Maximize Consecutive Elements in an Array After Modification

Problem Description

You are given a 0-indexed array nums consisting of positive integers. Initially, you can increase the value of any element in the array by at most 1. After that, you need to select one or more elements from the final array such that those elements are consecutive when sorted in increasing order. Return the maximum number of elements that you can select.

Key Insights

• You can increase any element in the array by at most 1, allowing some flexibility in creating consecutive sequences.
• Consecutive elements can be identified by checking the difference between the minimum and maximum values in a selected subset.
• A sliding window or two-pointer technique can be used to efficiently find the longest sequence of consecutive integers.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array. Space Complexity: O(n) - for storing the sorted version of the array.

Solution

To solve the problem, we can follow these steps:

1. First, sort the array nums to handle the elements in increasing order.
2. Use a sliding window (or two-pointer technique) to find the longest subsequence where the maximum element minus the minimum element is less than or equal to the size of that subsequence.
3. While iterating through the sorted array, consider that we can increase a number by 1, which allows us to adjust our range slightly.
4. Count the maximum length of the valid subsequence.

The main data structure used is an array (or list) to store the sorted values, and the algorithm is a two-pointer technique which helps in efficiently checking for valid consecutive sequences.

Code Solutions