How to Solve Minimum Cost for Cutting Cake I Problem
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Minimum Cost for Cutting Cake I
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 hor...
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Understanding the Minimum Cost for Cutting Cake I Problem
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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.
Minimum Cost for Cutting Cake I
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Examples
m = 3, n = 2, horizontalCut = [1,3], verticalCut = [5]13Perform 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.
m = 2, n = 2, horizontalCut = [7], verticalCut = [4]15Perform 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 <= 20horizontalCut.length == m - 1verticalCut.length == n - 11 <= horizontalCut[i], verticalCut[i] <= 103How Interview Coder Helps with Leetcode Problems
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