Lis-program E

Maximum Ascending sub-sequence

Description

　　The world financial crisis is quite a subject. Some people is more relaxed while others is quite anxious. John is one of the them. He is very concerned about the evolution of the stock exchange. He follows stock prices every day looking for rising trends. Given a sequence of numbers p1, p2,..., pn representing stock prices, a rising trend is a subsequence pi1 < Pi2 <. . < Pik, with I1 < I2 < ... < IK. John ' s problem is to find very quickly the longest rising trend.

Input

Each data set in the file stands for a particular set of the stock prices. A data set starts with the length L (l≤100000) of the sequence of numbers, followed by the numbers (a number fits a long Integer).
White spaces can occur freely in the input. The input data is correct and terminate with an end of file.

Output

The program prints the length of the longest rising trend.
For each set of data the program prints the result to the standard output from the beginning of a line.

Sample Input

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

Sample Output

3 1 1


The main idea: to give a series of sequences, which require the output of the maximum ascending sub-sequence.

Analysis: With dynamic planning, high efficiency; If the latter number is larger than the previous one, the ascending sequence length is increased by 1, otherwise the length is reduced by 1, and the smaller number is replaced by the former.




The code is as follows:

#include<iostream>#include<cstdio>#include<algorithm>Constint MAXN=100005;UsingNamespace Std;int a[MAXN],dp[MAXN],lenN;IntFind(int x){int L=1R=len, mid;While(l<=r){Mid= (l+r) >>1;If(x>dp[Mid]) L=mid+1;Elser=mid-1;}return L;}IntMain(){While(scanf("%d", &n)==1){len=0;For(int I=1; I<=n; I++)scanf("%d", &a[I]);For(int I=1; I<=n; I++){int k=find< Span class= "Sh-symbol" > (A[i[k]=a[i];len=max,k}printf ( "%d\n,len}return 0 "              

Lis-program E