LeetCode - Maximum Area of a Piece of Cake After Horizontal and Vertical Cuts

문제 설명

You are given a rectangular cake of size h x w and two arrays of integers horizontalCuts and verticalCuts where:

horizontalCuts[i] is the distance from the top of the rectangular cake to the ith horizontal cut and similarly, and
verticalCuts[j] is the distance from the left of the rectangular cake to the jth vertical cut.
Return the maximum area of a piece of cake after you cut at each horizontal and vertical position provided in the arrays horizontalCuts and verticalCuts. Since the answer can be a large number, return this modulo 109 + 7.

입출력 예시

Example 1:

Input: h = 5, w = 4, horizontalCuts = [1,2,4], verticalCuts = [1,3]
Output: 4
Explanation: The figure above represents the given rectangular cake. Red lines are the horizontal and vertical cuts. After you cut the cake, the green piece of cake has the maximum area.

Example 2:

Input: h = 5, w = 4, horizontalCuts = [3,1], verticalCuts = [1]
Output: 6
Explanation: The figure above represents the given rectangular cake. Red lines are the horizontal and vertical cuts. After you cut the cake, the green and yellow pieces of cake have the maximum area.

제약사항

Input: h = 5, w = 4, horizontalCuts = [3], verticalCuts = [3]
Output: 9

Solution

[전략]

• 세로선은 가로의 구역을 분할한다.
• 가로선은 세로의 구역을 분할한다.

1. 각 세로선과 가로선을 오름차순으로 정렬
2. 0과 h(높이) 사이에 가로선을 두고, [0, horizontal[0], ... ,horizontal[horizontalCuts.length-1], h] 각 경계와 경계 사이 가장 구간이 maxHeight가 된다.
3. 0과 w(너비) 사이에 세로선을 두고, [0, verticalCuts[0], ... ,verticalCuts[verticalCuts.length-1], w] 각 경계와 경계 사이 가장 구간이 maxWidth가 된다.
4. maxHeight*maxWidth => maxArea

import java.util.*;

class Solution {
    public int maxArea(int h, int w, int[] horizontalCuts, int[] verticalCuts) {

        int moduloVal = 1000000007;
        Arrays.sort(horizontalCuts);
        Arrays.sort(verticalCuts);

        int maxHeight = h - horizontalCuts[horizontalCuts.length - 1];
        maxHeight = Math.max(maxHeight, horizontalCuts[0]);
        for (int i = 0; i < horizontalCuts.length - 1; i++) {
            int diff = horizontalCuts[i + 1] - horizontalCuts[i];
            maxHeight = Math.max(maxHeight, diff);
        }

        int maxWidth = w - verticalCuts[verticalCuts.length - 1];
        maxWidth = Math.max(maxWidth, verticalCuts[0]);
        for (int i = 0; i < verticalCuts.length - 1; i++) {
            int diff = verticalCuts[i + 1] - verticalCuts[i];
            maxWidth = Math.max(maxWidth, diff);
        }
        maxWidth = maxWidth % moduloVal;
        maxHeight = maxHeight % moduloVal;

        long product=((long) maxWidth*(long) maxHeight)%(long)moduloVal;
        return (int) product;
    }
}