문제
개구리 왕눈이는 N개의 연꽃잎이 있는 연못에 살고 있다. 연꽃잎은 1부터 N까지 차례대로 번호가 매겨져 있다. 연못을 위에서 봤을 때 2차원 평면에 연꽃잎이 (x,y) 좌표에 떠 있는 것 처럼 보인다. 왕눈이는 대각선으로 뛰는 것과 음의 방향으로 뛰는 것을 무서워 한다. 좀 더 자세히 말하자면 (x 1 ,y1 )에서 (x2 ,y2 )로 뛰기 위해서는 아래 두 조건 중 하나를 만족해야한다.
x2 > x1 이고 y2 = y1
y2 > y1 이고 x2 = x1
각 연꽃잎 마다 일정 수의 파리가 있고, 왕눈이는 파리를 먹으며 힘을 회복한다.
왕눈이가 한 번 연꽃잎을 이동하기 위해서는 K 만큼 힘이 든다. 왕눈이는 처음 1번 연꽃잎에서 시작하여 N번 연꽃잎으로 이동하려고 한다. 다만, 도착하고 난 뒤 힘의 최대이고 싶어한다. 처음 왕눈이가 가진 힘은 0 이다. 힘은 항상 0 이상 이어야 한다.
왕눈이를 도와 연꽃잎 사이를 이동하는 경로를 출력하는 프로그램을 작성하시오.
출력
첫 줄에 N번 연꽃잎에 도착 한 뒤 최대 힘의 양을 출력한다.
두 번째 줄에는 1번 연꽃잎과 N번 연꽃잎을 포함하여 방문한 연꽃잎의 수 L을 출력한다.
다음 L개의 줄에 방문한 연꽃잎의 좌표들을 차례대로 출력한다.
만약, 가능한 답이 여러 가지인 경우 그 중 아무거나 하나 출력한다.
예제 출력 1
복사
5
4
1 1
2 1
2 3
3 3
[{"problem_id":"2989","problem_lang":"0","title":"\uac1c\uad6c\ub9ac \uc655\ub208\uc774","description":"<p>\uac1c\uad6c\ub9ac \uc655\ub208\uc774\ub294 N\uac1c\uc758 \uc5f0\uaf43\uc78e\uc774 \uc788\ub294 \uc5f0\ubabb\uc5d0 \uc0b4\uace0 \uc788\ub2e4. \uc5f0\uaf43\uc78e\uc740 1\ubd80\ud130 N\uae4c\uc9c0 \ucc28\ub840\ub300\ub85c \ubc88\ud638\uac00 \ub9e4\uaca8\uc838 \uc788\ub2e4. \uc5f0\ubabb\uc744 \uc704\uc5d0\uc11c \ubd24\uc744 \ub54c 2\ucc28\uc6d0 \ud3c9\uba74\uc5d0&nbsp;\uc5f0\uaf43\uc78e\uc774 (x,y) \uc88c\ud45c\uc5d0 \ub5a0 \uc788\ub294 \uac83 \ucc98\ub7fc \ubcf4\uc778\ub2e4. \uc655\ub208\uc774\ub294 \ub300\uac01\uc120\uc73c\ub85c \ub6f0\ub294 \uac83\uacfc \uc74c\uc758 \ubc29\ud5a5\uc73c\ub85c \ub6f0\ub294 \uac83\uc744 \ubb34\uc11c\uc6cc \ud55c\ub2e4. \uc880 \ub354 \uc790\uc138\ud788 \ub9d0\ud558\uc790\uba74 (x <sub>1<\/sub>,y<sub>1<\/sub>)\uc5d0\uc11c (x<sub>2<\/sub>,y<sub>2<\/sub>)\ub85c \ub6f0\uae30 \uc704\ud574\uc11c\ub294 \uc544\ub798 \ub450 \uc870\uac74 \uc911 \ud558\ub098\ub97c \ub9cc\uc871\ud574\uc57c\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>x<sub>2<\/sub> &gt; x<sub>1<\/sub> \uc774\uace0 y<sub>2<\/sub> = y<sub>1<\/sub><\/li>\r\n\t<li>y<sub>2<\/sub> &gt; y<sub>1<\/sub> \uc774\uace0 x<sub>2<\/sub> = x<sub>1<\/sub><\/li>\r\n<\/ul>\r\n\r\n<p>\uac01 \uc5f0\uaf43\uc78e \ub9c8\ub2e4 \uc77c\uc815 \uc218\uc758 \ud30c\ub9ac\uac00 \uc788\uace0, \uc655\ub208\uc774\ub294 \ud30c\ub9ac\ub97c \uba39\uc73c\uba70 \ud798\uc744 \ud68c\ubcf5\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc655\ub208\uc774\uac00 \ud55c \ubc88 \uc5f0\uaf43\uc78e\uc744 \uc774\ub3d9\ud558\uae30 \uc704\ud574\uc11c\ub294 K \ub9cc\ud07c \ud798\uc774&nbsp;\ub4e0\ub2e4. \uc655\ub208\uc774\ub294 \ucc98\uc74c 1\ubc88 \uc5f0\uaf43\uc78e\uc5d0\uc11c \uc2dc\uc791\ud558\uc5ec N\ubc88 \uc5f0\uaf43\uc78e\uc73c\ub85c \uc774\ub3d9\ud558\ub824\uace0 \ud55c\ub2e4. \ub2e4\ub9cc, \ub3c4\ucc29\ud558\uace0 \ub09c \ub4a4 \ud798\uc758 \ucd5c\ub300\uc774\uace0&nbsp;\uc2f6\uc5b4\ud55c\ub2e4. \ucc98\uc74c \uc655\ub208\uc774\uac00 \uac00\uc9c4 \ud798\uc740 0 \uc774\ub2e4. \ud798\uc740 \ud56d\uc0c1 0 \uc774\uc0c1 \uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc655\ub208\uc774\ub97c \ub3c4\uc640 \uc5f0\uaf43\uc78e \uc0ac\uc774\ub97c \uc774\ub3d9\ud558\ub294 \uacbd\ub85c\ub97c \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \uc5f0\uaf43\uc78e\uc758 \uc218 N\uacfc \ud55c \ubc88 \uc774\ub3d9\ud558\ub294\ub370 \ud544\uc694\ud55c \ud798 K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.&nbsp;(2 &le; N &le; 300 000, 1 &le; K &le; 1000)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 \uac01 \uc5f0\uaf43\uc78e\uc758 \uc88c\ud45c X, Y\uc640 \ud30c\ub9ac\uc758 \uc591 F\uac00&nbsp;\ucc28\ub840\ub300\ub85c&nbsp;\uc8fc\uc5b4\uc9c4\ub2e4. i+1\ubc88\uc9f8 \uc904\uc5d0 \uc8fc\uc5b4\uc9c0\ub294 \uc88c\ud45c\uc640 \ud30c\ub9ac\uc758 \uc591\uc740&nbsp;i\ubc88 \uc5f0\uaf43\uc78e\uc5d0 \uad00\ud55c \uc815\ubcf4\uc774\ub2e4. \uc5f0\uaf43\uc78e\uc758 \uc88c\ud45c\ub294 \uc11c\ub85c \ub2e4\ub974\ub2e4.&nbsp;(0 &le; X, Y &le; 100 000, 0 &le; F &le; 1000)<\/p>\r\n\r\n<p>\uc785\ub825\uc740&nbsp;\ud56d\uc0c1 \ub2f5\uc774 \uc874\uc7ac\ud558\ub3c4\ub85d \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab \uc904\uc5d0&nbsp;N\ubc88 \uc5f0\uaf43\uc78e\uc5d0 \ub3c4\ucc29 \ud55c \ub4a4 \ucd5c\ub300&nbsp;\ud798\uc758 \uc591\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub450&nbsp;\ubc88\uc9f8 \uc904\uc5d0\ub294 1\ubc88 \uc5f0\uaf43\uc78e\uacfc N\ubc88 \uc5f0\uaf43\uc78e\uc744 \ud3ec\ud568\ud558\uc5ec&nbsp;\ubc29\ubb38\ud55c \uc5f0\uaf43\uc78e\uc758 \uc218 L\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c L\uac1c\uc758 \uc904\uc5d0 \ubc29\ubb38\ud55c \uc5f0\uaf43\uc78e\uc758 \uc88c\ud45c\ub4e4\uc744 \ucc28\ub840\ub300\ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d, \uac00\ub2a5\ud55c \ub2f5\uc774 \uc5ec\ub7ec&nbsp;\uac00\uc9c0\uc778 \uacbd\uc6b0 \uadf8 \uc911 \uc544\ubb34\uac70\ub098 \ud558\ub098 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2989","problem_lang":"1","title":"BARICA","description":"<p>Barica is an unusual frog. She lives in a pond where N plants float on the surface of the water. The plants are numbered 1 through N. When viewing from above, the location of each plant is given by a pair of coordinates. What makes Barica unusual is her fear of jumping diagonally and in the negative direction. More precisely, she can jump from a plant at coordinates (x<sub>1<\/sub>, y<sub>1<\/sub>) to another at coordinates (x<sub>2<\/sub>, y<sub>2<\/sub>) only if:&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li>x<sub>2<\/sub> &gt; x<sub>1<\/sub> and y<sub>2<\/sub> = y<sub>1<\/sub>, or&nbsp;<\/li>\r\n\t<li>y<sub>2<\/sub> &gt; y<sub>1<\/sub> and x<sub>2<\/sub> = x<sub>1<\/sub><\/li>\r\n<\/ul>\r\n\r\n<p>For each plant, we know the number of flies in its immediate vicinity. Barica can use her swift tongue to eat all flies near the plant she is at.&nbsp;<\/p>\r\n\r\n<p>Barica absorbs one energy unit for each fly she eats, and uses K energy units for each jump she makes. Barica can not make a jump if she doesn&#39;t have enough energy units beforehand.&nbsp;<\/p>\r\n\r\n<p>Barica wants to go from plant 1 to plant N and have the largest amount of energy possible after arriving. Barica initially has no energy and must gather energy for her first jump from the flies around plant 1.&nbsp;<\/p>\r\n\r\n<p>Find the sequence of plants Barica should travel to achieve her goal.&nbsp;<\/p>\r\n","input":"<p>The first line of input contains two integers N and K (2 &le; N &le; 300 000, 1 &le; K &le; 1000) separated by a space.&nbsp;<\/p>\r\n\r\n<p>Each of the following N lines contains three integers X, Y and F (0 &le; X, Y &le; 100 000, 0 &le; F &le; 1000) separated by spaces, meaning that there is a plant at coordinates (X, Y) with F flies around it.&nbsp;<\/p>\r\n\r\n<p>The first plant in the input is plant 1, the second is plant 2 etc.&nbsp;<\/p>\r\n\r\n<p>No two plants will share the same pair of coordinates.&nbsp;<\/p>\r\n\r\n<p>Note: The input data will guarantee that a sequence of jumps, although not necessarily unique, will always exist.&nbsp;<\/p>\r\n","output":"<p>Output the final energy level on the first line.&nbsp;<\/p>\r\n\r\n<p>Output an integer L, the number of plants Barica should travel, including plants 1 and N.&nbsp;<\/p>\r\n\r\n<p>On the following L lines, output the sequence of plants Barica should travel.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]
