poj 2533 Longest Ordered Subsequence(最长上升子序列)

Longest Ordered Subsequence

Time Limit: 2000MS Memory Limit: 65536KTotal Submissions: 33657 Accepted: 14730

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

71 7 3 5 9 4 8

Sample Output

4

最长上升子序列（不一定连续）

dp[i]表示序列从j=0到j=i的最长上升子序列的长度。

#include <stdio.h>#include <string.h>#include <iostream>using namespace std;int num[1010],dp[1010];int main(){    int n,Max;    while (scanf("%d",&n)!=EOF)    {        Max=-1;        memset(dp, 0, sizeof(dp));        for (int i=0; i<n; i++)            scanf("%d",&num[i]);        for (int i=0; i<n; i++)        {            dp[i]=1;            for (int j=0; j<i; j++)            {                if(num[i]>num[j])                    dp[i]=max(dp[i],dp[j]+1);                            }            Max=max(dp[i],Max);        }        printf("%d\n",Max);            }    return 0;}