Solution: Next Greater Element I

Explore how to efficiently find the next greater elements for values in one array relative to their positions in another using hash maps and monotonic stacks. Understand and implement an optimized algorithm that improves time complexity by avoiding naive linear searches and apply these concepts to coding interview challenges involving arrays and hash maps.

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Statement
Solution
- Naive approach
- Optimized approach using hash map

Statement

Given the two distinct integer arrays, nums1 and nums2, where nums1 is a subset of nums2, find all the next greater elements for nums1 values in the corresponding places of nums2.

In general, the next greater element of an element, $x$ , in an array is the first greater element present on the right side of $x$ in the same array. However, in the context of this problem, for each element $x$ in nums1, find the next greater element present on the right side of $x$ in nums2 and store it in the ans array. If there is no such element, store $-1$ for this number. The ans array should be of the same length as nums1, and the order of the elements in the ans array should correspond to the order of the elements in nums1.

Return the ans array after finding the next greater elements.

Note: The input data may or may not be sorted.

Constraints:

$1 \leq$ nums1.length $\leq$ nums2.length $\leq 10^3$

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