1000. Minimum Cost to Merge Stones

Hard

2.1K

98

There are `n`

piles of `stones`

arranged in a row. The `i`

pile has ^{th}`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 = 2Output:20Explanation: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 = 3Output:-1Explanation: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 = 3Output:25Explanation: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`

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