{ "data": { "question": { "questionId": "3214", "questionFrontendId": "2943", "categoryTitle": "Algorithms", "boundTopicId": 2539398, "title": "Maximize Area of Square Hole in Grid", "titleSlug": "maximize-area-of-square-hole-in-grid", "content": "
There is a grid with n + 2
horizontal bars and m + 2
vertical bars, and initially containing 1 x 1
unit cells.
The bars are 1-indexed.
\n\nYou are given the two integers, n
and m
.
You are also given two integer arrays: hBars
and vBars
.
hBars
contains distinct horizontal bars in the range [2, n + 1]
.vBars
contains distinct vertical bars in the range [2, m + 1]
.You are allowed to remove bars that satisfy any of the following conditions:
\n\nhBars
.vBars
.Return an integer denoting the maximum area of a square-shaped hole in the grid after removing some bars (possibly none).
\n\n\n
Example 1:
\n\n\nInput: n = 2, m = 1, hBars = [2,3], vBars = [2]\nOutput: 4\nExplanation: The left image shows the initial grid formed by the bars.\nThe horizontal bars are in the range [1,4], and the vertical bars are in the range [1,3].\nIt is allowed to remove horizontal bars [2,3] and the vertical bar [2].\nOne way to get the maximum square-shaped hole is by removing horizontal bar 2 and vertical bar 2.\nThe resulting grid is shown on the right.\nThe hole has an area of 4.\nIt can be shown that it is not possible to get a square hole with an area more than 4.\nHence, the answer is 4.\n\n\n
Example 2:
\n\n\nInput: n = 1, m = 1, hBars = [2], vBars = [2]\nOutput: 4\nExplanation: The left image shows the initial grid formed by the bars.\nThe horizontal bars are in the range [1,3], and the vertical bars are in the range [1,3].\nIt is allowed to remove the horizontal bar [2] and the vertical bar [2].\nTo get the maximum square-shaped hole, we remove horizontal bar 2 and vertical bar 2.\nThe resulting grid is shown on the right.\nThe hole has an area of 4.\nHence, the answer is 4, and it is the maximum possible.\n\n\n
Example 3:
\n\n\nInput: n = 2, m = 3, hBars = [2,3], vBars = [2,3,4]\nOutput: 9\nExplanation: The left image shows the initial grid formed by the bars.\nThe horizontal bars are in the range [1,4], and the vertical bars are in the range [1,5].\nIt is allowed to remove horizontal bars [2,3] and vertical bars [2,3,4].\nOne way to get the maximum square-shaped hole is by removing horizontal bars 2 and 3, and vertical bars 3 and 4.\nThe resulting grid is shown on the right.\nThe hole has an area of 9.\nIt can be shown that it is not possible to get a square hole with an area more than 9.\nHence, the answer is 9.\n\n\n
\n
Constraints:
\n\n1 <= n <= 109
1 <= m <= 109
1 <= hBars.length <= 100
2 <= hBars[i] <= n + 1
1 <= vBars.length <= 100
2 <= vBars[i] <= m + 1
hBars
are distinct.vBars
are distinct.给你一个网格图,由 n + 2
条 横线段 和 m + 2
条 竖线段 组成,一开始所有区域均为 1 x 1
的单元格。
所有线段的编号从 1 开始。
\n\n给你两个整数 n
和 m
。
同时给你两个整数数组 hBars
和 vBars
。
hBars
包含区间 [2, n + 1]
内 互不相同 的横线段编号。vBars
包含 [2, m + 1]
内 互不相同的 竖线段编号。如果满足以下条件之一,你可以 移除 两个数组中的部分线段:
\n\nhBars
中的值。vBars
中的值。请你返回移除一些线段后(可能不移除任何线段),剩余网格图中 最大正方形 空洞的面积,正方形空洞的意思是正方形 内部 不含有任何线段。
\n\n\n\n
示例 1:
\n\n\n输入:n = 2, m = 1, hBars = [2,3], vBars = [2]\n输出:4\n解释:左边的图是一开始的网格图。\n横线编号的范围是区间 [1,4] ,竖线编号的范围是区间 [1,3] 。\n可以移除的横线段为 [2,3] ,竖线段为 [2] 。\n一种得到最大正方形面积的方法是移除横线段 2 和竖线段 2 。\n操作后得到的网格图如右图所示。\n正方形空洞面积为 4。\n无法得到面积大于 4 的正方形空洞。\n所以答案为 4 。\n\n\n
示例 2:
\n\n\n输入:n = 1, m = 1, hBars = [2], vBars = [2]\n输出:4\n解释:左边的图是一开始的网格图。\n横线编号的范围是区间 [1,3] ,竖线编号的范围是区间 [1,3] 。\n可以移除的横线段为 [2] ,竖线段为 [2] 。\n一种得到最大正方形面积的方法是移除横线段 2 和竖线段 2 。\n操作后得到的网格图如右图所示。\n正方形空洞面积为 4。\n无法得到面积大于 4 的正方形空洞。\n所以答案为 4 。\n\n\n
示例 3:
\n\n\n输入:n = 2, m = 3, hBars = [2,3], vBars = [2,3,4]\n输出:9\n解释:左边的图是一开始的网格图。\n横线编号的范围是区间 [1,4] ,竖线编号的范围是区间 [1,5] 。\n可以移除的横线段为 [2,3] ,竖线段为 [2,3,4] 。\n一种得到最大正方形面积的方法是移除横线段 2、3 和竖线段 3、4 。\n操作后得到的网格图如右图所示。\n正方形空洞面积为 9。\n无法得到面积大于 9 的正方形空洞。\n所以答案为 9 。\n\n\n
\n\n
提示:
\n\n1 <= n <= 109
1 <= m <= 109
1 <= hBars.length <= 100
2 <= hBars[i] <= n + 1
1 <= vBars.length <= 100
2 <= vBars[i] <= m + 1
hBars
中的值互不相同。vBars
中的值互不相同。hBars
and vBars
and consider them separately.",
"Compute the longest sequence of consecutive integer values in each array, denoted as [hx, hy]
and [vx, vy]
, respectively.",
"The maximum square length we can get is min(hy - hx + 2, vy - vx + 2)
.",
"Square the maximum square length to get the area."
],
"solution": null,
"status": null,
"sampleTestCase": "2\n1\n[2,3]\n[2]",
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