5670번 - 휴대폰 자판 다국어

시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 192 MB83562962190232.248%

문제

휴대폰에서 길이가 P인 영단어를 입력하려면 버튼을 P번 눌러야 한다. 그러나 시스템프로그래밍 연구실에 근무하는 승혁연구원은 사전을 사용해 이 입력을 더 빨리 할 수 있는 자판 모듈을 개발하였다. 이 모듈은 사전 내에서 가능한 다음 글자가 하나뿐이라면 그 글자를 버튼 입력 없이 자동으로 입력해 준다! 자세한 작동 과정을 설명하자면 다음과 같다.

  1. 모듈이 단어의 첫 번째 글자를 추론하지는 않는다. 즉, 사전의 모든 단어가 같은 알파벳으로 시작하더라도 반드시 첫 글자는 사용자가 버튼을 눌러 입력해야 한다.
  2. 길이가 1 이상인 문자열 c1c2...cn이 지금까지 입력되었을 때, 사전 안의 모든 c1c2...cn으로 시작하는 단어가 c1c2...cnc로도 시작하는 글자 c가 존재한다면 모듈은 사용자의 버튼 입력 없이도 자동으로 c를 입력해 준다. 그렇지 않다면 사용자의 입력을 기다린다.

예를 들면, 사전에 "hello", "hell", "heaven", "goodbye" 4개의 단어가 있고 사용자가 "h"를 입력하면 모듈은 자동으로 "e"를 입력해 준다. 사전상의 "h"로 시작하는 단어들은 모두 그 뒤에 "e"가 오기 때문이다. 그러나 단어들 중 "hel"로 시작하는 것도, "hea"로 시작하는 것도 있기 때문에 여기서 모듈은 사용자의 입력을 기다린다. 이어서 사용자가 "l"을 입력하면 모듈은 "l"을 자동으로 입력해 준다. 그러나 여기서 끝나는 단어인 "hell"과 그렇지 않은 단어인 "hello"가 공존하므로 모듈은 다시 입력을 기다린다. 사용자가 "hell"을 입력하기 원한다면 여기서 입력을 멈출 것이고, "hello"를 입력하기 원한다면 직접 "o" 버튼을 눌러서 입력해 줘야 한다. 따라서 "hello"를 입력하려면 사용자는 총 3번 버튼을 눌러야 하고, "hell", "heaven"은 2번이다. "heaven"의 경우 "he"에서 "a"를 입력하면 바로 뒷부분이 모두 자동으로 입력되기 때문이다. 비슷하게, "goodbye"는 단 한 번만 버튼을 눌러도 입력이 완료될 것이다. "g"를 입력하는 순간 뒤에 오는 글자가 항상 유일하므로 끝까지 자동으로 입력되기 때문이다. 이때 사전에 있는 단어들을 입력하기 위해 버튼을 눌러야 하는 횟수의 평균은 (3 + 2 + 2 + 1)/4 = 2.00이다.

사전이 주어졌을 때, 이 모듈을 사용하면서 이와 같이 각 단어를 입력하기 위해 버튼을 눌러야 하는 횟수의 평균을 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다.

각 테스트 케이스의 첫째 줄에 사전에 속한 단어의 개수 N이 주어지며(1 ≤ N ≤ 105), 이어서 N개의 줄에 1~80글자인 영어 소문자로만 이루어진 단어가 하나씩 주어진다. 이 단어들로 사전이 구성되어 있으며, 똑같은 단어는 두 번 주어지지 않는다. 각 테스트 케이스마다 입력으로 주어지는 단어의 길이 총합은 최대 106이다.

출력

각 테스트 케이스마다 한 줄에 걸쳐 문제의 정답을 소수점 둘째 자리까지 반올림하여 출력한다.

예제 입력 1 

4
hello
hell
heaven
goodbye
3
hi
he
h
7
structure
structures
ride
riders
stress
solstice
ridiculous

예제 출력 1 

2.00
1.67
2.71
[{"problem_id":"5670","problem_lang":"0","title":"\ud734\ub300\ud3f0 \uc790\ud310","description":"<p>\ud734\ub300\ud3f0\uc5d0\uc11c \uae38\uc774\uac00 P\uc778 \uc601\ub2e8\uc5b4\ub97c \uc785\ub825\ud558\ub824\uba74 \ubc84\ud2bc\uc744 P\ubc88 \ub20c\ub7ec\uc57c \ud55c\ub2e4. \uadf8\ub7ec\ub098 \uc2dc\uc2a4\ud15c\ud504\ub85c\uadf8\ub798\ubc0d \uc5f0\uad6c\uc2e4\uc5d0 \uadfc\ubb34\ud558\ub294 \uc2b9\ud601\uc5f0\uad6c\uc6d0\uc740 \uc0ac\uc804\uc744 \uc0ac\uc6a9\ud574 \uc774 \uc785\ub825\uc744 \ub354 \ube68\ub9ac \ud560 \uc218 \uc788\ub294 \uc790\ud310 \ubaa8\ub4c8\uc744 \uac1c\ubc1c\ud558\uc600\ub2e4. \uc774 \ubaa8\ub4c8\uc740 \uc0ac\uc804 \ub0b4\uc5d0\uc11c \uac00\ub2a5\ud55c \ub2e4\uc74c \uae00\uc790\uac00 \ud558\ub098\ubfd0\uc774\ub77c\uba74 \uadf8 \uae00\uc790\ub97c \ubc84\ud2bc \uc785\ub825 \uc5c6\uc774 \uc790\ub3d9\uc73c\ub85c \uc785\ub825\ud574 \uc900\ub2e4! \uc790\uc138\ud55c \uc791\ub3d9 \uacfc\uc815\uc744 \uc124\uba85\ud558\uc790\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\ubaa8\ub4c8\uc774 \ub2e8\uc5b4\uc758 \uccab \ubc88\uc9f8 \uae00\uc790\ub97c \ucd94\ub860\ud558\uc9c0\ub294 \uc54a\ub294\ub2e4. \uc989, \uc0ac\uc804\uc758 \ubaa8\ub4e0 \ub2e8\uc5b4\uac00 \uac19\uc740 \uc54c\ud30c\ubcb3\uc73c\ub85c \uc2dc\uc791\ud558\ub354\ub77c\ub3c4 \ubc18\ub4dc\uc2dc \uccab \uae00\uc790\ub294 \uc0ac\uc6a9\uc790\uac00 \ubc84\ud2bc\uc744 \ub20c\ub7ec \uc785\ub825\ud574\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>\uae38\uc774\uac00 1 \uc774\uc0c1\uc778 \ubb38\uc790\uc5f4 c<sub>1<\/sub>c<sub>2<\/sub>...c<sub>n<\/sub>\uc774 \uc9c0\uae08\uae4c\uc9c0 \uc785\ub825\ub418\uc5c8\uc744 \ub54c, \uc0ac\uc804 \uc548\uc758 \ubaa8\ub4e0 c<sub>1<\/sub>c<sub>2<\/sub>...c<sub>n<\/sub>\uc73c\ub85c \uc2dc\uc791\ud558\ub294 \ub2e8\uc5b4\uac00 c<sub>1<\/sub>c<sub>2<\/sub>...c<sub>n<\/sub>c\ub85c\ub3c4 \uc2dc\uc791\ud558\ub294 \uae00\uc790 c\uac00 \uc874\uc7ac\ud55c\ub2e4\uba74 \ubaa8\ub4c8\uc740 \uc0ac\uc6a9\uc790\uc758 \ubc84\ud2bc \uc785\ub825 \uc5c6\uc774\ub3c4 \uc790\ub3d9\uc73c\ub85c c\ub97c \uc785\ub825\ud574 \uc900\ub2e4. \uadf8\ub807\uc9c0 \uc54a\ub2e4\uba74 \uc0ac\uc6a9\uc790\uc758 \uc785\ub825\uc744 \uae30\ub2e4\ub9b0\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc608\ub97c \ub4e4\uba74, \uc0ac\uc804\uc5d0 &quot;hello&quot;, &quot;hell&quot;, &quot;heaven&quot;, &quot;goodbye&quot; 4\uac1c\uc758 \ub2e8\uc5b4\uac00 \uc788\uace0 \uc0ac\uc6a9\uc790\uac00 &quot;h&quot;\ub97c \uc785\ub825\ud558\uba74 \ubaa8\ub4c8\uc740 \uc790\ub3d9\uc73c\ub85c &quot;e&quot;\ub97c \uc785\ub825\ud574 \uc900\ub2e4. \uc0ac\uc804\uc0c1\uc758 &quot;h&quot;\ub85c \uc2dc\uc791\ud558\ub294 \ub2e8\uc5b4\ub4e4\uc740 \ubaa8\ub450 \uadf8 \ub4a4\uc5d0 &quot;e&quot;\uac00 \uc624\uae30 \ub54c\ubb38\uc774\ub2e4. \uadf8\ub7ec\ub098 \ub2e8\uc5b4\ub4e4 \uc911 &quot;hel&quot;\ub85c \uc2dc\uc791\ud558\ub294 \uac83\ub3c4, &quot;hea&quot;\ub85c \uc2dc\uc791\ud558\ub294 \uac83\ub3c4 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc5ec\uae30\uc11c \ubaa8\ub4c8\uc740 \uc0ac\uc6a9\uc790\uc758 \uc785\ub825\uc744 \uae30\ub2e4\ub9b0\ub2e4. \uc774\uc5b4\uc11c \uc0ac\uc6a9\uc790\uac00 &quot;l&quot;\uc744 \uc785\ub825\ud558\uba74 \ubaa8\ub4c8\uc740 &quot;l&quot;\uc744 \uc790\ub3d9\uc73c\ub85c \uc785\ub825\ud574 \uc900\ub2e4. \uadf8\ub7ec\ub098 \uc5ec\uae30\uc11c \ub05d\ub098\ub294 \ub2e8\uc5b4\uc778 &quot;hell&quot;\uacfc \uadf8\ub807\uc9c0 \uc54a\uc740 \ub2e8\uc5b4\uc778 &quot;hello&quot;\uac00 \uacf5\uc874\ud558\ubbc0\ub85c \ubaa8\ub4c8\uc740 \ub2e4\uc2dc \uc785\ub825\uc744 \uae30\ub2e4\ub9b0\ub2e4. \uc0ac\uc6a9\uc790\uac00 &quot;hell&quot;\uc744 \uc785\ub825\ud558\uae30 \uc6d0\ud55c\ub2e4\uba74 \uc5ec\uae30\uc11c \uc785\ub825\uc744 \uba48\ucd9c \uac83\uc774\uace0, &quot;hello&quot;\ub97c \uc785\ub825\ud558\uae30 \uc6d0\ud55c\ub2e4\uba74 \uc9c1\uc811 &quot;o&quot; \ubc84\ud2bc\uc744 \ub20c\ub7ec\uc11c \uc785\ub825\ud574 \uc918\uc57c \ud55c\ub2e4. \ub530\ub77c\uc11c &quot;hello&quot;\ub97c \uc785\ub825\ud558\ub824\uba74 \uc0ac\uc6a9\uc790\ub294 \ucd1d 3\ubc88 \ubc84\ud2bc\uc744 \ub20c\ub7ec\uc57c \ud558\uace0, &quot;hell&quot;, &quot;heaven&quot;\uc740 2\ubc88\uc774\ub2e4. &quot;heaven&quot;\uc758 \uacbd\uc6b0 &quot;he&quot;\uc5d0\uc11c &quot;a&quot;\ub97c \uc785\ub825\ud558\uba74 \ubc14\ub85c \ub4b7\ubd80\ubd84\uc774 \ubaa8\ub450 \uc790\ub3d9\uc73c\ub85c \uc785\ub825\ub418\uae30 \ub54c\ubb38\uc774\ub2e4. \ube44\uc2b7\ud558\uac8c, &quot;goodbye&quot;\ub294 \ub2e8 \ud55c \ubc88\ub9cc \ubc84\ud2bc\uc744 \ub20c\ub7ec\ub3c4 \uc785\ub825\uc774 \uc644\ub8cc\ub420 \uac83\uc774\ub2e4. &quot;g&quot;\ub97c \uc785\ub825\ud558\ub294 \uc21c\uac04 \ub4a4\uc5d0 \uc624\ub294 \uae00\uc790\uac00 \ud56d\uc0c1 \uc720\uc77c\ud558\ubbc0\ub85c \ub05d\uae4c\uc9c0 \uc790\ub3d9\uc73c\ub85c \uc785\ub825\ub418\uae30 \ub54c\ubb38\uc774\ub2e4. \uc774\ub54c \uc0ac\uc804\uc5d0 \uc788\ub294 \ub2e8\uc5b4\ub4e4\uc744 \uc785\ub825\ud558\uae30 \uc704\ud574 \ubc84\ud2bc\uc744 \ub20c\ub7ec\uc57c \ud558\ub294 \ud69f\uc218\uc758 \ud3c9\uade0\uc740 (3 + 2 + 2 + 1)\/4 = 2.00\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc0ac\uc804\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc774 \ubaa8\ub4c8\uc744 \uc0ac\uc6a9\ud558\uba74\uc11c \uc774\uc640 \uac19\uc774 \uac01 \ub2e8\uc5b4\ub97c \uc785\ub825\ud558\uae30 \uc704\ud574 \ubc84\ud2bc\uc744 \ub20c\ub7ec\uc57c \ud558\ub294 \ud69f\uc218\uc758 \ud3c9\uade0\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0 \uc0ac\uc804\uc5d0 \uc18d\ud55c \ub2e8\uc5b4\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c0\uba70(1 &le; N &le; 10<sup>5<\/sup>), \uc774\uc5b4\uc11c N\uac1c\uc758 \uc904\uc5d0 1~80\uae00\uc790\uc778 \uc601\uc5b4 \uc18c\ubb38\uc790\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc9c4 \ub2e8\uc5b4\uac00 \ud558\ub098\uc529 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \ub2e8\uc5b4\ub4e4\ub85c \uc0ac\uc804\uc774 \uad6c\uc131\ub418\uc5b4 \uc788\uc73c\uba70, \ub611\uac19\uc740 \ub2e8\uc5b4\ub294 \ub450 \ubc88 \uc8fc\uc5b4\uc9c0\uc9c0 \uc54a\ub294\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ub2e8\uc5b4\uc758 \uae38\uc774 \ucd1d\ud569\uc740 \ucd5c\ub300 10<sup>6<\/sup>\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ud55c \uc904\uc5d0 \uac78\uccd0 \ubb38\uc81c\uc758 \uc815\ub2f5\uc744 \uc18c\uc218\uc810 \ub458\uc9f8 \uc790\ub9ac\uae4c\uc9c0 \ubc18\uc62c\ub9bc\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"5670","problem_lang":"1","title":"Cellphone Typing","description":"<p>A research team is developing a new technology to save time when typing text messages in mobile devices. They are working on a new model that has a complete keyboard, so users can type any single letter by pressing the corresponding key. In this way, a user needs P keystrokes to type a word of length P.<\/p>\r\n\r\n<p>However, this is not fast enough. The team is going to put together a dictionary of the common words that a user may type. The goal is to reduce the average number of keystrokes needed to type words that are in the dictionary. During the typing of a word, whenever the following letter is uniquely determined, the cellphone system will input it automatically, without the need for a keystroke. To be more precise, the behavior of the cellphone system will be determined by the following rules:<\/p>\r\n\r\n<ol>\r\n\t<li>The system never guesses the first letter of a word, so the first letter always has to be input manually by pressing the corresponding key.<\/li>\r\n\t<li>If a non-empty succession of letters c<sub>1<\/sub>c<sub>2<\/sub>...c<sub>n<\/sub> has been input, and there is a letter c such that every word in the dictionary which starts with c<sub>1<\/sub>c<sub>2<\/sub>...c<sub>n<\/sub> also starts with c<sub>1<\/sub>c<sub>2<\/sub>...c<sub>n<\/sub>c, then the system inputs c automatically, without the need of a keystroke. Otherwise, the system waits for the user.<\/li>\r\n<\/ol>\r\n\r\n<p>For instance, if the dictionary is composed of the words &ldquo;hello&rdquo;, &ldquo;hell&rdquo;, &ldquo;heaven&rdquo; and &ldquo;goodbye&rdquo;, and the user presses &ldquo;h&rdquo;, the system will input &ldquo;e&rdquo; automatically, because every word which starts with &ldquo;h&rdquo; also starts with &ldquo;he&rdquo;. However, since there are words that start with &ldquo;hel&rdquo; and with &ldquo;hea&rdquo;, the system now needs to wait for the user. If the user then presses &ldquo;l&rdquo;, obtaining the partial word &ldquo;hel&rdquo;, the system will input a second &ldquo;l&rdquo; automatically. When it has &ldquo;hell&rdquo; as input, the system cannot guess, because it is possible that the word is over, or it is also possible that the user may want to press &ldquo;o&rdquo; to get &ldquo;hello&rdquo;. In this fashion, to type the word &ldquo;hello&rdquo; the user needs three keystrokes, &ldquo;hell&rdquo; requires two, and &ldquo;heaven&rdquo; also requires two, because when the current input is &ldquo;hea&rdquo; the system can automatically input the remainder of the word by repeatedly applying the second rule. Similarly, the word &ldquo;goodbye&rdquo; needs just one keystroke, because after pressing the initial &ldquo;g&rdquo; the system will automatically fill in the entire word. In this example, the average number of keystrokes needed to type a word in the dictionary is then (3 + 2 + 2 + 1)\/4 = 2.00.<\/p>\r\n\r\n<p>Your task is, given a dictionary, to calculate the average number of keystrokes needed to type a word in the dictionary with the new cellphone system.<\/p>\r\n","input":"<p>Each test case is described using several lines. The first line contains an integer N representing the number of words in the dictionary (1 &le; N &le; 10<sup>5<\/sup>). Each of the next N lines contains a non-empty string of at most 80 lowercase letters from the English alphabet, representing a word in the dictionary. Within each test case all words are different, and the sum of the lengths of all words is at most 10<sup>6<\/sup>.<\/p>\r\n","output":"<p>For each test case output a line with a rational number representing the average number of keystrokes needed to type a word in the dictionary. The result must be output as a rational number with exactly two digits after the decimal point, rounded if necessary.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Latin America > Latin America Regional Contests 2012 C번

  • 문제를 번역한 사람: kks227
  • 문제를 만든 사람: Pablo Ariel Heiber

Baekjoon Online Judge

채점 현황

문제

유저 대회 / 고등학교 대회

출처

대학교 대회

도움말

© 2023 All Rights Reserved. 주식회사 스타트링크 | 서비스 약관 | 개인정보 보호 | 결제 이용 약관 | 도움말 | 광고 문의 | 업데이트 노트 | 이슈 | TODO

  • 사업자 등록 번호: 541-88-00682
  • 대표자명: 최백준
  • 주소: 서울시 서초구 서초대로74길 29 서초파라곤 412호
  • 전화번호: 02-521-0487 (이메일로 연락 주세요)
  • 이메일: contacts@startlink.io
  • 통신판매신고번호: 제 2017-서울서초-2193 호

한국어 | English (Beta)