{ "data": { "question": { "questionId": "3262", "questionFrontendId": "2971", "categoryTitle": "Algorithms", "boundTopicId": 2575515, "title": "Find Polygon With the Largest Perimeter", "titleSlug": "find-polygon-with-the-largest-perimeter", "content": "
You are given an array of positive integers nums
of length n
.
A polygon is a closed plane figure that has at least 3
sides. The longest side of a polygon is smaller than the sum of its other sides.
Conversely, if you have k
(k >= 3
) positive real numbers a1
, a2
, a3
, ..., ak
where a1 <= a2 <= a3 <= ... <= ak
and a1 + a2 + a3 + ... + ak-1 > ak
, then there always exists a polygon with k
sides whose lengths are a1
, a2
, a3
, ..., ak
.
The perimeter of a polygon is the sum of lengths of its sides.
\n\nReturn the largest possible perimeter of a polygon whose sides can be formed from nums
, or -1
if it is not possible to create a polygon.
\n
Example 1:
\n\n\nInput: nums = [5,5,5]\nOutput: 15\nExplanation: The only possible polygon that can be made from nums has 3 sides: 5, 5, and 5. The perimeter is 5 + 5 + 5 = 15.\n\n\n
Example 2:
\n\n\nInput: nums = [1,12,1,2,5,50,3]\nOutput: 12\nExplanation: The polygon with the largest perimeter which can be made from nums has 5 sides: 1, 1, 2, 3, and 5. The perimeter is 1 + 1 + 2 + 3 + 5 = 12.\nWe cannot have a polygon with either 12 or 50 as the longest side because it is not possible to include 2 or more smaller sides that have a greater sum than either of them.\nIt can be shown that the largest possible perimeter is 12.\n\n\n
Example 3:
\n\n\nInput: nums = [5,5,50]\nOutput: -1\nExplanation: There is no possible way to form a polygon from nums, as a polygon has at least 3 sides and 50 > 5 + 5.\n\n\n
\n
Constraints:
\n\n3 <= n <= 105
1 <= nums[i] <= 109
给你一个长度为 n
的 正 整数数组 nums
。
多边形 指的是一个至少有 3
条边的封闭二维图形。多边形的 最长边 一定 小于 所有其他边长度之和。
如果你有 k
(k >= 3
)个 正 数 a1
,a2
,a3
, ...,ak
满足 a1 <= a2 <= a3 <= ... <= ak
且 a1 + a2 + a3 + ... + ak-1 > ak
,那么 一定 存在一个 k
条边的多边形,每条边的长度分别为 a1
,a2
,a3
, ...,ak
。
一个多边形的 周长 指的是它所有边之和。
\n\n请你返回从 nums
中可以构造的 多边形 的 最大周长 。如果不能构造出任何多边形,请你返回 -1
。
\n\n
示例 1:
\n\n\n输入:nums = [5,5,5]\n输出:15\n解释:nums 中唯一可以构造的多边形为三角形,每条边的长度分别为 5 ,5 和 5 ,周长为 5 + 5 + 5 = 15 。\n\n\n
示例 2:
\n\n\n输入:nums = [1,12,1,2,5,50,3]\n输出:12\n解释:最大周长多边形为五边形,每条边的长度分别为 1 ,1 ,2 ,3 和 5 ,周长为 1 + 1 + 2 + 3 + 5 = 12 。\n我们无法构造一个包含变长为 12 或者 50 的多边形,因为其他边之和没法大于两者中的任何一个。\n所以最大周长为 12 。\n\n\n
示例 3:
\n\n\n输入:nums = [5,5,50]\n输出:-1\n解释:无法构造任何多边形,因为多边形至少要有 3 条边且 50 > 5 + 5 。\n\n\n
\n\n
提示:
\n\n3 <= n <= 105
1 <= nums[i] <= 109
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