这么巧妙思路（二）Longest Ordered Subsequence

C - Longest Ordered Subsequence

Time Limit: 2000 MS Memory Limit: 65536 KB

64-bit integer IO format: %I64d , %I64u Java class name: Main

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Description

A numeric sequence of ai is ordered if a1 < a2 < ... < aN. Let the subsequence of the given numeric sequence (a1,a2, ..., aN) be any sequence (ai1, ai2, ..., aiK), where 1 <= i1 < i2 < ... < iK <= 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

#include<stdio.h>#include<algorithm>using namespace std;int main(){    int dp[110000];    int a[110000];    int n,i,j;    scanf("%d",&n);    for(i=0;i<n;i++)        scanf("%d",&a[i]);        for(i=0;i<n;i++)            dp[i]=0;    for(i=1;i<n;i++)    {        for(j=0;j<i;j++)        {            if(a[i]>a[j]&&dp[i]<dp[j]+1)                dp[i]=dp[j]+1;        }       // printf("%d ",dp[i]);    }    sort(dp,dp+n);    printf("%d\n",dp[n-1]+1);