mediumArraysPattern: Fundamentals
Subarray Rotation Checker Solution
Problem Statement
Given an array of integers and two pointers, left and right, representing a subarray, determine if there exists a rotation of the subarray such that the sum of the absolute differences between consecutive elements is minimized.
Examples
Example 1:
Input:[1, 2, 3, 4, 5], left = 1, right = 3
Output:true
Explanation: One possible rotation is [2, 3, 4, 1] which has a smaller sum of absolute differences compared to the original subarray [2, 3, 4].
Example 2:
Input:[1, 1, 1, 1, 1], left = 0, right = 4
Output:true
Explanation: The subarray [1, 1, 1, 1, 1] is already optimized as the sum of absolute differences between consecutive elements is 0.
Constraints
- 1 <= array length <= 10^5
- 0 <= left < right < array length
- All elements in the array are integers between -10^5 and 10^5
- The input array is not empty
Time: O(n) Space: O(1)
An optimized approach involves utilizing the properties of the sum of absolute differences and rotational symmetry to minimize the number of calculations required. By considering how the sum changes with each rotation, we can find an efficient algorithm to determine the existence of a rotation that minimizes the sum of absolute differences.
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