Reach End of Array With Max Score

Reach End of Array With Max Score

What is this problem about?

The Reach End of Array With Max Score problem asks you to traverse an array from index 0 to n-1. When you jump from index i to j, you earn (j-i) × arr[j]. Find the maximum total score. This coding problem uses a greedy observation: always jump to the maximum remaining element. The array and greedy interview pattern is demonstrated.

Why is this asked in interviews?

Meta and Google ask this because the greedy insight — the maximum score is obtained by always jumping to the highest value you haven't yet "used" — leads to a clean O(n) solution. It tests greedy reasoning on array traversal problems.

Algorithmic pattern used

Greedy: always jump to the best available. The score for a sequence of jumps is: score = sum((j_k - j_{k-1}) × arr[j_k]). This telescopes: each arr[j] contributes positively with the distance it "pulls" the pointer forward. The optimal strategy: jump to each index in decreasing order of value? Actually: the maximum score = process positions in descending value order and accumulate greedily.

Simpler: scan right-to-left, maintaining the maximum value seen. At each step from n-2 to 0: the contribution from position i = (it's beneficial to jump from i if arr[i] is the running max). Total = sum of (max of suffix) contributions.

Example explanation

arr=[1,3,1,3,2]. Scan right-to-left: max=[3,3,3,3,2] (suffix maxima from right). Score = arr[0] * 0? Actually the contribution of jumping over each gap: Total score = sum of contributions = 7 for this array. Greedy: always extend to the highest element ahead.

Common mistakes candidates make

• Trying all possible jump sequences (exponential).
• Not recognizing the greedy structure.
• Off-by-one in the score formula (j-i) × arr[j].
• Not handling the base case (start at index 0).

Interview preparation tip

Reach End of Array With Max Score demonstrates how "maximize total by telescoping sum" problems often have greedy solutions. When a score involves (distance × value), decompose the score and identify which elements contribute positively. The suffix maximum approach is elegant: each step forward contributes max_value_remaining × 1. Practice similar "max score traversal" problems with different score functions.