Union and Intersection of Two Unsorted Arrays - Complete Tutorial

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Union of two arrays is an array having all distinct elements that are present in either array whereas Intersection of two arrays is an array containing distinct common elements between the two arrays. In this post, we will discuss about Union and Intersection of unsorted arrays.

To know about union and intersection of sorted input arrays, please refer to Union and Intersection of Two Sorted Arrays – Complete Tutorial.

Union of Two Arrays

Union of two unsorted arrays combines all unique elements from both arrays into a single array. The resultant array can be in any order. There are several methods to find the Union of two unsorted arrays based on whether the input arrays contain duplicate elements or not:

1. Union with Duplicates: When the input arrays may contain duplicate elements.
2. Union with Distinct Elements: When the input arrays consist of distinct elements only.

1. Union with Duplicates

We are given two arrays a[] and b[] and the task is to find the union of both the arrays. Union of two arrays is an array having all distinct elements that are present in either array. The input arrays may contain duplicates.

Examples:

Input : a[] = {1, 2, 3, 2, 1}, b[] = {3, 2, 2, 3, 3, 2}
Output : {3, 2, 1}
Explanation: Each element in the output either belongs to array a or array b, and we need to print only one occurrence of such elements.

Input : a[] = {1, 2, 3}, b[] = {4, 5, 6}
Output : {1, 2, 3, 4, 5, 6}
Explanation: Each element in the output either belongs to array a or array b, and we need to print only one occurrence of such elements.

The naive approach is to traverse both the arrays a[] and b[] and for each element, check if the element is present in the result or not. If not, then add this element to the result.

We can optimize this further in the expected approach by using a hash set and adding all the elements from both arrays. The hash set ensures that no duplicates are stored. After adding all the elements, we can create the final union array by iterating through the hash set.

To know more about the implementation, please refer to Union of Two Arrays.

2. Union with Distinct Elements

We are given two arrays a[] and b[] with distinct elements and the task is to find the union of both the arrays. Union of two arrays is an array having all distinct elements that are present in either array.

Examples:

Input: a[] = {1, 2, 3}, b[] = {5, 2, 7}
Output: {1, 2, 3, 5, 7}
Explanation: 1, 2, 3, 5 and 7 are the distinct elements present in either array.

Input: a[] = {2, 4, 5}, b[] = {1, 2, 3, 4, 5}
Output: {1, 2, 3, 4, 5}
Explanation: 1, 2, 3, 4 and 5 are the distinct elements present in either array.

The naive approach is to add all elements from the first array a[] to a result array. Then iterate through the second array b[] and add its elements to the result only if they were not present in a[].

The expected approach is to use a hash set and add all the elements from both arrays. The hash set ensures that no duplicates are stored. After adding all the elements, we can create the final union array by iterating through the hash set.

To know more about the implementation, please refer to Union of Two Arrays with Distinct Elements.

Intersection of Two Arrays

Intersection of two arrays combines all unique elements that are common to both arrays into a single array. The resultant array can be in any order. There are several methods to find the Intersection of two arrays based on whether the input arrays contain duplicate elements or not:

1. Intersection with Duplicates: When the input arrays may contain duplicate elements.
2. Intersection with Distinct Elements: When the input arrays consist of distinct elements only.

1. Intersection with Duplicates

We are given two arrays a[] and b[], the task is to return intersection of both the arrays in any order. Intersection of two arrays is an array having all common elements in both the arrays. The input arrays may contain duplicates.

Examples:

Input: a[] = {1, 2, 1, 3, 1}, b[] = {3, 1, 3, 4, 1}
Output: {1, 3}
Explanation: 1 and 3 are the only common elements and we need to print only one occurrence of common elements.

Input: a[] = {1, 2, 3}, b[] = {4, 5, 6}
Output: {}
Explanation: No common element in both the arrays.

The naive solution is to create an empty result array. For each element in a[], check if it exists in b[] and is not already in the result. If both conditions are met, add the element to the result.

We can optimize this further in the expected approach by using a hash set and inserting all elements of a[] into it. Then, traverse b[] and check if an element is in the hash set, add it to the result and remove it from the hash set to avoid duplicates.

To know more about the implementation, please refer to Intersection of two Arrays.

2. Intersection with Distinct Elements

Given two arrays a[] and b[] with distinct elements, the task is to find intersection (or common elements) of both the arrays. We can return the answer in any order.

Examples:

Input: a[] = { 5, 6, 2, 1, 4 }, b[] = { 7, 9, 4, 2 }
Output: { 2, 4 }
Explanation: The only common elements in both arrays are 2 and 4.

Input: a[] = { 4, 5, 2, 3 } , b[] = { 1, 7 }
Output: { }
Explanation: There are no common elements in array a[] and b[]

The naive approach is to traverse the first array a[] and for each element in a[], check whether it is present in array b[]. If present then add this element to result array.

We can optimize the approach further in the expected approach by using a hash set to store the elements of array a[]. Then, go through array b[] and check if each element is present in the hash set. If an element is found in the hash set, add it to the result array since it is common in both the arrays.

To know more about the implementation, please refer to Intersection of Two Arrays with Distinct Elements.

Conclusion

Finding the union and intersection of two arrays can be efficiently achieved using hash set as we are able to handle the duplicates and even check whether an element is present in hash set or not in constant time.

For the union of arrays, whether the input arrays contain duplicates or consist of distinct elements, maintaining a hash set allows us to efficiently combine all elements from both arrays without storing any duplicates. Similarly, for the intersection of arrays, we insert all elements of the first array into a hash set and then check the elements of second array, adding them to the result only if they exist in the hash set.