Remove One Element to Make the Array Strictly Increasing

Problem Description

Given a 0-indexed integer array nums, return true if it can be made strictly increasing after removing exactly one element, or false otherwise. If the array is already strictly increasing, return true.

The array nums is strictly increasing if nums[i - 1] < nums[i] for each index (1 <= i < nums.length).

Key Insights

• The array is strictly increasing if each element is less than the next one.
• Removing one element can potentially fix a violation in the strictly increasing condition.
• We need to check the array for at most one violation of the strictly increasing condition.
• If a violation occurs, we have two choices: remove the current element or the next element.

Space and Time Complexity

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

Solution

We can use a single pass through the array to check for violations of the strictly increasing condition. We maintain a count of violations. If we encounter more than one violation, we return false. If there is exactly one violation, we check if removing either of the two elements involved in the violation results in a strictly increasing array.

1. Traverse the array and check each pair of adjacent elements.
2. Count the number of violations where nums[i] >= nums[i + 1].
3. If there is more than one violation, return false.
4. If there is one violation, check the two possible scenarios by removing one of the elements around the violation.

Code Solutions