Leetcode #2786: Visit Array Positions to Maximize Score
In this guide, we solve Leetcode #2786 Visit Array Positions to Maximize 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
You are given a 0-indexed integer array nums and a positive integer x. You are initially at position 0 in the array and you can visit other positions according to the following rules: If you are currently in position i, then you can move to any position j such that i < j.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Array, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: nums = [2,3,6,1,9,2], x = 5
Output: 13
Explanation: We can visit the following positions in the array: 0 -> 2 -> 3 -> 4.
The corresponding values are 2, 6, 1 and 9. Since the integers 6 and 1 have different parities, the move 2 -> 3 will make you lose a score of x = 5.
The total score will be: 2 + 6 + 1 + 9 - 5 = 13.
Python Solution
class Solution:
def maxScore(self, nums: List[int], x: int) -> int:
f = [-inf] * 2
f[nums[0] & 1] = nums[0]
for v in nums[1:]:
f[v & 1] = max(f[v & 1], f[v & 1 ^ 1] - x) + v
return max(f)
Complexity
The time complexity is , where is the length of the array . The space complexity is .
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.