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1000. Minimum Cost to Merge Stones

Difficulty Topics

Description

There are n piles of stones arranged in a row. The ith 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.

Return the minimum cost to merge all piles of stones into one pile. If it is impossible, return -1.

 

Example 1:

Input: stones = [3,2,4,1], k = 2
Output: 20
Explanation: We start with [3, 2, 4, 1].
We merge [3, 2] for a cost of 5, and we are left with [5, 4, 1].
We merge [4, 1] for a cost of 5, and we are left with [5, 5].
We merge [5, 5] for a cost of 10, and we are left with [10].
The total cost was 20, and this is the minimum possible.

Example 2:

Input: stones = [3,2,4,1], k = 3
Output: -1
Explanation: After any merge operation, there are 2 piles left, and we can't merge anymore.  So the task is impossible.

Example 3:

Input: stones = [3,5,1,2,6], k = 3
Output: 25
Explanation: We start with [3, 5, 1, 2, 6].
We merge [5, 1, 2] for a cost of 8, and we are left with [3, 8, 6].
We merge [3, 8, 6] for a cost of 17, and we are left with [17].
The total cost was 25, and this is the minimum possible.

 

Constraints:

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

Solution

minimum-cost-to-merge-stones.py
class Solution:
    def mergeStones(self, stones: List[int], k: int) -> int:
        n = len(stones)
        if (n - 1) % (k - 1): return -1
        prefix = [0] + list(accumulate(stones))

        @cache
        def go(i, j):
            if (j - i + 1) < k: return 0

            res = min(go(i, mid) + go(mid + 1, j) for mid in range(i, j, k - 1))

            if (j - i) % (k - 1) == 0:
                res += prefix[j + 1] - prefix[i]

            return res

        return go(0, n - 1)