A dragon symbolizes wisdom, power and wealth. On Lunar New Year's Day, people model a dragon with bamboo strips and clothes, raise them with rods, and hold the rods high and low to resemble a flying dragon.
A performer holding the rod low is represented by a 1, while one holding it high is represented by a 2. Thus, the line of performers can be represented by a sequence a1, a2, ..., an.
Little Tommy is among them. He would like to choose an interval [l, r] (1 ≤ l ≤ r ≤ n), then reverse al, al + 1, ..., ar so that the length of the longest non-decreasing subsequence of the new sequence is maximum.
A non-decreasing subsequence is a sequence of indices p1, p2, ..., pk, such that p1 < p2 < ... < pk and ap1 ≤ ap2 ≤ ... ≤ apk. The length of the subsequence is k.
The first line contains an integer n (1 ≤ n ≤ 2000), denoting the length of the original sequence.
The second line contains n space-separated integers, describing the original sequence a1, a2, ..., an (1 ≤ ai ≤ 2, i = 1, 2, ..., n).
Print a single integer, which means the maximum possible length of the longest non-decreasing subsequence of the new sequence.
4 1 2 1 2
4
10 1 1 2 2 2 1 1 2 2 1
9
In the first example, after reversing [2, 3], the array will become [1, 1, 2, 2], where the length of the longest non-decreasing subsequence is 4.
In the second example, after reversing [3, 7], the array will become [1, 1, 1, 1, 2, 2, 2, 2, 2, 1], where the length of the longest non-decreasing subsequence is 9.
A dragon symbolizes wisdom, power and wealth. On Lunar New Year's Day, people model a dragon with bamboo strips and clothes, raise them with rods, and hold the rods high and low to resemble a flying dragon.
A performer holding the rod low is represented by a 1, while one holding it high is represented by a 2. Thus, the line of performers can be represented by a sequence a1, a2, ..., an.
Little Tommy is among them. He would like to choose an interval [l, r] (1 ≤ l ≤ r ≤ n), then reverse al, al + 1, ..., ar so that the length of the longest non-decreasing subsequence of the new sequence is maximum.
A non-decreasing subsequence is a sequence of indices p1, p2, ..., pk, such that p1 < p2 < ... < pk and ap1 ≤ ap2 ≤ ... ≤ apk. The length of the subsequence is k.
The first line contains an integer n (1 ≤ n ≤ 2000), denoting the length of the original sequence.
The second line contains n space-separated integers, describing the original sequence a1, a2, ..., an (1 ≤ ai ≤ 2, i = 1, 2, ..., n).
Print a single integer, which means the maximum possible length of the longest non-decreasing subence of the new sequence.
4 1 2 1 2
4
10 1 1 2 2 2 1 1 2 2 1
9
In the first example, after reversing [2, 3], the array will become [1, 1, 2, 2], where the length of the longest non-decreasing subsequence is 4.
In the second example, after reversing [3, 7], the array will become [1, 1, 1, 1, 2, 2, 2, 2, 2, 1], where the length of the longest non-decreasing subsequence is 9.
题目大意:给一个序列,选择一个区间翻转,问怎样翻转才能让所得的序列中的不降子序列最长,输出最长的长度
思路:
1.做的时候以为上升序列要是连续的所以死活没有做出来....
2.预处理1的前缀和和2的后缀和 pri[i]表示（1－> i）中1的个数,sur[i]表示（n－> i）中2的个数。
3.题目要求翻转过后的最长不降子序列,那么首先想到的方法就是处理每个区间的最长不增子序列(翻转后就是不降了),假设这个区间是x,y;那么答案就是pre[x-1]+LIS[x,y]+sur[y+1];复杂度是N方
4.没电脑手机打的...回寝室了继续写