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hoj_10001_朴素DP（LIS）

2024-07-05 00:12:06   223人阅读

Longest Ordered Subsequence
Time Limit: 1000ms, Special Time Limit:2500ms, Memory Limit:32768KB
Total submit users: 1937, Accepted users: 1621
Problem 10001 : No special judgement
Problem 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 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 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

 

  这是求lis的一道题，也一个最基本的O(n*n)的一维DP，更是我算法之路的开始~~~~~~

  对于给定的a[N]数组，从1到n每次分别求对应a[i]的lis，最后即为最终的lis。

  AC代码如下：

 

 1 #include<cstdio>
 2 using namespace std;
 3 int main()
 4 {
 5     int t;
 6     int n;
 7     int a[1005],b[1005];
 8     while(scanf("%d",&n)!=EOF)
 9     {
10         for(int i=0;i<n;i++)
11             scanf("%d",&a[i]);
12         b[0]=1;
13         for(int i=1;i<n;i++)
14         {
15             b[i]=1;
16             for(int j=0;j<i;j++)
17             {
18                 if(a[i]>a[j] && b[j]+1>b[i])
19                 {
20                     b[i]=b[j]+1;
21                 }
22             }
23         }
24         t=b[0];
25         for(int i=0;i<n;i++)
26         {
27             if(b[i]>t)
28                 t=b[i];
29         }
30         printf("%d\n",t);
31     }
32     return 0;
33 }

 


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