Divide an Array Into Subarrays With Minimum Cost II
You are given a 0-indexed array of integers nums of length n, and two positive integers k and dist.
The cost of an array is the value of its first element. For example, the cost of [1, 2, 3] is 1 while the cost of [3, 4, 1] is 3.
You need to divide nums into k disjoint contiguous subarrays, such that the difference between the starting index of the second subarray and the starting index of the kth subarray should be less than or equal to dist.
In other words, if you divide nums into the subarrays nums[0..(i1 - 1)], nums[i1..(i2 - 1)], ..., nums[ik-1..(n - 1)], then ik-1 - i1 <= dist.
Return the minimum possible sum of the cost of these subarrays.
Example 1
Input
nums = [1,3,2,6,4,2], k = 3, dist = 3Output
5The best valid division is [1,3], [2,6,4], and [2], giving total cost 1 + 2 + 2 = 5.
Example 2
Input
nums = [10,1,2,2,2,1], k = 4, dist = 3Output
15The best valid division is [10], [1], [2], and [2,2,1], giving total cost 10 + 1 + 2 + 2 = 15.
Constraints
- 3 <= n <= 10^5
- 1 <= nums[i] <= 10^9
- 3 <= k <= n
- k - 2 <= dist <= n - 2