POJ 2533 Longest Ordered Subsequence

最新推荐文章于 2023-03-17 01:34:36 发布

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原文链接：http://www.cnblogs.com/fht-litost/p/8855310.html

本文介绍了一种寻找给定数列中最长上升子序列长度的算法实现，通过动态规划的方法，针对每个元素找到以它结尾的最长上升子序列，并记录最长结果。

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

4

分析 
最长上升子序列。定义d[i]为以第i个元素为起始的LIS，那么d[i]=max(d[j])+1,(j>i)。初始是d[n]=1。

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<algorithm>
#include<cstring>
#include <queue>
#include <vector>
#include<bitset>
#include<map>
#include<deque>
using namespace std;
typedef long long LL;
const int maxn = 1e4+5;
const int mod = 77200211+233;
typedef pair<int,int> pii;
#define X first
#define Y second
#define pb push_back
//#define mp make_pair
#define ms(a,b) memset(a,b,sizeof(a))
const int inf = 0x3f3f3f3f;
#define lson l,m,2*rt
#define rson m+1,r,2*rt+1
typedef long long ll;
#define N 100010

int a[maxn];
int dp[maxn];
int main(){
    int n;
    scanf("%d",&n);

    for(int i=1;i<=n;i++) scanf("%d",&a[i]);
    ms(dp,-1);
    for(int i=n;i>=1;i--){
        dp[i]=1;
        int res=0;
        for(int j=i+1;j<=n;j++){
            if(a[i]<a[j]){
                res=max(res,dp[j]);
            }
        }
        dp[i]+=res;
    }
    int ans=-1;
    for(int i=1;i<=n;i++){
        ans=max(ans,dp[i]);
    }
    cout<<ans<<endl;
    return 0;
}

转载于:https://www.cnblogs.com/fht-litost/p/8855310.html