시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 129 29 28 48.276%

문제

학생들이 너무 떠드는 것을 보다 못한 나머지, 원장님은 결단을 내리셨다. 반을 나누기로.

학생들은 친한 친구들과 떨어지는 것이 싫어서 몹시 거세게 반발했고, 원장님은 이를 잠재우기 위하여 한 가지 방안을 제시하셨다. 인터넷 메신저로 대화할 수 있게 허락해 주신 것이다.

단, 두 사람이 메신저로 대화를 나누기 위해서는 서로가 서로의 메신저 아이디를 알고 있어야 하는데, 모든 학생이 모든 학생의 아이디를 알고 있는 것은 아니다.

이러한 상황에서, 원장님은 최대한 반을 잘게 나누고자 하신다. 다른 반에 속한 학생들끼리는 메신저로 대화해야 하므로, 반드시 서로의 메신저 아이디를 알고 있어야만 한다.

어떤 학생들끼리 서로의 메신저 아이디를 알고 있는지 주어졌을 때, 가장 많은 반을 편성하려면 어떻게 해야 하는지 알아내는 프로그램을 작성하시오.

입력

첫째 줄 학생들의 수 n과, 서로 메신저 아이디를 알고 있는 학생들 쌍의 수 m이 공백을 사이에 두고 주어진다. (2<=n<=100,000. 1<=m<=2,000,000) 이후 m개의 줄에는 서로 메신저 아이디를 알고 있는 학생들 번호의 쌍이 두 개의 정수로 주어진다. 두 학생의 번호는 1이상 n이하의 정수이다.

출력

첫째 줄에, 최대로 편성할 수 있는 반이 몇 개인지 출력한다. 둘째 줄에는, 최대로 편성했을 때 각 반별 인원수를 오름차순으로 출력한다.

예제 입력 1

7 16
1 3
1 4
1 5
2 3
3 4
4 5
4 7
4 6
5 6
6 7
2 4
2 7
2 5
3 5
3 7
1 7

예제 출력 1

3
1 2 4

힌트

4번 학생 혼자 한 반, 5번과 7번 학생 둘이서 한 반, 나머지 학생 네 명이서 한 반이 되도록 반을 편성하면 된다.

[{"problem_id":"1741","problem_lang":"0","title":"\ubc18 \ub098\ub204\uae30","description":"<p>\ud559\uc0dd\ub4e4\uc774 \ub108\ubb34 \ub5a0\ub4dc\ub294 \uac83\uc744 \ubcf4\ub2e4 \ubabb\ud55c \ub098\uba38\uc9c0, \uc6d0\uc7a5\ub2d8\uc740 \uacb0\ub2e8\uc744 \ub0b4\ub9ac\uc168\ub2e4. \ubc18\uc744 \ub098\ub204\uae30\ub85c.<\/p>\r\n\r\n<p>\ud559\uc0dd\ub4e4\uc740 \uce5c\ud55c \uce5c\uad6c\ub4e4\uacfc \ub5a8\uc5b4\uc9c0\ub294 \uac83\uc774 \uc2eb\uc5b4\uc11c \ubab9\uc2dc \uac70\uc138\uac8c \ubc18\ubc1c\ud588\uace0, \uc6d0\uc7a5\ub2d8\uc740 \uc774\ub97c \uc7a0\uc7ac\uc6b0\uae30 \uc704\ud558\uc5ec \ud55c \uac00\uc9c0 \ubc29\uc548\uc744 \uc81c\uc2dc\ud558\uc168\ub2e4. \uc778\ud130\ub137 \uba54\uc2e0\uc800\ub85c \ub300\ud654\ud560 \uc218 \uc788\uac8c \ud5c8\ub77d\ud574 \uc8fc\uc2e0 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2e8, \ub450 \uc0ac\ub78c\uc774 \uba54\uc2e0\uc800\ub85c \ub300\ud654\ub97c \ub098\ub204\uae30 \uc704\ud574\uc11c\ub294 \uc11c\ub85c\uac00 \uc11c\ub85c\uc758 \uba54\uc2e0\uc800 \uc544\uc774\ub514\ub97c \uc54c\uace0 \uc788\uc5b4\uc57c \ud558\ub294\ub370, \ubaa8\ub4e0 \ud559\uc0dd\uc774 \ubaa8\ub4e0 \ud559\uc0dd\uc758 \uc544\uc774\ub514\ub97c \uc54c\uace0 \uc788\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uc774\ub7ec\ud55c \uc0c1\ud669\uc5d0\uc11c, \uc6d0\uc7a5\ub2d8\uc740 \ucd5c\ub300\ud55c \ubc18\uc744 \uc798\uac8c \ub098\ub204\uace0\uc790 \ud558\uc2e0\ub2e4. \ub2e4\ub978 \ubc18\uc5d0 \uc18d\ud55c \ud559\uc0dd\ub4e4\ub07c\ub9ac\ub294 \uba54\uc2e0\uc800\ub85c \ub300\ud654\ud574\uc57c \ud558\ubbc0\ub85c, \ubc18\ub4dc\uc2dc \uc11c\ub85c\uc758 \uba54\uc2e0\uc800 \uc544\uc774\ub514\ub97c \uc54c\uace0 \uc788\uc5b4\uc57c\ub9cc \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ub5a4 \ud559\uc0dd\ub4e4\ub07c\ub9ac \uc11c\ub85c\uc758 \uba54\uc2e0\uc800 \uc544\uc774\ub514\ub97c \uc54c\uace0 \uc788\ub294\uc9c0 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uac00\uc7a5 \ub9ce\uc740 \ubc18\uc744 \ud3b8\uc131\ud558\ub824\uba74 \uc5b4\ub5bb\uac8c \ud574\uc57c \ud558\ub294\uc9c0 \uc54c\uc544\ub0b4\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904 \ud559\uc0dd\ub4e4\uc758 \uc218 n\uacfc, \uc11c\ub85c \uba54\uc2e0\uc800 \uc544\uc774\ub514\ub97c \uc54c\uace0 \uc788\ub294 \ud559\uc0dd\ub4e4 \uc30d\uc758 \uc218 m\uc774 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4. (2&lt;=n&lt;=100,000. 1&lt;=m&lt;=2,000,000) \uc774\ud6c4 m\uac1c\uc758 \uc904\uc5d0\ub294 \uc11c\ub85c \uba54\uc2e0\uc800 \uc544\uc774\ub514\ub97c \uc54c\uace0 \uc788\ub294 \ud559\uc0dd\ub4e4 \ubc88\ud638\uc758 \uc30d\uc774 \ub450 \uac1c\uc758 \uc815\uc218\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \ud559\uc0dd\uc758 \ubc88\ud638\ub294 1\uc774\uc0c1 n\uc774\ud558\uc758 \uc815\uc218\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0, \ucd5c\ub300\ub85c \ud3b8\uc131\ud560 \uc218 \uc788\ub294 \ubc18\uc774 \uba87 \uac1c\uc778\uc9c0 \ucd9c\ub825\ud55c\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294, \ucd5c\ub300\ub85c \ud3b8\uc131\ud588\uc744 \ub54c \uac01 \ubc18\ubcc4 \uc778\uc6d0\uc218\ub97c \uc624\ub984\ucc28\uc21c\uc73c\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>4\ubc88 \ud559\uc0dd \ud63c\uc790 \ud55c \ubc18, 5\ubc88\uacfc 7\ubc88 \ud559\uc0dd \ub458\uc774\uc11c \ud55c \ubc18, \ub098\uba38\uc9c0 \ud559\uc0dd \ub124 \uba85\uc774\uc11c \ud55c \ubc18\uc774 \ub418\ub3c4\ub85d \ubc18\uc744 \ud3b8\uc131\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1741","problem_lang":"1","title":"Offices","description":"<p>Bytel is a mobile telephony potentate. Each employee has been issued a company phone, the memory of which holds the numbers of some of his co-workers (all of them have his number in their phones as well). Due to dynamic growth of their operations the board of directors intends to move company headquaters to new office buildings. It has been decided - in order to boost work efficiency - that every pair of employees working in different buildings should know (reciprocally) each others phone number i.e. the memory of their company phone ought to hold necessary phone numbers.<\/p>\r\n\r\n<p>Simultaneously, the board have decided to rent as many office buildings as possible to ensure good working conditions. Help the board of Bytel to plan the number of office buildings and their size in accordance with the aforementioned requirements.<\/p>\r\n\r\n<p>Write a programme which:<\/p>\r\n\r\n<ul>\r\n\t<li>reads the description of employees&#39; phone number lists from the standard input<\/li>\r\n\t<li>calculates the maximal number of office buildings and their sizes, satisfying board&#39;s conditions<\/li>\r\n\t<li>writes the outcome to the standard output.<\/li>\r\n<\/ul>\r\n","input":"<p>The first line of the standard input consists of two integers: n and m (2 &le; n &le; 100 000, 1 &le; m &le; 2 000 000), separated by single spaces, denoting the number of Bytel employees and the number of pairs of employees who have their numbers in company phones, respectively. The employees are numbered from 1 to n.<\/p>\r\n\r\n<p>Each of the following m lines contains a single pair of integers a<sub>i<\/sub> and b<sub>i<\/sub> (1 &le; a<sub>i<\/sub> &lt; b<sub>i<\/sub> &le; n for 1 &le; i &le; m), separated by a single space, denoting that employees ai and bi have their numbers (reciprocally) in company phones&#39; memory. Each pair of integers denoting a pair of employees shall occur once at the most in the standard input.<\/p>\r\n","output":"<p>The first line of the standard output should contain a single integer: the maximal number of office buildings that Bytel should rent. The second should contain a non-decreasing sequence of positive integers, separated by singe spaces, denoting the sizes of the office buildings (i.e. the numbers of employees working there). Should there exist more than one correct answer - write out any one of them.<\/p>\r\n","hint":"<p>An exemplary correct distribution of employees in the office buildings: employee number 4 in the first office, numbers 5 and 7 in the second office, numbers 1, 2, 3, 6 in the third office building.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > Polish Olympiad in Informatics > POI 2006/2007 > Stage 1 2번

  • 문제의 오타를 찾은 사람: andy627
  • 문제를 번역한 사람: author10