#1330

Hard

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Reverse Subarray To Maximize Array Value

Maximize the value of an array by reversing a subarray, focusing on greedy choices and invariant validation.

Problem Statement

Given an integer array nums, the value of the array is calculated as the sum of the absolute differences between consecutive elements, i.e., |nums[i] - nums[i + 1]| for all 0 <= i < nums.length - 1. You can perform one operation: reverse a single subarray of nums to maximize the array's value.

Your task is to find the maximum possible value of the array after reversing one subarray. Consider how the value changes when reversing different subarrays and ensure your solution is optimal.

Examples

Example 1

Input: nums = [2,3,1,5,4]

Output: 10

By reversing the subarray [3,1,5] the array becomes [2,5,1,3,4] whose value is 10.

Example 2

Input: nums = [2,4,9,24,2,1,10]

Output: 68

Example details omitted.

Constraints

2 <= nums.length <= 3 * 104
-105 <= nums[i] <= 105
The answer is guaranteed to fit in a 32-bit integer.

Solution Approach

Greedy Choice and Validation

A greedy approach works by iterating through the array to check how reversing each potential subarray affects the value. Track changes in the sum of absolute differences and compare the outcomes to find the optimal subarray to reverse.

Calculate Array Value Before and After Reversal

You need to calculate the initial value of the array, then for each subarray, compute the effect of reversal on the value. Focus on how the reversal alters adjacent elements and ensure the maximum value is achieved after the operation.

Edge Case Handling

Make sure to account for cases where no reversal results in a better value, or where the array is already maximized. Special handling for the smallest or largest arrays is also essential to avoid unnecessary calculations.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depend on the approach chosen. For a brute-force method, the time complexity would be O(n^2), but with a more optimized greedy approach, it can be reduced to O(n). Space complexity will vary accordingly, with the optimized solution using O(1) extra space, while brute-force solutions may require O(n) space for storing intermediate results.

What Interviewers Usually Probe

Evaluate the candidate's ability to apply greedy algorithms effectively.
Watch for the candidate's understanding of invariant validation and how to prove it's valid.
Check if the candidate optimizes the solution to handle larger inputs efficiently.

Common Pitfalls or Variants

Common pitfalls

Failing to correctly calculate the value of the array before and after reversal can lead to incorrect results.
Misunderstanding the impact of the reversed subarray on adjacent elements, leading to inefficient or incorrect solutions.
Overcomplicating the problem by attempting brute-force methods when a greedy solution is more efficient.

Follow-up variants

Consider implementing the solution for arrays with only two elements.
Extend the problem to handle arrays with additional constraints, like larger numbers or specific patterns.
Explore ways to modify the problem so that multiple subarrays can be reversed for optimization.

FAQ

What is the pattern for solving the Reverse Subarray To Maximize Array Value problem?

The pattern involves greedy choice and invariant validation, where you reverse a subarray and validate how it maximizes the array's value.

How do I optimize my approach for larger arrays in the Reverse Subarray To Maximize Array Value problem?

To optimize for larger arrays, use a greedy approach that minimizes redundant calculations and ensures efficient handling of large inputs.

What common mistakes should I avoid when solving the Reverse Subarray To Maximize Array Value problem?

Common mistakes include incorrect value calculation before and after reversal, overlooking the impact of adjacent elements, and relying on inefficient brute-force methods.

Can I reverse more than one subarray in the Reverse Subarray To Maximize Array Value problem?

The problem specifies reversing exactly one subarray. Modifying it to handle multiple reversals would be a variant of the problem.

What should I do if the Reverse Subarray To Maximize Array Value problem seems too complex?

Break down the problem by focusing on the greedy approach and carefully considering the impact of each reversal on the array's value.

terminal

Solution

Solution 1: Classification Discussion + Enumeration

According to the problem description, we need to find the maximum value of the array $\sum_{i=0}^{n-2} |a_i - a_{i+1}|$ when reversing a subarray once.

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class Solution:
    def maxValueAfterReverse(self, nums: List[int]) -> int:
        ans = s = sum(abs(x - y) for x, y in pairwise(nums))
        for x, y in pairwise(nums):
            ans = max(ans, s + abs(nums[0] - y) - abs(x - y))
            ans = max(ans, s + abs(nums[-1] - x) - abs(x - y))
        for k1, k2 in pairwise((1, -1, -1, 1, 1)):
            mx, mi = -inf, inf
            for x, y in pairwise(nums):
                a = k1 * x + k2 * y
                b = abs(x - y)
                mx = max(mx, a - b)
                mi = min(mi, a + b)
            ans = max(ans, s + max(mx - mi, 0))
        return ans

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