1000. Minimum Cost to Merge Stones

https://leetcode.com/problems/minimum-cost-to-merge-stones

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

ac