LeetCode 3218: Minimum Cost for Cutting Cake I Solution

Master LeetCode problem 3218 (Minimum Cost for Cutting Cake I), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

3218. Minimum Cost for Cutting Cake I

Medium

Array Dynamic Programming Greedy Sorting

Problem Explanation

Explanation

To solve this problem, we can first sort the horizontal and vertical cut costs in descending order. Then, we iterate over the sorted costs and calculate the total cost of each cut. We maintain the current number of horizontal and vertical cuts made so far and multiply it with the current cut cost to get the total cost. Finally, we return the sum of all these total costs as the minimum total cost for cutting the cake into 1 x 1 pieces.

Sort the horizontal and vertical cut costs in descending order.
Initialize variables to keep track of horizontal and vertical cuts made so far.
Iterate over the sorted costs to calculate total cost for each cut.
Return the sum of all total costs as the minimum total cost.

Time complexity: O((m-1)log(m-1) + (n-1)log(n-1))
Space complexity: O(1)

Solution Code

class Solution {
    public int minCost(int m, int n, int[] horizontalCuts, int[] verticalCuts) {
        Arrays.sort(horizontalCuts);
        Arrays.sort(verticalCuts);
        
        long hMax = Math.max(horizontalCuts[0], m - horizontalCuts[horizontalCuts.length - 1]);
        long vMax = Math.max(verticalCuts[0], n - verticalCuts[verticalCuts.length - 1]);
        
        for (int i = 1; i < horizontalCuts.length; i++) {
            hMax = Math.max(hMax, horizontalCuts[i] - horizontalCuts[i - 1]);
        }
        
        for (int i = 1; i < verticalCuts.length; i++) {
            vMax = Math.max(vMax, verticalCuts[i] - verticalCuts[i - 1]);
        }
        
        return (int)((hMax * vMax) % 1000000007);
    }
}

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