Leetcode #2898: Maximum Linear Stock Score
In this guide, we solve Leetcode #2898 Maximum Linear Stock Score in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given a 1-indexed integer array prices, where prices[i] is the price of a particular stock on the ith day, your task is to select some of the elements of prices such that your selection is linear. A selection indexes, where indexes is a 1-indexed integer array of length k which is a subsequence of the array [1, 2, ..., n], is linear if: For every 1 < j <= k, prices[indexes[j]] - prices[indexes[j - 1]] == indexes[j] - indexes[j - 1].
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Array, Hash Table
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: prices = [1,5,3,7,8]
Output: 20
Explanation: We can select the indexes [2,4,5]. We show that our selection is linear:
For j = 2, we have:
indexes[2] - indexes[1] = 4 - 2 = 2.
prices[4] - prices[2] = 7 - 5 = 2.
For j = 3, we have:
indexes[3] - indexes[2] = 5 - 4 = 1.
prices[5] - prices[4] = 8 - 7 = 1.
The sum of the elements is: prices[2] + prices[4] + prices[5] = 20.
It can be shown that the maximum sum a linear selection can have is 20.
Python Solution
class Solution:
def maxScore(self, prices: List[int]) -> int:
cnt = Counter()
for i, x in enumerate(prices):
cnt[x - i] += x
return max(cnt.values())
Complexity
The time complexity is , and the space complexity is , where is the length of the array. The space complexity is , where is the length of the array.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.