Longest Ordered Subsequence
Time Limit: 2000MSMemory Limit: 65536K
Total Submissions: 39374Accepted: 17315
Description
A numeric sequence of ai is ordered ifa1 < 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
Source
, Far-Eastern Subregion
#include<iostream>#include<cstdio>#include<cstring>#include<cmath>#include<queue>#include<stack>using namespace std;int a[10000];int dp[10000];int main(){int n;while(~scanf("%d",&n)){for(int i=1; i<=n; i++)scanf("%d",&a[i]);memset(dp,0,sizeof(dp));for(int i=1; i<=n; i++){for(int j=i-1; j>=1; j–){if(a[i]>a[j]){<span id="transmark"></span>dp[i]=max(dp[i],dp[j]+1);}}}int Max=-1;for(int i=1;i<=n;i++) //不一定dp[n]最大if(Max<dp[i])Max=dp[i];printf("%d\n",Max+1);}}
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