Minimum Cost to Merge Stones

arraydynamic programmingprefix sum

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.

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

Examples

Example 1

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

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming