Minimum Cost for Cutting Cake I

arraytwo pointersdynamic programming

Problem Statement

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.

Examples

Example 1

Input: m = 3, n = 2, horizontalCut = [1,3], verticalCut = [5]
Output: 13
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
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

1 <= m, n <= 20

horizontalCut.length == m - 1

verticalCut.length == n - 1

1 <= horizontalCut[i], verticalCut[i] <= 10 ^3

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicTwo Pointers