Find Indices With Index and Value Difference II

Problem Description

You are given a 0-indexed integer array nums having length n, an integer indexDifference, and an integer valueDifference. Your task is to find two indices i and j, both in the range [0, n - 1], that satisfy the following conditions:

• abs(i - j) >= indexDifference
• abs(nums[i] - nums[j]) >= valueDifference

Return an integer array answer, where answer = [i, j] if there are two such indices, and answer = [-1, -1] otherwise.

Key Insights

• The problem requires finding pairs of indices that satisfy both distance constraints on indices and values.
• The constraints on the index and value differences allow for a two-pointer or sliding window approach to minimize the search space.
• The solution must efficiently handle up to 10^5 elements in the array.

Space and Time Complexity

Time Complexity: O(n) Space Complexity: O(1)

Solution

To solve the problem, we can use a nested loop approach with early exits when conditions are violated, or we can utilize a two-pointer technique to check pairs of indices while maintaining the conditions. We traverse through the array and for each element, we search for a valid pair that satisfies the index and value differences.

Data structures used:

• An integer array to store the indices.
• We can utilize basic loop constructs to implement the searches.

Algorithm:

1. Iterate through the array with an outer loop for index i.
2. For each i, use an inner loop to check subsequent indices j where j >= i + indexDifference.
3. For each pair (i, j), check if abs(nums[i] - nums[j]) >= valueDifference.
4. If a valid pair is found, return it. If no valid pairs are found after the loops, return [-1, -1].

Code Solutions