시간 제한 | 메모리 제한 | 제출 | 정답 | 맞힌 사람 | 정답 비율 |
---|---|---|---|---|---|
7 초 (추가 시간 없음) | 1024 MB | 11 | 4 | 4 | 50.000% |
IOI Zoo is famous for giraffes. There are $N$ giraffes in IOI Zoo, numbered from $1$ to $N$ in ascending order of their heights. The heights of the giraffes are different from each other. There are $N$ cages placed in a straight line, numbered from $1$ to $N$ from left to right. In each cage, a giraffe is living in it. The giraffe $P_i$ is living in the cage $i$.
Mr. APIO is the curator of IOI Zoo. He is worrying about the ratings of IOI Zoo in reviews. IOI Zoo receives low ratings for the reason that “the visual quality of the giraffes is bad.” Precisely, when a visitor takes a picture of giraffes, the visitor chooses integers $l$, $r$ ($1 ≤ l ≤ r ≤ N$) and takes a picture of the giraffes in the cages $l, l + 1, \dots ,r$. Then, the visual quality of the giraffes becomes bad if both of the following conditions are satisfied.
Mr. APIO will arrange the positions of the giraffes so that the visual quality of the giraffes does not become bad for any choice of $l$, $r$ ($1 ≤ l ≤ r ≤ N$) when a visitor takes a picture. Since it takes a lot of work to move a giraffe from one cage to another cage, he wants to minimize the number of giraffes which are moved. Of course, after he finishes moving the giraffes, in each cage, a giraffe should be living in it.
Given information of the current positions of the giraffes, write a program which calculates the minimum number of giraffes which are moved. Since Mr. APIO arranged the current positions of the giraffes at random, you may assume that the values $P_i$ ($1 ≤ i ≤ N$) are generated at random (See Generation of Input Data for details).
Read the following data from the standard input. Given values are all integers.
$N$
$P_1 P_2 \cdots P_N$
Write one line to the standard output. The output should contain the minimum number of giraffes which are moved.
번호 | 배점 | 제한 |
---|---|---|
1 | 10 | $N ≤ 7$. |
2 | 22 | $N ≤ 13$. |
3 | 27 | $N ≤ 300$. |
4 | 41 | No additional constraints. |
6 5 4 6 1 3 2
2
There are $6$ giraffes in IOI Zoo. From the left, the giraffes $5$, $4$, $6$, $1$, $3$, $2$ are living in the cages in this order. In this arrangement, if a visitor takes a picture for $l = 2$, $r = 5$, the visual quality of the giraffes becomes bad. The two conditions are satisfied as follows.
If Mr. APIO moves the giraffe $1$ from the cage $4$ to the cage $1$, and he moves the giraffe $5$ from the cage $1$ to the cage $4$, the visual quality of the giraffes does not become bad for any choice of $l$, $r$ when a visitor takes a picture. Mr. APIO achieves the goal by moving $2$ giraffes. Since it is the minimum value, output $2$.
This sample input satisfies the constraints of all the subtasks.
4 4 1 3 2
0
There are $4$ giraffes in IOI Zoo. From the left, the giraffes $4$, $1$, $3$, $2$ are living in the cages in this order. In this arrangement, the visual quality of the giraffes does not become bad for any choice of $l$, $r$ when a visitor takes a picture. Mr. APIO does not need to move giraffes. Therefore, output $0$.
This sample input satisfies the constraints of all the subtasks.
7 3 1 6 7 4 2 5
2
For example, if Mr. APIO moves the giraffes so that the giraffes $3$, $5$, $6$, $7$, $4$, $2$, $1$ are living in the cages in this order. Then, the visual quality of the giraffes does not become bad for any choice of $l$, $r$ when a visitor takes a picture. Mr. APIO achieves the goal by moving $2$ giraffes. Since it is the minimum value, output $2$.
This sample input satisfies the constraints of all the subtasks.
13 8 5 6 13 4 2 11 3 9 1 10 7 12
6
This sample input satisfies the constraints of Subtasks 2, 3, 4.
Generation of Input Data
In this task, except for Sample Input, there are 10 test cases which satisfy the constraints of Subtasks 1, 2, 3, 4. Also, there are 10 test cases which satisfy the constraints of Subtasks 2, 3, 4 only, there are 10 test cases which satisfy the constraints of Subtasks 3, 4 only, and there are 10 test cases which satisfy the constraints of Subtask 4 only. In total, including Sample Input, 44 test cases are used for grading. All the 44 test cases for this task are generated by the following way.