Problem Description
You are given a 0-indexed array nums consisting of positive integers. You can perform the operation of merging adjacent elements in the array any number of times, where you choose an index i such that 0 <= i < nums.length - 1 and nums[i] <= nums[i + 1]. The operation consists of replacing nums[i + 1] with nums[i] + nums[i + 1] and deleting nums[i] from the array. The goal is to return the value of the largest element that can possibly be obtained in the final array.
Key Insights
- The merging operation can increase the value of adjacent elements, leading to a larger final element.
- We must ensure that the merging is done in a way that respects the condition
nums[i] <= nums[i + 1]. - The optimal strategy is to always merge the smallest available element with the next larger or equal element to maximize the final outcome.
- The problem can be effectively solved using a greedy approach to continuously combine elements.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
The problem can be solved using a greedy algorithm. We iterate through the array and maintain a running sum of the current maximum possible value. Whenever we encounter a value that can be merged with the next one (i.e., nums[i] <= nums[i + 1]), we add it to the sum of the next value and continue this until we reach the end of the array. The final value will be the largest element that can be obtained.
We can achieve this with a single traversal of the array, ensuring that we efficiently calculate the maximum possible sum without needing additional space for a new array.