   # bzoj4758: [Usaco2017 Jan]Subsequence Reversal(区间dp)

## 4758: [Usaco2017 Jan]Subsequence Reversal

Time Limit: 10 Sec  Memory Limit: 128 MB
Submit: 76  Solved: 52
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## Description

Farmer John is arranging his NN cows in a line to take a photo (1≤N≤50). The height of the iith co
w in sequence is a(i), and Farmer John thinks it would make for an aesthetically pleasing photo if t
he cow lineup has a large increasing subsequence of cows by height.To recall, a subsequence is a sub
set a(i1),a(i2),…,a(ik)) of elements from the cow sequence, found at some series of indices i1<i2<
…<ik, We say the subsequence is increasing if a(i1)≤a(i2)≤…≤a(ik).FJ would like there to be a l
ong increasing subsequence within his ordering of the cows. In order to ensure this, he allows himse
lf initially to choose any subsequence and reverse its elements.

For example, if we had the list

1 6 2 3 4 3 5 3 4
We can reverse the chosen elements

1 6 2 3 4 3 5 3 4
^         ^ ^ ^
to get

1 4 2 3 4 3 3 5 6
^         ^ ^ ^
Observe how the subsequence being reversed ends up using the same indices as it initially occupied,
leaving the other elements unchanged.Please find the maximum possible length of an increasing subseq
uence, given that you can choose to reverse an arbitrary subsequence once.

## Input

The first line of input contains N. The remaining N lines contain a(1)…a(N),
each an integer in the range 1…50.

## Output

Output the number of elements that can possibly form a longest increasing subsequence
after reversing the contents of at most one subsequence.

9
1
2
3
9
5
6
8
7
4

9

## Source

Platinum

/*

*/
#include<bits/stdc++.h>

#define N 51

using namespace std;
int n,a[N],ans;
int dp[N][N][N][N];

{
int x=0,f=1;char c=getchar();
while(c>'9'||c<'0'){if(c=='-')f=-1;c=getchar();}
while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
return x*f;
}

int main()
{
for(int i=1; i <= n; ++i) a[i]=read(),dp[i][i][a[i]][a[i]]=1;

for(int len=2; len <= n; ++len) for(int i=1; i+len-1 <= n; ++i)//当前区间
{
int j=i+len-1;
for(int l=1; l <= 50; ++l) for(int L=1; L+l-1 <= 50; ++L)//当前值域
{
int R=L+l-1;
ans=dp[i][j][L][R];
ans=max(ans,max(dp[i+1][j][L][R],dp[i][j-1][L][R]));
ans=max(ans,max(dp[i][j][L+1][R],dp[i][j][L][R-1]));
dp[i][j][L][R]=ans;
//copy小区间的答案
dp[i][j][min(L,a[i])][R]=max(dp[i][j][min(L,a[i])][R],dp[i+1][j][L][R]+(a[i] <= L));
dp[i][j][L][max(R,a[j])]=max(dp[i][j][L][max(R,a[j])],dp[i][j-1][L][R]+(a[j] >= R));
dp[i][j][min(L,a[i])][max(R,a[j])]=max(dp[i][j][min(L,a[i])][max(R,a[j])],dp[i+1][j-1][L][R]+(a[j] >= R)+(a[i] <= L));
//a[i]与a[j]不交换
dp[i][j][min(L,a[j])][R]=max(dp[i][j][min(L,a[j])][R],dp[i+1][j-1][L][R]+(a[j] <= L));
dp[i][j][L][max(R,a[i])]=max(dp[i][j][L][max(R,a[i])],dp[i+1][j-1][L][R]+(a[i] >= R));
dp[i][j][min(L,a[j])][max(R,a[i])]=max(dp[i][j][min(L,a[j])][max(R,a[i])],dp[i+1][j-1][L][R]+(a[i] >= R)+(a[j] <= L));
//a[i]与a[j]交换
}
}
cout<<dp[n]<<endl;
return 0;
}

posted @ 2018-10-31 16:34  安月冷  阅读(240)  评论(0编辑  收藏  举报