문제
KSA에는 1ドル$번부터 $N$번까지의 건물이 있고 두 건물 사이를 양방향으로 연결하는 $N-1$개의 통로가 있다. $i$번 통로는 $A_i$번 건물과 $B_i$번 건물을 연결하며 임의의 건물에서 다른 건물로 가는 경로가 항상 존재한다. 민찬이와 에릭은 여기서 숨바꼭질하고 있다. 민찬이가 술래고 1ドル$번부터 $N$번 건물 중 어딘가에 숨은 에릭을 찾아야 한다.
민찬이는 남몰래 에릭의 옷에 숨겨놓았던 위치 추적 장치의 도움을 받아 숨바꼭질에서 이기려고 한다. 이 위치 추적 장치는 다음과 같은 방법으로만 위치를 알려준다.
- 위치 추적 장치의 리모컨에 정수 $x$ $(1 \leq x \leq N)$를 입력하면 $x$번 건물에서부터 에릭이 숨어있는 건물까지 가기 위해 지나야 할 최소 통로 수를 화면에 띄워준다.
위치 추적 장치의 배터리가 얼마 남지 않았기 때문에 민찬이는 위치 추적 장치를 많이 사용할 수 없다. 다음 행동을 $k$번 해서 에릭이 숨어있는 건물을 알 수 있는 가장 작은 $k$를 구해보자.
- 어떤 수 $x$ $(1 \leq x \leq N)$를 선택해서 리모컨에 입력한 후, 리모컨에 띄워지는 수를 확인한다.
단, 민찬이는 다음 행동을 결정할 때, 그 전 행동들에서 얻은 정보를 사용할 수 있다.
출력
에릭이 숨어있는 건물을 알기 위한 최소의 $k$를 출력한다.
제한
- 2ドル \leq N \leq 2000$
- 1ドル \leq A_i < B_i \leq N$ $(1 \leq i \leq N-1)$
- 1ドル \leq i < j \leq N$인 모든 $i,ドル $j$에 대해서 $i$번 건물과 $j$번 건물을 연결하는 경로가 존재
서브태스크
| 번호 | 배점 | 제한 | | 1 | 7 | $A_i = 1$ $(1 \leq i \leq N-1)$
|
| 2 | 44 | $N \leq 100$
|
| 3 | 49 | 추가 제약 조건 없음
|
리모컨에 2ドル$번을 입력해서 한 번 만에 에릭이 숨어있는 건물을 알 수 있다.
[{"problem_id":"29204","problem_lang":"0","title":"KSA\uc5d0\uc11c \uc228\ubc14\uaf2d\uc9c8","description":"<p>KSA\uc5d0\ub294 $1$\ubc88\ubd80\ud130 $N$\ubc88\uae4c\uc9c0\uc758 \uac74\ubb3c\uc774 \uc788\uace0 \ub450 \uac74\ubb3c \uc0ac\uc774\ub97c \uc591\ubc29\ud5a5\uc73c\ub85c \uc5f0\uacb0\ud558\ub294 $N-1$\uac1c\uc758 \ud1b5\ub85c\uac00 \uc788\ub2e4. $i$\ubc88 \ud1b5\ub85c\ub294 $A_i$\ubc88 \uac74\ubb3c\uacfc $B_i$\ubc88 \uac74\ubb3c\uc744 \uc5f0\uacb0\ud558\uba70 \uc784\uc758\uc758 \uac74\ubb3c\uc5d0\uc11c \ub2e4\ub978 \uac74\ubb3c\ub85c \uac00\ub294 \uacbd\ub85c\uac00 \ud56d\uc0c1 \uc874\uc7ac\ud55c\ub2e4. \ubbfc\ucc2c\uc774\uc640 \uc5d0\ub9ad\uc740 \uc5ec\uae30\uc11c \uc228\ubc14\uaf2d\uc9c8\ud558\uace0 \uc788\ub2e4. \ubbfc\ucc2c\uc774\uac00 \uc220\ub798\uace0 $1$\ubc88\ubd80\ud130 $N$\ubc88 \uac74\ubb3c \uc911 \uc5b4\ub518\uac00\uc5d0 \uc228\uc740 \uc5d0\ub9ad\uc744 \ucc3e\uc544\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ubbfc\ucc2c\uc774\ub294 \ub0a8\ubab0\ub798 \uc5d0\ub9ad\uc758 \uc637\uc5d0 \uc228\uaca8\ub193\uc558\ub358 \uc704\uce58 \ucd94\uc801 \uc7a5\uce58\uc758 \ub3c4\uc6c0\uc744 \ubc1b\uc544 \uc228\ubc14\uaf2d\uc9c8\uc5d0\uc11c \uc774\uae30\ub824\uace0 \ud55c\ub2e4. \uc774 \uc704\uce58 \ucd94\uc801 \uc7a5\uce58\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\ubc95\uc73c\ub85c\ub9cc \uc704\uce58\ub97c \uc54c\ub824\uc900\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uc704\uce58 \ucd94\uc801 \uc7a5\uce58\uc758 \ub9ac\ubaa8\ucee8\uc5d0 \uc815\uc218 $x$ $(1 \\leq x \\leq N)$\ub97c \uc785\ub825\ud558\uba74 $x$\ubc88 \uac74\ubb3c\uc5d0\uc11c\ubd80\ud130 \uc5d0\ub9ad\uc774 \uc228\uc5b4\uc788\ub294 \uac74\ubb3c\uae4c\uc9c0 \uac00\uae30 \uc704\ud574 \uc9c0\ub098\uc57c \ud560 \ucd5c\uc18c \ud1b5\ub85c \uc218\ub97c \ud654\uba74\uc5d0 \ub744\uc6cc\uc900\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc704\uce58 \ucd94\uc801 \uc7a5\uce58\uc758 \ubc30\ud130\ub9ac\uac00 \uc5bc\ub9c8 \ub0a8\uc9c0 \uc54a\uc558\uae30 \ub54c\ubb38\uc5d0 \ubbfc\ucc2c\uc774\ub294 \uc704\uce58 \ucd94\uc801 \uc7a5\uce58\ub97c \ub9ce\uc774 \uc0ac\uc6a9\ud560 \uc218 \uc5c6\ub2e4. \ub2e4\uc74c \ud589\ub3d9\uc744 $k$\ubc88 \ud574\uc11c \uc5d0\ub9ad\uc774 \uc228\uc5b4\uc788\ub294 \uac74\ubb3c\uc744 \uc54c \uc218 \uc788\ub294 \uac00\uc7a5 \uc791\uc740 $k$\ub97c \uad6c\ud574\ubcf4\uc790.<\/p>\r\n\r\n<ul>\r\n\t<li>\uc5b4\ub5a4 \uc218 $x$ $(1 \\leq x \\leq N)$\ub97c \uc120\ud0dd\ud574\uc11c \ub9ac\ubaa8\ucee8\uc5d0 \uc785\ub825\ud55c \ud6c4, \ub9ac\ubaa8\ucee8\uc5d0 \ub744\uc6cc\uc9c0\ub294 \uc218\ub97c \ud655\uc778\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub2e8, \ubbfc\ucc2c\uc774\ub294 \ub2e4\uc74c \ud589\ub3d9\uc744 \uacb0\uc815\ud560 \ub54c, \uadf8 \uc804 \ud589\ub3d9\ub4e4\uc5d0\uc11c \uc5bb\uc740 \uc815\ubcf4\ub97c \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>$i+1$\ubc88\uc9f8 \uc904\uc5d0 \ub450 \uc815\uc218 $A_i$\uc640 $B_i$\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\leq i \\leq N-1)$<\/p>\r\n","output":"<p>\uc5d0\ub9ad\uc774 \uc228\uc5b4\uc788\ub294 \uac74\ubb3c\uc744 \uc54c\uae30 \uc704\ud55c \ucd5c\uc18c\uc758 $k$\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$2 \\leq N \\leq 2000$<\/li>\r\n\t<li>$1 \\leq A_i &lt; B_i \\leq N$ $(1 \\leq i \\leq N-1)$<\/li>\r\n\t<li>$1 \\leq i &lt; j \\leq N$\uc778 \ubaa8\ub4e0 $i$, $j$\uc5d0 \ub300\ud574\uc11c $i$\ubc88 \uac74\ubb3c\uacfc $j$\ubc88 \uac74\ubb3c\uc744 \uc5f0\uacb0\ud558\ub294 \uacbd\ub85c\uac00 \uc874\uc7ac<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$A_i = 1$ $(1 \\leq i \\leq N-1)$<\/p>\r\n","subtask2":"<p>$N \\leq 100$<\/p>\r\n","subtask3":"<p>\ucd94\uac00 \uc81c\uc57d \uc870\uac74 \uc5c6\uc74c<\/p>\r\n","sample_explain_1":"<p>\ub9ac\ubaa8\ucee8\uc5d0 $2$\ubc88\uc744 \uc785\ub825\ud574\uc11c \ud55c \ubc88 \ub9cc\uc5d0 \uc5d0\ub9ad\uc774 \uc228\uc5b4\uc788\ub294 \uac74\ubb3c\uc744 \uc54c \uc218 \uc788\ub2e4.<\/p>\r\n"},{"problem_id":"29204","problem_lang":"1","title":"Hide and Seek in KSA","description":"<p>In KSA, there are buildings numbered from $1$ to $N$, and there are $N-1$ corridors connecting the buildings in both directions. Corridor $i$ connects building $A_i$ and building $B_i$., and there&nbsp;always exists&nbsp;a path from any building to any other building. Minchan and Eric are playing hide and seek here. Minchan is the seeker and needs to find Eric, who is hiding in one of the buildings numbered from $1$ to $N$.<\/p>\r\n\r\n<p>Minchan wants to win the game with the help of&nbsp;location tracking device which was secretly hidden on Eric&#39;s clothes. This tracking device only reveals the location in the following way:<\/p>\r\n\r\n<ul>\r\n\t<li>If you input an integer $x$ $(1 \\le x \\le N)$ on the remote control of the tracking device, it will display the minimum number of corridors that need to be passed to reach the building where Eric is hiding&nbsp;from building $x$.<\/li>\r\n<\/ul>\r\n\r\n<p>Since the battery of the tracking device is running low, Minchan cannot use it too many times. Please find the smallest integer $k$, so that Minchan can secure the number of the building where Eric is hiding in using $k$ operations of the following kind:<\/p>\r\n\r\n<ul>\r\n\t<li>Select an integer $x$ $(1 \\le x \\le N)$, and find out the number output by the tracking device, when the integer&nbsp;$x$ is the input to the remote control.<\/li>\r\n<\/ul>\r\n\r\n<p>Note that upon deciding on the next operation, Minchan can use the information acquired from the previous operations.<\/p>\r\n","input":"<p>The first line contains an integer&nbsp;$N$.<\/p>\r\n\r\n<p>The $i+1$-th line contains two space-separated integers $A_i$ and $B_i$. $(1 \\leq i \\leq N-1)$<\/p>\r\n","output":"<p>Print the smallest integer $k$ to secure the number of the building where Eric is hiding in.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$2 \\leq N \\leq 2000$<\/li>\r\n\t<li>$1 \\leq A_i &lt; B_i \\leq N$ $(1 \\leq i \\leq N-1)$<\/li>\r\n\t<li>For all $i$, $j$ satisfying $1 \\leq i &lt;&nbsp;j \\leq N$, a path connecting&nbsp;building $i$ and&nbsp;building $j$&nbsp;exists<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$A_i = 1$ $(1 \\leq i \\leq N-1)$<\/p>\r\n","subtask2":"<p>$N \\leq 100$<\/p>\r\n","subtask3":"<p>No additional constraints<\/p>\r\n","sample_explain_1":"<p>By inputting the number $2$ on the remote control, you can immediately know the building where Eric is hiding in.<\/p>\r\n"}]