poj 2533 Longest Ordered Subsequence

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sunnykema

最新推荐文章于 2023-10-21 19:11:28 发布

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本文介绍了一种寻找最长上升子序列的有效算法，并通过一个具体示例演示了如何使用动态规划解决此类问题。文章提供了一个简洁的 C++ 实现，帮助读者理解算法原理。

Longest Ordered Subsequence

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 35239		Accepted: 15471

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

求最长上升子序列。定义一个一位数组dp[n]，dp[i]表示到第i个数的最长上升子序列。

代码如下：

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

using namespace std;
#define maxn 1005
#define inf 0x7ffffff
int arr[maxn];
int dp[maxn];
int n;
int main()
{
    scanf("%d",&n);
    for(int i = 0;i < n; i++){
        scanf("%d",&arr[i]);
    }
    for(int i = 0; i <= n; i++){
        dp[i] = 1;
    }
    for(int i = 0; i < n; i++){
        for(int j = i ;j >= 0;j--){
            if(arr[i] > arr[j]){
                dp[i] = max(dp[i],dp[j]+1);
            }
        }
    }
    for(int i = 0; i < n; i++){
        dp[n] = max(dp[n],dp[i]);
    }
    printf("%d\n",dp[n]);
    return 0;
}