POJ-2533-Longest Ordered Subsequence(DP)

Posted 2021-01-24 yzhhh

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

7 
1 7 3 5 9 4 8

Sample Output

4

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题意：最长上升子序列长度。

思路：动态规划。

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 1 #include<cstdio>
 2 #include<cstring>
 3 #include<algorithm>
 4 using namespace std;
 5 
 6 int a[1005];
 7 int dp[1005];
 8 
 9 int main(){
10     int n;
11      while(~scanf("%d",&n)){
12          memset(a,0,sizeof(a));
13          int ans=0;
14         for(int i=1;i<=n;i++){        
15             scanf("%d",&a[i]);
16             dp[i]=1;//memset不能更新成1； 
17         }
18         for(int i=1;i<=n;i++){
19             for(int j=1;j<i;j++){
20                 if(a[i]>a[j]) dp[i]=max(dp[i],dp[j]+1); 
21             }
22         }    
23         for(int i=1;i<=n;i++){
24             ans=max(ans,dp[i]);
25         } 
26         printf("%d
",ans);
27     }
28     
29     return 0;
30 } 

 

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