poj - 2533 最长上升子序列 Java

最新推荐文章于 2021-07-18 14:26:21 发布

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最新推荐文章于 2021-07-18 14:26:21 发布

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本文介绍了一种解决最长递增子序列问题的有效算法，并通过一个示例详细展示了如何使用该算法来找到给定序列中最长递增子序列的长度。输入包括序列长度及具体数值，输出为最长递增子序列的长度。

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Longest Ordered Subsequence

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 54798		Accepted: 24552

Description

A numeric sequence of a_i is ordered if a₁ < a₂ < ... < a_N. Let the subsequence of the given numeric sequence (a₁, a₂, ..., a_N) be any sequence (a_i₁, a_i₂, ..., a_{i_K}), where 1 <= i₁ < i₂ < ... < i_K <= N. For example, sequence (1, 7, 3, 5, 9, 4, 8) has ordered subsequences, e. g., (1, 7), (3, 4, 8) and many others. All longest ordered subsequences are of length 4, e. g., (1, 3, 5, 8).

Your program, when given the numeric sequence, must find the length of its longest ordered subsequence.

Input

The first line of input file contains the length of sequence N. The second line contains the elements of sequence - N integers in the range from 0 to 10000 each, separated by spaces. 1 <= N <= 1000

Output

Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

Sample Input

7
1 7 3 5 9 4 8

Sample Output

题意：给n个数，求最大上升子序列   裸题。

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		while (sc.hasNext()) {
			int n = sc.nextInt();
			int arr[] = new int[n];
			for (int i = 0; i < arr.length; i++) {
				arr[i] = sc.nextInt();
			}
			
			int len = 0;
			int g[] = new int[n + 1];
			g[0]=Integer.MIN_VALUE;
			for (int i = 1; i <= arr.length; i++) {
				if (g[len] < arr[i - 1]) {
					len = len + 1;
					g[len] = arr[i - 1];
				} 
              g[ef(arr[i-1],g,1,len)]=arr[i-1];
				
			}
			System.out.println(len);
		}
	}
	public static int ef(int arr, int g[], int start, int end) {

		while (start < end) {
			int mix = (start + end) >> 1;

			if (g[mix] > arr) {
                end=mix;
			}else {
				start=mix+1;
			}

		}
		return start;

	}

}