[LeetCode] 1000. Minimum Cost to Merge Stones
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 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.
Note:
1 <= stones.length <= 30
2 <= K <= 30
1 <= stones[i] <= 100
class Solution { private Integer[][][] dp; private int[] prefixSum; public int mergeStones(int[] stones, int K) { int n = stones.length; dp = new Integer[n][n][K + 1]; for(int i = 0; i < n; i++) { dp[i][i][1] = 0; } prefixSum = new int[n + 1]; for(int i = 1; i <= n; i++){ prefixSum[i] = prefixSum[i - 1] + stones[i - 1]; } int res = merge(stones, 0, n - 1, 1, K); return res == Integer.MAX_VALUE ? -1 : res; } private int merge(int[] stones, int start, int end, int numOfPiles, int K) { if((end - start + 1 - numOfPiles) % (K - 1) != 0) { return Integer.MAX_VALUE; } if(dp[start][end][numOfPiles] != null) { return dp[start][end][numOfPiles]; } int minCost = Integer.MAX_VALUE; if(numOfPiles == 1) { int mergeCost = merge(stones, start, end, K, K); if(mergeCost != Integer.MAX_VALUE) { minCost = mergeCost + prefixSum[end + 1] - prefixSum[start]; } } else { for(int mid = start; mid < end; mid++) { int leftMergeCost = merge(stones, start, mid, 1, K); if(leftMergeCost == Integer.MAX_VALUE) { continue; } int rightMergeCost = merge(stones, mid + 1, end, numOfPiles - 1, K); if(rightMergeCost == Integer.MAX_VALUE) { continue; } minCost = Math.min(minCost, leftMergeCost + rightMergeCost); } } dp[start][end][numOfPiles] = minCost; return minCost; } }
Related Problems
Stone Game (A special case of K == 2)