3219 - Minimum Cost for Cutting Cake II.

Hard

There is an m x n cake that needs to be cut into 1 x 1 pieces.

You are given integers m, n, and two arrays:

• horizontalCut of size m - 1, where horizontalCut[i] represents the cost to cut along the horizontal line i.

• verticalCut of size n - 1, where verticalCut[j] represents the cost to cut along the vertical line j.

In one operation, you can choose any piece of cake that is not yet a 1 x 1 square and perform one of the following cuts:

• Cut along a horizontal line i at a cost of horizontalCut[i].

• Cut along a vertical line j at a cost of verticalCut[j].

After the cut, the piece of cake is divided into two distinct pieces.

The cost of a cut depends only on the initial cost of the line and does not change.

Return the minimum total cost to cut the entire cake into 1 x 1 pieces.

Example 1:

Input: m = 3, n = 2, horizontalCut = 1,3, verticalCut = 5

Output: 13

Explanation:

• Perform a cut on the vertical line 0 with cost 5, current total cost is 5.

• Perform a cut on the horizontal line 0 on 3 x 1 subgrid with cost 1.

• Perform a cut on the horizontal line 0 on 3 x 1 subgrid with cost 1.

• Perform a cut on the horizontal line 1 on 2 x 1 subgrid with cost 3.

• Perform a cut on the horizontal line 1 on 2 x 1 subgrid with cost 3.

The total cost is 5 + 1 + 1 + 3 + 3 = 13.

Example 2:

Input: m = 2, n = 2, horizontalCut = 7, verticalCut = 4

Output: 15

Explanation:

• Perform a cut on the horizontal line 0 with cost 7.

• Perform a cut on the vertical line 0 on 1 x 2 subgrid with cost 4.

• Perform a cut on the vertical line 0 on 1 x 2 subgrid with cost 4.

The total cost is 7 + 4 + 4 = 15.

Constraints:

• <code>1 <= m, n <= 10⁵</code>

• horizontalCut.length == m - 1

• verticalCut.length == n - 1

• <code>1 <= horizontalCuti, verticalCuti<= 10³</code>