POJ2533:Longest Ordered Subsequence

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最新推荐文章于 2023-03-17 01:34:36 发布

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本文介绍了一种使用动态规划解决最长递增子序列问题的方法，并通过一个示例程序详细展示了如何找到给定序列中最长递增子序列的长度。

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Longest Ordered Subsequence

Longest Ordered Subsequence

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 31680		Accepted: 13848

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

这是一道动归题。

n=3

dp[]=0;

1	ap[1]=0
7	dp[2]=1
3	dp[3]=1
5	d[4]=2
9	d[5]=3
4	d[6]=2
8	d[7]=3

最后找出最大值然后加一；

具体实现如下：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>

using namespace std;

const int M = 1000+5;
int sequence[M];    //输入的数据
int dp[M];          

int main()
{
    int n;
    while(scanf("%d", &n)!=EOF)
    {
        for(int i=1; i<=n; i++)
            scanf("%d",  &sequence[i]);
        memset(dp, 0, sizeof(dp));          //初始化为0
        for(int i=1; i<=n; i++)
            for(int j=1; j<i; j++)
            {
                if(sequence[i]>sequence[j])
                    dp[i] = max(dp[i], dp[j] + 1);    //动归方程
            }
        int ans=0;
        for(int i=1; i<=n; i++)
            ans = max(ans, dp[i]);
        printf("%d\n", ans+1);
    }
    return 0;
}