here's a diagram illustrating the process:
Array A: [1, 2, 3]
Array B: [2, 4, 5]
Union:
[1] (not present in Array B)
[2] (present in both arrays)
[3] (not present in Array B)
[4] (only present in Array B)
[5] (only present in Array B)
Resulting Union: [1, 2, 3, 4, 5]
The time complexity of this solution is O(n), where n is the total number of elements in both arrays. The space complexity is also O(n), as we need to store all unique elements.
Optimized Solutions
Java
import java.util.HashSet;
import java.util.Set;
public class UnionOfTwoSets {
public static int[] union(int[] arr1, int[] arr2) {
Set<Integer> set = new HashSet<>();
for (int num : arr1) {
set.add(num);
}
for (int num : arr2) {
set.add(num);
}
int[] result = new int[set.size()];
int i = 0;
for (Integer num : set) {
result[i++] = num;
}
return result;
}
}