Longest Ordered Subsequence

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
 1 //简单动态规划问题
 2 
 3 #include <stdio.h>
 4 
 5 #define MAX 1005
 6 
 7 int main()
 8 {
 9     int n;
10     int num[MAX];
11     int maxLen[MAX];
12     int max = -1;
13     int i,j;
14     scanf("%d",&n);
15     for (i=1; i<=n; i++)
16       scanf("%d",&num[i]);
17     for (i=1; i<=n; i++)
18       maxLen[i] = 1;
19     for (i=1; i<=n; i++)
20       for (j=1; j<i; j++)
21     {
22       if(num[i]>num[j]&&maxLen[i]<=maxLen[j])
23         maxLen[i] = maxLen[j]+1;
24     }
25     for (i=1; i<=n; i++)
26       if (maxLen[i]>max)
27         max = maxLen[i];
28     printf("%d",max);
29     return 0;
30 }

 

posted @ 2018-11-18 22:56  路漫漫我不畏  阅读(306)  评论(0)  编辑  收藏  举报