{ "data": { "question": { "questionId": "1723", "questionFrontendId": "1601", "categoryTitle": "Algorithms", "boundTopicId": 425307, "title": "Maximum Number of Achievable Transfer Requests", "titleSlug": "maximum-number-of-achievable-transfer-requests", "content": "
We have n
buildings numbered from 0
to n - 1
. Each building has a number of employees. It's transfer season, and some employees want to change the building they reside in.
You are given an array requests
where requests[i] = [fromi, toi]
represents an employee's request to transfer from building fromi
to building toi
.
All buildings are full, so a list of requests is achievable only if for each building, the net change in employee transfers is zero. This means the number of employees leaving is equal to the number of employees moving in. For example if n = 3
and two employees are leaving building 0
, one is leaving building 1
, and one is leaving building 2
, there should be two employees moving to building 0
, one employee moving to building 1
, and one employee moving to building 2
.
Return the maximum number of achievable requests.
\n\n\n
Example 1:
\n\n\nInput: n = 5, requests = [[0,1],[1,0],[0,1],[1,2],[2,0],[3,4]]\nOutput: 5\nExplantion: Let's see the requests:\nFrom building 0 we have employees x and y and both want to move to building 1.\nFrom building 1 we have employees a and b and they want to move to buildings 2 and 0 respectively.\nFrom building 2 we have employee z and they want to move to building 0.\nFrom building 3 we have employee c and they want to move to building 4.\nFrom building 4 we don't have any requests.\nWe can achieve the requests of users x and b by swapping their places.\nWe can achieve the requests of users y, a and z by swapping the places in the 3 buildings.\n\n\n
Example 2:
\n\n\nInput: n = 3, requests = [[0,0],[1,2],[2,1]]\nOutput: 3\nExplantion: Let's see the requests:\nFrom building 0 we have employee x and they want to stay in the same building 0.\nFrom building 1 we have employee y and they want to move to building 2.\nFrom building 2 we have employee z and they want to move to building 1.\nWe can achieve all the requests.\n\n
Example 3:
\n\n\nInput: n = 4, requests = [[0,3],[3,1],[1,2],[2,0]]\nOutput: 4\n\n\n
\n
Constraints:
\n\n1 <= n <= 20
1 <= requests.length <= 16
requests[i].length == 2
0 <= fromi, toi < n
我们有 n
栋楼,编号从 0
到 n - 1
。每栋楼有若干员工。由于现在是换楼的季节,部分员工想要换一栋楼居住。
给你一个数组 requests
,其中 requests[i] = [fromi, toi]
,表示一个员工请求从编号为 fromi
的楼搬到编号为 toi
的楼。
一开始 所有楼都是满的,所以从请求列表中选出的若干个请求是可行的需要满足 每栋楼员工净变化为 0 。意思是每栋楼 离开 的员工数目 等于 该楼 搬入 的员工数数目。比方说 n = 3
且两个员工要离开楼 0
,一个员工要离开楼 1
,一个员工要离开楼 2
,如果该请求列表可行,应该要有两个员工搬入楼 0
,一个员工搬入楼 1
,一个员工搬入楼 2
。
请你从原请求列表中选出若干个请求,使得它们是一个可行的请求列表,并返回所有可行列表中最大请求数目。
\n\n\n\n
示例 1:
\n\n\n\n输入:n = 5, requests = [[0,1],[1,0],[0,1],[1,2],[2,0],[3,4]]\n输出:5\n解释:请求列表如下:\n从楼 0 离开的员工为 x 和 y ,且他们都想要搬到楼 1 。\n从楼 1 离开的员工为 a 和 b ,且他们分别想要搬到楼 2 和 0 。\n从楼 2 离开的员工为 z ,且他想要搬到楼 0 。\n从楼 3 离开的员工为 c ,且他想要搬到楼 4 。\n没有员工从楼 4 离开。\n我们可以让 x 和 b 交换他们的楼,以满足他们的请求。\n我们可以让 y,a 和 z 三人在三栋楼间交换位置,满足他们的要求。\n所以最多可以满足 5 个请求。\n\n
示例 2:
\n\n\n\n输入:n = 3, requests = [[0,0],[1,2],[2,1]]\n输出:3\n解释:请求列表如下:\n从楼 0 离开的员工为 x ,且他想要回到原来的楼 0 。\n从楼 1 离开的员工为 y ,且他想要搬到楼 2 。\n从楼 2 离开的员工为 z ,且他想要搬到楼 1 。\n我们可以满足所有的请求。\n\n
示例 3:
\n\n输入:n = 4, requests = [[0,3],[3,1],[1,2],[2,0]]\n输出:4\n\n\n
\n\n
提示:
\n\n1 <= n <= 20
1 <= requests.length <= 16
requests[i].length == 2
0 <= fromi, toi < n
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