# C2. Increasing Subsequence (hard version) (water)

Keywords: PHP

## Main idea:

Give you n numbers. Each time you can choose to take it from the left or from the right, but each time you take it, you must be the last time big, and then ask you to find the longest ascending subsequence.

# Specific ideas:

If the left and right endpoints are not equal, the smaller one is preferred, so we can take the larger one after we choose the smaller one.

If the left and right endpoints are equal, if one of them is selected at this time, it is the only way to go to the end. Because after taking one, the other boundary cannot be taken, so it is better to choose the longest ascending subsequence from both sides.

Note: note what was last selected in each storage. We need to compare every time.

AC Code:

```  1 #include<bits/stdc++.h>
2 using namespace std;
3 # define ll long long
4 const int maxn = 2e5+100;
5 int a[maxn];
6 string str;
7 int n;
8 int judge_L(int pos)
9 {
10     int num=1;
11     for(int i=pos; i<=n; i++)
12     {
13         if(a[i]<a[i+1])
14         {
15             num++;
16         }
17         else
18             break;
19     }
20     return num;
21 }
22 int judge_R(int pos)
23 {
24     int num=1;
25     for(int i=pos; i>=1; i--)
26     {
27         if(a[i]<a[i-1])
28         {
29             num++;
30         }
31         else
32             break;
33     }
34     return num;
35 }
36 int main()
37 {
38     cin>>n;
39     for( int  i = 1 ; i <= n ; i++ )
40     {
41         cin>>a[i];
42     }
43     //a=0;
44     // cout<<judge_R(1)<<endl;
45     int l=1,r=n;
46     int pre=0;
47     while(l<=r&&l<=n&&r>=1)
48     {
49         int flag=1;
50         if(a[l]==a[r]&&a[l]>pre)
51         {
52             flag=0;
53             int t1=judge_L(l);
54             int t2=judge_R(r);
55             if(t1>t2)
56             {
57                 for(int i=l; i<=l+t1-1; i++)
58                 {
59                     str+='L';
60                 }
61                 break;
62             }
63             else
64             {
65                 for(int i=r; i>=r-t2+1; i--)
66                 {
67                     str+='R';
68                 }
69                 break;
70             }
71         }
72         if(a[l]>pre)
73         {
74             flag=0;
75             if(a[r]<a[l]&&a[r]>pre)
76             {
77                 str+='R';
78                 pre=a[r];
79                 r--;
80             }
81             else
82             {
83                 str+='L';
84                 pre=a[l];
85                 l++;
86             }
87         }
88         else if(a[r]>pre)
89         {
90             flag=0;
91             if(a[l]<a[r]&&a[l]>pre)
92             {
93                 str+='L';
94                 pre=a[l];
95                 l++;
96             }
97             else
98             {
99                 str+='R';
100                 pre=a[r];
101                 r--;
102             }
103         }
104         if(flag)
105             break;
106     }
107     cout<<str.size()<<endl;
108     cout<<str<<endl;
109 }```

Posted by watts on Mon, 04 Nov 2019 10:37:26 -0800