Poj 3903 Stock Exchange（LIS）

一、Description

The world financial crisis is quite a subject. Some people are more relaxed while others are quite anxious. John is one of 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 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 are 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.

二、题解

        这道题目是典型的求最长递增序列的问题，在之前有关于LIS的分析最长递增子序列（LIS）。

三、java代码

import java.util.Scanner;

public class Main{
static int MAXN = 100005;
static int[] a=new int [MAXN];
static int[] MaxV=new int [MAXN];
static int len,n;
static int BinSearch(int[] MaxV, int size, int x){
    int left = 0, right = size-1;
    while(left <= right){
        int mid = (left + right) / 2;
        if(MaxV[mid] < x){
            left = mid + 1;
        }else{
            right = mid - 1;
        }
    }
    return left;
}

static int getLIS(int[] arr){
	len = 1;
	MaxV[0] =arr[0];
    for(int i = 1; i < n; ++i){
        if(arr[i] > MaxV[len-1]){
            MaxV[len++] = arr[i];
        }else{
            int pos = BinSearch(MaxV,len,arr[i]);
            MaxV[pos] = arr[i];
        }
    }
    return len;
}
public static void main(String[] args){
	Scanner cin = new Scanner(System.in);
	int i;
	while(cin.hasNext()){
	   n=cin.nextInt();
	   for(i=0;i<n;i++){
		   a[i]=cin.nextInt();
	   }
	 System.out.println(getLIS(a));
	}
 }
}

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