Problem Description
You are given an integer array nums of length n. Your goal is to start at index 0 and reach index n - 1. You can only jump to indices greater than your current index. The score for a jump from index i to index j is calculated as (j - i) * nums[i]. Return the maximum possible total score by the time you reach the last index.
Key Insights
- You can only jump to indices greater than the current index.
- The score for each jump is dependent on the distance jumped and the value at the starting index.
- A greedy approach can be used to maximize the score by choosing the best jump options at each step.
- Dynamic programming can help keep track of maximum scores up to each index.
Space and Time Complexity
Time Complexity: O(n^2) in a naive approach; O(n) with a more optimized method using a stack.
Space Complexity: O(n) for storing scores or stack data.
Solution
To solve this problem, we can use a greedy approach combined with a stack to keep track of the best possible scores as we iterate through the array. We maintain a stack that helps us determine the maximum score obtainable by jumping from the current index to the future indices. The algorithm iterates through the nums array and updates scores based on the jumps that can be made, ensuring that we always choose the option that maximizes the score at each step.