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Problem 19: Minimal Fusion Cost

Problem Statement

There are n piles of stones arranged in a row. The i-th pile has stones[i] stones. A move consists of merging exactly k consecutive piles into one pile, and the cost of this move is equal to the total number of stones in these k piles. Find the minimum cost to merge all piles into one pile. If it is impossible, return -1.

Input Format

  • An array of integers stones.
  • An integer k.

Output Format

  • An integer representing the minimum cost.

Constraints

  • 1 <= stones.length <= 30
  • 2 <= k <= 30
  • 1 <= stones[i] <= 100

Example

Input: stones = [3, 2, 4, 1], k = 2
Output: 20
Explanation:

  • Merge [3, 2] for cost 5. Result: [5, 4, 1]
  • Merge [4, 1] for cost 5. Result: [5, 5]
  • Merge [5, 5] for cost 10. Result: [10]
  • Total cost = 5 + 5 + 10 = 20.