POJ 2533 - Longest Ordered Subsequence（最长上升子序列） 题解

Posted 2020-09-28

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题目链接：http://poj.org/problem?id=2533

 

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_iK), 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

4

Source

Northeastern Europe 2002, Far-Eastern Subregion

 

 

分析：

DP不解释

 

AC代码：

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<algorithm>
 4 #include<cmath>
 5 using namespace std;
 6 int ans,n,num[1002],line[1002];
 7 //line[i]的意义是已经算到第i个数的最长公共子序列 
 8 int main()
 9 {
10     scanf("%d",&n);
11     for(int i = 1;i <= n;++ i)
12         scanf("%d",&num[i]),line[i] = 1;
13     for(int i = 2;i <= n;++ i)
14         for(int j = 1;j < i;++ j)
15             if(num[j] < num[i])
16                 line[i] = max(line[i],line[j]+1);
17     for(int i = 1;i <= n;++ i)
18         ans = max(ans,line[i]);
19     printf("%d\n",ans);
20     return 0;
21 }