시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

아이잔은 N개의 정수 S[0], S[1], ..., S[N-1]로 이루어진 수열 S를 가지고 있다. 수열은 0부터 N-1까지 서로 다른 N개의 정수로 이루어져있다. 아이잔은 두 수의 위치를 바꾸며 이 수열을 오름차순으로 정렬하려고 한다. 아이잔의 오랜 친구인 에르맥도 수열에서 두 수를 바꾸는데, 아이잔과는 다르게 정렬하려는 목적 없이 아무렇게나 바꾼다.

아이잔과 에르맥은 라운드를 거치며 수열을 조작한다. 각 라운드마다, 에르맥이 먼저 위치 바꾸기를 하고 그 다음 아이잔이 위치 바꾸기를 한다. 위치 바꾸기에 대해서 좀 더 자세히 말하자면, 바꿀 두 위치를 정하고 그 위치에 있는 값을 맞바꾼다. 이 때 정하는 두 위치가 다를 필요는 없다. 만약 정한 두 위치가 같으면 수열에 아무런 변화가 없다.

아이잔은 에르맥이 수열 S를 정렬하려는 목적 없이 아무렇게나 바꾼다는 사실을 알고 있다. 더 나아가서 라운드를 시작하기 전부터 에르맥이 어떻게 위치 바꾸기를 할 건지 미리 다 알고 있다. 에르맥은 M 라운드에 대한 계획을 가지고 있다. 라운드의 번호를 순서대로 0 부터 M-1 까지 매겼을 때, i번 라운드에서 에르맥이 바꿀 두 위치는 X[i]와 Y[i]이다.

아이잔은 수열 S를 오름차순으로 정렬하길 원한다. 각 라운드를 시작하기 전에 만약 수열이 이미 정렬되어 있다면 라운드를 더 이상 진행하지 않고 멈출 수 있다. 처음 수열 S에 대한 정보와 에르맥이 M 라운드 동안 어떻게 위치 바꾸기를 할지에 대한 정보가 주어졌을 때, 아이잔이 어떻게 위치 바꾸기를 해야할지 구하시오. 추가적으로, 어떤 부분 문제에 대해서는 가능한 가장 적은 라운드 만에 정렬을 해야할 수도 있다. 언제나 M 라운드 안에 정렬이 가능하도록 입력이 주어진다.

만약 어떤 라운드에서 에르맥이 위치 바꾸기를 한 뒤 수열이 정렬되어 있다면, 아이잔은 같은 두 위치를 맞바꿔주면 된다 (예를 들어 0번 위치와 0번 위치). 그러면 이 라운드의 끝에서 수열 S는 정렬되고 아이잔은 멈출 수 있다. 또한 처음부터 수열 S가 정렬되어 있다면 필요한 라운드의 최소 수는 0 이다.

예제 1

  • 처음 수열 S = 4, 3, 2, 1, 0
  • 에르맥은 M = 6라운드를 진행하려 한다.
  • 에르맥이 바꿀 위치에 대한 정보 X와 Y는 X = 0, 1, 2, 3, 0, 1이며, Y = 1, 2, 3, 4, 1, 2 이다. 다르게 얘기하면 에르맥은 (0, 1), (1,2), (2,3), (3,4), (0, 1) 그리고 (1, 2) 순서대로 위치를 바꿀 계획이다.

이러한 상황에서 아이잔은 3 라운드 만에 수열 S를 0, 1, 2, 3, 4로 정렬할 수 있다. 아이잔은 (0, 4), (1, 3) 그리고 (3, 4) 순서대로 위치 바꾸기를 하면 된다.

아래 표는 각 위치 바꾸기마다 수열 S의 내용이 어떻게 바뀌는지 나타내고 있다.

라운드 사람 바꿀 두 위치 수열
초기     4, 3, 2, 1, 0
0 에르맥 (0, 1) 3, 4, 2, 1, 0
0 아이잔 (0, 4) 0, 4, 2, 1, 3
1 에르맥 (1, 2) 0, 2, 4, 1, 3
1 아이잔 (1, 3) 0, 1, 4, 2, 3
2 에르맥 (2, 3) 0, 1, 2, 4, 3
2 아이잔 (3, 4) 0, 1, 2, 3, 4

예제 2

  • 처음 수열 S = 3, 0, 4, 2, 1
  • 에르맥은 M = 5라운드를 진행하려 한다.
  • 에르맥은 (1, 1), (4, 0), (2, 3), (1, 4) 그리고 (0, 4) 순서대로 위치를 바꿀 계획이다.

이러한 상황에서 아이잔은 3 라운드 만에 수열 S를 정렬할 수 있다. 아이잔은 (1, 4), (4, 2) 그리고 (2, 2) 순서대로 위치 바꾸기를 하면 된다.

아래 표는 각 위치 바꾸기마다 수열 S의 내용이 어떻게 바뀌는지 나타내고 있다.

라운드 사람 바꿀 두 위치 수열
초기     3, 0, 4, 2, 1
0 에르맥 (1, 1) 3, 0, 4, 2, 1
0 아이잔 (1, 4) 3, 1, 4, 2, 0
1 에르맥 (4, 0) 0, 1, 4, 2, 3
1 아이잔 (4, 2) 0, 1, 3, 2, 4
2 에르맥 (2, 3) 0, 1, 2, 3, 4
2 아이잔 (2, 2) 0, 1, 2, 3, 4

수열 S와 정수 M, 그리고 X, Y가 주어진다.

아이잔이 수열 S를 정렬하기 위해 어떻게 위치를 바꿀지에 대해 계산하자. 정렬할 수 있는 가능한 가장 적은 라운드 안에 정렬 해야한다.

다음 함수 findSwapPairs를 구현해야 한다.

  • findSwapPairs(N, S, M, X, Y, P, Q) — 이 함수는 단 한 번 그레이더에 의해 호출된다.
    • N: 수열 S의 크기
    • S: 처음 수열 S에 대한 정보를 가지고 있는 정수 배열
    • M: 에르맥이 계획한 라운드 수
    • X, Y: 크기가 M인 정수 배열들. 0 ≤ i ≤ M-1 인 i에 대해 i번 라운드에서 에르맥은 두 위치 X[i], Y[i]에 있는 수를 맞바꾼다.
    • P, Q: 정수 배열들. 아이잔이 바꿀 위치에 대한 정보를 위해 필요한 배열이다. R이 여러분이 구한 정렬하기 위해 필요한 라운드 수라고 하자. 0과 R-1 사이의 i에 대해서 i번 라운드에 아이잔이 고른 맞바꿀 두 위치를 P[i]와 Q[i]에 저장한다. 배열 P와 Q는 이미 크기 M으로 메모리가 잡혀있다.
    • 이 함수는 위에 정의된 R 값을 리턴해야 한다.

M라운드 혹은 보다 더 일찍 정렬 가능하도록 입력이 주어진다.

입력

  • 1번 줄: N
  • 2번 줄: S[0] … S[N - 1]
  • 3번 줄: M
  • 4 ~ M + 3번 줄: X[i] Y[i]

6 ≤ N ≤ 200,000, M = 3N, R은 가능한 작은 값이어야 한다.

출력

findSwapPairs가 리턴한 값을 출력한다.

다음 양식에 따라 출력한다:

  • 1번 줄: findSwapPairs의 리턴값 R
  • 2+i번 줄 (0 ≤ i < R): P[i] Q[i]

예제 입력 1

5
4 3 2 1 0
6
0 1
1 2
2 3
3 4
0 1
1 2

예제 출력 1

3
0 4
1 3
3 4

힌트

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\uc0ac\uc2e4\uc744 \uc54c\uace0 \uc788\ub2e4. \ub354 \ub098\uc544\uac00\uc11c \ub77c\uc6b4\ub4dc\ub97c \uc2dc\uc791\ud558\uae30 \uc804\ubd80\ud130 \uc5d0\ub974\ub9e5\uc774 \uc5b4\ub5bb\uac8c \uc704\uce58 \ubc14\uafb8\uae30\ub97c \ud560 \uac74\uc9c0 \ubbf8\ub9ac \ub2e4 \uc54c\uace0 \uc788\ub2e4. \uc5d0\ub974\ub9e5\uc740 M \ub77c\uc6b4\ub4dc\uc5d0 \ub300\ud55c \uacc4\ud68d\uc744 \uac00\uc9c0\uace0 \uc788\ub2e4. \ub77c\uc6b4\ub4dc\uc758 \ubc88\ud638\ub97c \uc21c\uc11c\ub300\ub85c 0 \ubd80\ud130 M-1 \uae4c\uc9c0 \ub9e4\uacbc\uc744 \ub54c, i\ubc88 \ub77c\uc6b4\ub4dc\uc5d0\uc11c \uc5d0\ub974\ub9e5\uc774 \ubc14\uafc0 \ub450 \uc704\uce58\ub294 X[i]\uc640 Y[i]\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc544\uc774\uc794\uc740 \uc218\uc5f4 S\ub97c \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub82c\ud558\uae38 \uc6d0\ud55c\ub2e4. \uac01 \ub77c\uc6b4\ub4dc\ub97c \uc2dc\uc791\ud558\uae30 \uc804\uc5d0 \ub9cc\uc57d \uc218\uc5f4\uc774 \uc774\ubbf8 \uc815\ub82c\ub418\uc5b4 \uc788\ub2e4\uba74 \ub77c\uc6b4\ub4dc\ub97c \ub354 \uc774\uc0c1 \uc9c4\ud589\ud558\uc9c0 \uc54a\uace0 \uba48\ucd9c \uc218 \uc788\ub2e4. \ucc98\uc74c \uc218\uc5f4 S\uc5d0 \ub300\ud55c \uc815\ubcf4\uc640 \uc5d0\ub974\ub9e5\uc774 M \ub77c\uc6b4\ub4dc \ub3d9\uc548 \uc5b4\ub5bb\uac8c \uc704\uce58 \ubc14\uafb8\uae30\ub97c \ud560\uc9c0\uc5d0 \ub300\ud55c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc544\uc774\uc794\uc774 \uc5b4\ub5bb\uac8c \uc704\uce58 \ubc14\uafb8\uae30\ub97c \ud574\uc57c\ud560\uc9c0 \uad6c\ud558\uc2dc\uc624. \ucd94\uac00\uc801\uc73c\ub85c, \uc5b4\ub5a4 \ubd80\ubd84 \ubb38\uc81c\uc5d0 \ub300\ud574\uc11c\ub294 \uac00\ub2a5\ud55c \uac00\uc7a5 \uc801\uc740 \ub77c\uc6b4\ub4dc \ub9cc\uc5d0 \uc815\ub82c\uc744 \ud574\uc57c\ud560 \uc218\ub3c4 \uc788\ub2e4. \uc5b8\uc81c\ub098 M \ub77c\uc6b4\ub4dc \uc548\uc5d0 \uc815\ub82c\uc774 \uac00\ub2a5\ud558\ub3c4\ub85d \uc785\ub825\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d \uc5b4\ub5a4 \ub77c\uc6b4\ub4dc\uc5d0\uc11c \uc5d0\ub974\ub9e5\uc774 \uc704\uce58 \ubc14\uafb8\uae30\ub97c \ud55c \ub4a4 \uc218\uc5f4\uc774 \uc815\ub82c\ub418\uc5b4 \uc788\ub2e4\uba74, \uc544\uc774\uc794\uc740 \uac19\uc740 \ub450 \uc704\uce58\ub97c \ub9de\ubc14\uafd4\uc8fc\uba74 \ub41c\ub2e4 (\uc608\ub97c \ub4e4\uc5b4 0\ubc88 \uc704\uce58\uc640 0\ubc88 \uc704\uce58). \uadf8\ub7ec\uba74 \uc774 \ub77c\uc6b4\ub4dc\uc758 \ub05d\uc5d0\uc11c \uc218\uc5f4 S\ub294 \uc815\ub82c\ub418\uace0 \uc544\uc774\uc794\uc740 \uba48\ucd9c \uc218 \uc788\ub2e4. \ub610\ud55c \ucc98\uc74c\ubd80\ud130 \uc218\uc5f4 S\uac00 \uc815\ub82c\ub418\uc5b4 \uc788\ub2e4\uba74 \ud544\uc694\ud55c \ub77c\uc6b4\ub4dc\uc758 \ucd5c\uc18c \uc218\ub294 0 \uc774\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 1<\/p>\r\n\r\n<ul>\r\n\t<li>\ucc98\uc74c \uc218\uc5f4 S = 4, 3, 2, 1, 0<\/li>\r\n\t<li>\uc5d0\ub974\ub9e5\uc740 M = 6\ub77c\uc6b4\ub4dc\ub97c \uc9c4\ud589\ud558\ub824 \ud55c\ub2e4.<\/li>\r\n\t<li>\uc5d0\ub974\ub9e5\uc774 \ubc14\uafc0 \uc704\uce58\uc5d0 \ub300\ud55c \uc815\ubcf4 X\uc640 Y\ub294 X = 0, 1, 2, 3, 0, 1\uc774\uba70, Y = 1, 2, 3, 4, 1, 2 \uc774\ub2e4. \ub2e4\ub974\uac8c \uc598\uae30\ud558\uba74 \uc5d0\ub974\ub9e5\uc740 (0, 1), (1,2), (2,3), (3,4), (0, 1) \uadf8\ub9ac\uace0 (1, 2) \uc21c\uc11c\ub300\ub85c \uc704\uce58\ub97c \ubc14\uafc0 \uacc4\ud68d\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc774\ub7ec\ud55c \uc0c1\ud669\uc5d0\uc11c \uc544\uc774\uc794\uc740 3 \ub77c\uc6b4\ub4dc \ub9cc\uc5d0 \uc218\uc5f4 S\ub97c 0, 1, 2, 3, 4\ub85c \uc815\ub82c\ud560 \uc218 \uc788\ub2e4. \uc544\uc774\uc794\uc740 (0, 4), (1, 3) \uadf8\ub9ac\uace0 (3, 4) \uc21c\uc11c\ub300\ub85c \uc704\uce58 \ubc14\uafb8\uae30\ub97c \ud558\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798 \ud45c\ub294 \uac01 \uc704\uce58 \ubc14\uafb8\uae30\ub9c8\ub2e4 \uc218\uc5f4 S\uc758 \ub0b4\uc6a9\uc774 \uc5b4\ub5bb\uac8c \ubc14\ub00c\ub294\uc9c0 \ub098\ud0c0\ub0b4\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:30%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>\ub77c\uc6b4\ub4dc<\/th>\r\n\t\t\t<th>\uc0ac\ub78c<\/th>\r\n\t\t\t<th>\ubc14\uafc0 \ub450 \uc704\uce58<\/th>\r\n\t\t\t<th>\uc218\uc5f4<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>\ucd08\uae30<\/td>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<td>4, 3, 2, 1, 0<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>\uc5d0\ub974\ub9e5<\/td>\r\n\t\t\t<td>(0, 1)<\/td>\r\n\t\t\t<td>3, 4, 2, 1, 0<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>\uc544\uc774\uc794<\/td>\r\n\t\t\t<td>(0, 4)<\/td>\r\n\t\t\t<td>0, 4, 2, 1, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>\uc5d0\ub974\ub9e5<\/td>\r\n\t\t\t<td>(1, 2)<\/td>\r\n\t\t\t<td>0, 2, 4, 1, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>\uc544\uc774\uc794<\/td>\r\n\t\t\t<td>(1, 3)<\/td>\r\n\t\t\t<td>0, 1, 4, 2, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>\uc5d0\ub974\ub9e5<\/td>\r\n\t\t\t<td>(2, 3)<\/td>\r\n\t\t\t<td>0, 1, 2, 4, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>\uc544\uc774\uc794<\/td>\r\n\t\t\t<td>(3, 4)<\/td>\r\n\t\t\t<td>0, 1, 2, 3, 4<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>\uc608\uc81c 2<\/p>\r\n\r\n<ul>\r\n\t<li>\ucc98\uc74c \uc218\uc5f4 S = 3, 0, 4, 2, 1<\/li>\r\n\t<li>\uc5d0\ub974\ub9e5\uc740 M = 5\ub77c\uc6b4\ub4dc\ub97c \uc9c4\ud589\ud558\ub824 \ud55c\ub2e4.<\/li>\r\n\t<li>\uc5d0\ub974\ub9e5\uc740 (1, 1), (4, 0), (2, 3), (1, 4) \uadf8\ub9ac\uace0 (0, 4) \uc21c\uc11c\ub300\ub85c \uc704\uce58\ub97c \ubc14\uafc0 \uacc4\ud68d\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc774\ub7ec\ud55c \uc0c1\ud669\uc5d0\uc11c \uc544\uc774\uc794\uc740 3 \ub77c\uc6b4\ub4dc \ub9cc\uc5d0 \uc218\uc5f4 S\ub97c \uc815\ub82c\ud560 \uc218 \uc788\ub2e4. \uc544\uc774\uc794\uc740 (1, 4), (4, 2) \uadf8\ub9ac\uace0 (2, 2) \uc21c\uc11c\ub300\ub85c \uc704\uce58 \ubc14\uafb8\uae30\ub97c \ud558\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798 \ud45c\ub294 \uac01 \uc704\uce58 \ubc14\uafb8\uae30\ub9c8\ub2e4 \uc218\uc5f4 S\uc758 \ub0b4\uc6a9\uc774 \uc5b4\ub5bb\uac8c \ubc14\ub00c\ub294\uc9c0 \ub098\ud0c0\ub0b4\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:30%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>\ub77c\uc6b4\ub4dc<\/th>\r\n\t\t\t<th>\uc0ac\ub78c<\/th>\r\n\t\t\t<th>\ubc14\uafc0 \ub450 \uc704\uce58<\/th>\r\n\t\t\t<th>\uc218\uc5f4<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>\ucd08\uae30<\/td>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<td>3, 0, 4, 2, 1<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>\uc5d0\ub974\ub9e5<\/td>\r\n\t\t\t<td>(1, 1)<\/td>\r\n\t\t\t<td>3, 0, 4, 2, 1<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>\uc544\uc774\uc794<\/td>\r\n\t\t\t<td>(1, 4)<\/td>\r\n\t\t\t<td>3, 1, 4, 2, 0<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>\uc5d0\ub974\ub9e5<\/td>\r\n\t\t\t<td>(4, 0)<\/td>\r\n\t\t\t<td>0, 1, 4, 2, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>\uc544\uc774\uc794<\/td>\r\n\t\t\t<td>(4, 2)<\/td>\r\n\t\t\t<td>0, 1, 3, 2, 4<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>\uc5d0\ub974\ub9e5<\/td>\r\n\t\t\t<td>(2, 3)<\/td>\r\n\t\t\t<td>0, 1, 2, 3, 4<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>\uc544\uc774\uc794<\/td>\r\n\t\t\t<td>(2, 2)<\/td>\r\n\t\t\t<td>0, 1, 2, 3, 4<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>\uc218\uc5f4 S\uc640 \uc815\uc218 M, \uadf8\ub9ac\uace0 X, Y\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uc544\uc774\uc794\uc774 \uc218\uc5f4 S\ub97c \uc815\ub82c\ud558\uae30 \uc704\ud574 \uc5b4\ub5bb\uac8c \uc704\uce58\ub97c \ubc14\uafc0\uc9c0\uc5d0 \ub300\ud574 \uacc4\uc0b0\ud558\uc790.&nbsp;\uc815\ub82c\ud560 \uc218 \uc788\ub294 \uac00\ub2a5\ud55c \uac00\uc7a5 \uc801\uc740 \ub77c\uc6b4\ub4dc \uc548\uc5d0 \uc815\ub82c \ud574\uc57c\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \ud568\uc218 findSwapPairs\ub97c \uad6c\ud604\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>findSwapPairs(N, S, M, X, Y, P, Q) &mdash; \uc774 \ud568\uc218\ub294 \ub2e8 \ud55c \ubc88 \uadf8\ub808\uc774\ub354\uc5d0 \uc758\ud574 \ud638\ucd9c\ub41c\ub2e4.\r\n\t<ul>\r\n\t\t<li>N: \uc218\uc5f4 S\uc758 \ud06c\uae30<\/li>\r\n\t\t<li>S: \ucc98\uc74c \uc218\uc5f4 S\uc5d0 \ub300\ud55c \uc815\ubcf4\ub97c \uac00\uc9c0\uace0 \uc788\ub294 \uc815\uc218 \ubc30\uc5f4<\/li>\r\n\t\t<li>M: \uc5d0\ub974\ub9e5\uc774 \uacc4\ud68d\ud55c \ub77c\uc6b4\ub4dc \uc218<\/li>\r\n\t\t<li>X, Y: \ud06c\uae30\uac00 M\uc778 \uc815\uc218 \ubc30\uc5f4\ub4e4. 0 &le; i &le; M-1 \uc778 i\uc5d0 \ub300\ud574 i\ubc88 \ub77c\uc6b4\ub4dc\uc5d0\uc11c \uc5d0\ub974\ub9e5\uc740 \ub450 \uc704\uce58 X[i], Y[i]\uc5d0 \uc788\ub294 \uc218\ub97c \ub9de\ubc14\uafbc\ub2e4.<\/li>\r\n\t\t<li>P, Q: \uc815\uc218 \ubc30\uc5f4\ub4e4. \uc544\uc774\uc794\uc774 \ubc14\uafc0 \uc704\uce58\uc5d0 \ub300\ud55c \uc815\ubcf4\ub97c \uc704\ud574 \ud544\uc694\ud55c \ubc30\uc5f4\uc774\ub2e4. R\uc774 \uc5ec\ub7ec\ubd84\uc774 \uad6c\ud55c \uc815\ub82c\ud558\uae30 \uc704\ud574 \ud544\uc694\ud55c \ub77c\uc6b4\ub4dc \uc218\ub77c\uace0 \ud558\uc790. 0\uacfc R-1 \uc0ac\uc774\uc758 i\uc5d0 \ub300\ud574\uc11c i\ubc88 \ub77c\uc6b4\ub4dc\uc5d0 \uc544\uc774\uc794\uc774 \uace0\ub978 \ub9de\ubc14\uafc0 \ub450 \uc704\uce58\ub97c P[i]\uc640 Q[i]\uc5d0 \uc800\uc7a5\ud55c\ub2e4. \ubc30\uc5f4 P\uc640 Q\ub294 \uc774\ubbf8 \ud06c\uae30 M\uc73c\ub85c \uba54\ubaa8\ub9ac\uac00 \uc7a1\ud600\uc788\ub2e4.<\/li>\r\n\t\t<li>\uc774 \ud568\uc218\ub294 \uc704\uc5d0 \uc815\uc758\ub41c R \uac12\uc744 \ub9ac\ud134\ud574\uc57c \ud55c\ub2e4.<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n\r\n<p>M\ub77c\uc6b4\ub4dc \ud639\uc740 \ubcf4\ub2e4 \ub354 \uc77c\ucc0d \uc815\ub82c \uac00\ub2a5\ud558\ub3c4\ub85d \uc785\ub825\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","input":"<ul>\r\n\t<li>1\ubc88 \uc904: N<\/li>\r\n\t<li>2\ubc88 \uc904: S[0] &hellip; S[N - 1]<\/li>\r\n\t<li>3\ubc88 \uc904: M<\/li>\r\n\t<li>4 ~ M + 3\ubc88 \uc904: X[i] Y[i]<\/li>\r\n<\/ul>\r\n\r\n<p>6 &le; N &le; 200,000, M = 3N, R\uc740 \uac00\ub2a5\ud55c \uc791\uc740 \uac12\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n","output":"<p>findSwapPairs\uac00 \ub9ac\ud134\ud55c \uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc591\uc2dd\uc5d0 \ub530\ub77c \ucd9c\ub825\ud55c\ub2e4:<\/p>\r\n\r\n<ul>\r\n\t<li>1\ubc88 \uc904: findSwapPairs\uc758 \ub9ac\ud134\uac12 R<\/li>\r\n\t<li>2+i\ubc88 \uc904 (0 &le; i &lt; R): P[i] Q[i]<\/li>\r\n<\/ul>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10924","problem_lang":"1","title":"Sorting 2","description":"<p>Aizhan has a sequence of N integers S[0], S[1], ..., S[N-1]. The sequence consists of distinct numbers from 0 to N-1. She is trying to sort this sequence in ascending order by swapping some pairs of elements. Her friend Ermek is also going to swap some pairs of elements &mdash; not necessarily in a helpful way.<\/p>\r\n\r\n<p>Ermek and Aizhan are going to modify the sequence in a series of rounds. In each round, first Ermek makes a swap and then Aizhan makes another swap. More precisely, the person making a swap chooses two valid indices and swaps the elements at those indices. Note that the two indices do not have to be distinct. If they are equal, the current person swaps an element with itself, which does not change the sequence.<\/p>\r\n\r\n<p>Aizhan knows that Ermek does not actually care about sorting the sequence S. She also knows the exact indices Ermek is going to choose. Ermek plans to take part in M rounds of swapping. We number these rounds from 0 to M-1. For each between 0 and M-1 inclusive, Ermek will choose the indices X[i] and Y[i] in round i.<\/p>\r\n\r\n<p>Aizhan wants to sort the sequence S. Before each round, if Aizhan sees that the sequence is already sorted in ascending order, she will terminate the entire process. Given the original sequence S and the indices Ermek is going to choose, your task is to find a sequence of swaps, which Aizhan can use to sort the sequence S. In addition, in some subtasks you are required to find a sequence of swaps that is as short as possible. You may assume that it is possible to sort the sequence S in M or fewer rounds.<\/p>\r\n\r\n<p>Note that if Aizhan sees that the sequence S is sorted after Ermek&rsquo;s swap, she can choose to swap two equal indices (e.g., 0 and 0). As a result the sequence S is also sorted after the entire round, so Aizhan reaches her goal. Also note that if the initialsequence S is already sorted, the minimal number of rounds needed to sort it is 0.<\/p>\r\n\r\n<p>Example 1<\/p>\r\n\r\n<p>Suppose that:<\/p>\r\n\r\n<ul>\r\n\t<li>The initialsequence is S = 4, 3, 2, 1, 0.<\/li>\r\n\t<li>Ermek is willing to make M = 6 swaps.<\/li>\r\n\t<li>The sequences and that describe the indices Ermek is going to choose are X = 0, 1, 2, 3, 0, 1 and Y = 1, 2, 3, 4, 1, 2. In other words, the pairs of indices that Ermek plans to choose are (0, 1), (1, 2), (2, 3), (3, 4), (0, 1), and (1, 2).<\/li>\r\n<\/ul>\r\n\r\n<p>In this setting Aizhan can sort the sequence S into the order 0, 1, 2, 3, 4 in three rounds. She can do so by choosing the indices (0, 4), (1, 3), and then (3, 4).<\/p>\r\n\r\n<p>The following table shows how Ermek and Aizhan modify the sequence.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:30%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>Round<\/th>\r\n\t\t\t<th>Player<\/th>\r\n\t\t\t<th>Piar of swapped indices<\/th>\r\n\t\t\t<th>Sequence<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>beginning<\/td>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<td>4, 3, 2, 1, 0<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>Ermek<\/td>\r\n\t\t\t<td>(0, 1)<\/td>\r\n\t\t\t<td>3, 4, 2, 1, 0<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>Aizhan<\/td>\r\n\t\t\t<td>(0, 4)<\/td>\r\n\t\t\t<td>0, 4, 2, 1, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>Ermek<\/td>\r\n\t\t\t<td>(1, 2)<\/td>\r\n\t\t\t<td>0, 2, 4, 1, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>Aizhan<\/td>\r\n\t\t\t<td>(1, 3)<\/td>\r\n\t\t\t<td>0, 1, 4, 2, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>Ermek<\/td>\r\n\t\t\t<td>(2, 3)<\/td>\r\n\t\t\t<td>0, 1, 2, 4, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>Aizhan<\/td>\r\n\t\t\t<td>(3, 4)<\/td>\r\n\t\t\t<td>0, 1, 2, 3, 4<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>Example 2<\/p>\r\n\r\n<p>Suppose that:<\/p>\r\n\r\n<ul>\r\n\t<li>The initialsequence is S = 3, 0, 4, 2, 1.<\/li>\r\n\t<li>Ermek is willing to make M = 5 swaps.<\/li>\r\n\t<li>The pairs of indices that Ermek plans to choose are (1, 1), (4, 0), (2, 3), (1, 4), and (0, 4).<\/li>\r\n<\/ul>\r\n\r\n<p>In this setting Aizhan can sort the sequence Sin three rounds, for example by choosing the pairs of indices (1, 4), (4, 2), and then (2, 2). The following table shows how Ermek and Aizhan modify the sequence.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:30%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th>Round<\/th>\r\n\t\t\t<th>Player<\/th>\r\n\t\t\t<th>Pair of swapped indices<\/th>\r\n\t\t\t<th>Sequence<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>\ucd08\uae30<\/td>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<td>3, 0, 4, 2, 1<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>Ermek<\/td>\r\n\t\t\t<td>(1, 1)<\/td>\r\n\t\t\t<td>3, 0, 4, 2, 1<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>Aizhan<\/td>\r\n\t\t\t<td>(1, 4)<\/td>\r\n\t\t\t<td>3, 1, 4, 2, 0<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>Ermek<\/td>\r\n\t\t\t<td>(4, 0)<\/td>\r\n\t\t\t<td>0, 1, 4, 2, 3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>Aizhan<\/td>\r\n\t\t\t<td>(4, 2)<\/td>\r\n\t\t\t<td>0, 1, 3, 2, 4<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>Ermek<\/td>\r\n\t\t\t<td>(2, 3)<\/td>\r\n\t\t\t<td>0, 1, 2, 3, 4<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>Aizhan<\/td>\r\n\t\t\t<td>(2, 2)<\/td>\r\n\t\t\t<td>0, 1, 2, 3, 4<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>You are given the sequence S, the number M, and the sequences of indices X and Y. Compute a sequence of swaps, which Aizhan can use to sort the sequence S.&nbsp;The sequence of swaps you find has to be the shortest possible.<\/p>\r\n\r\n<p>You need to implement the function findSwapPairs:<\/p>\r\n\r\n<ul>\r\n\t<li>findSwapPairs(N, S, M, X, Y, P, Q) &mdash; This function will be called by the grader exactly once.\r\n\t<ul>\r\n\t\t<li>N: the length of the sequence S.<\/li>\r\n\t\t<li>S: an array of integers containing the initial sequence S.<\/li>\r\n\t\t<li>M: the number of swaps Ermek plans to make.<\/li>\r\n\t\t<li>X, Y: arrays of integers of length M. For 0 &le; i &le; M-1, in round i Ermek plans to swap numbers at indices X[i] and Y[i].<\/li>\r\n\t\t<li>P, Q: arrays of integers. Use these arrays to report one possible sequence of swaps Aizhan can make to sort the sequence S. Denote by R the length of the sequence of swaps that your program has found. For each i between 0 and R-1 inclusive, the indices Aizhan should choose in round i should be stored into P[i] and Q[i]. You may assume that the arrays P and Q have already been allocated to M elements each.<\/li>\r\n\t\t<li>This function should return the value of R (defined above).<\/li>\r\n\t<\/ul>\r\n\t<\/li>\r\n<\/ul>\r\n","input":"<ul>\r\n\t<li>line 1: N<\/li>\r\n\t<li>line 2: S[0] &hellip; S[N - 1]<\/li>\r\n\t<li>line 3: M<\/li>\r\n\t<li>lines 4, &hellip;, M + 3: X[i] Y[i]<\/li>\r\n<\/ul>\r\n","output":"<p>The sample grader prints the following output:<\/p>\r\n\r\n<ul>\r\n\t<li>line 1: the return value R of findSwapPairs<\/li>\r\n\t<li>line 2+i, for 0 &le; i &lt; R: P[i] Q[i]<\/li>\r\n<\/ul>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]