Largest Combined Array

Given two arrays a[] and b[] of size n (each containing distinct integers, but possibly sharing some), construct an array res[] of size n that contains the largest n unique values from both arrays combined, where elements taken from a[] appear first in their original order, followed by elements from b[] in their original order, and no value appears more than once.

Examples:

Input: a[] = [9, 7, 2, 3, 6], b[] = [7, 4, 8, 0, 1]
Output: [9, 7, 6, 4, 8]
Explanation:
Largest 5 unique elements from both arrays: {9, 8, 7, 6, 4}.
From a[], take elements in order that are in top 5: 9, 7, 6.
From b[], take remaining top elements: 4, 8.
Resulting array: [9, 7, 6, 4, 8].

Input: a[] = [6, 7, 5, 3], b[] = [5, 6, 2, 9]
Output: [6, 7, 5, 9]
Explanation:
Largest 4 unique elements from both arrays: {9, 7, 6, 5}.
From a[], take elements in order: 6, 7, 5.
From b[], add remaining top element: 9.
Resulting array: [6, 7, 5, 9].

[Approach] Using Set - O(n log(n)) Time and O(n) Space

We can use a set (or similar data structure) that always maintains the n largest unique elements while scanning both arrays. As we insert elements from a[] and then b[], remove the smallest whenever the set size exceeds n. After processing both arrays, this set represents the final chosen values.

To build the result, traverse a[] first and pick the elements that appear in the set, then traverse b[] for the remaining ones. This keeps the largest possible n values and preserves the required order: elements from a[] first, followed by elements from b[].

9 7 6 4 8