2533:Longest Ordered Subsequence（动态规划）

 

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总时间限制: 

2000ms

 

内存限制: 

65536kB

描述

A numeric sequence of  a_i is ordered if  a₁ <  a₂ < ... <  a_N. Let the subsequence of the given numeric sequence ( a₁,  a₂, ...,  a_N) be any sequence ( a_i1,  a_i2, ...,  a_iK), where 1 <=  i₁ <  i₂ < ... <  i_K <=  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.

输入

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

输出

Output file must contain a single integer - the length of the longest ordered subsequence of the given sequence.

样例输入

7
1 7 3 5 9 4 8

样例输出

4

来源

Northeastern Europe 2002, Far-Eastern Subregion

memset()函数，不可以初始化int为1，只能初始化为0或-1.

 

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 
 4 int main() {//1 7 3 5 9 4 8
 5 
 6     int n,ans=0;
 7     cin>>n;
 8     int a[n],b[n];
 9     memset(b,0,sizeof(b));
10     for(int i=0;i<n;i++){
11         cin>>a[i];
12         for(int j=0;j<i;j++){
13             if(a[i]>a[j]){
14                 b[i]=max(b[i],b[j]+1);
15             }
16         }
17         ans=max(ans,b[i]);
18     }
19     cout<<ans+1<<endl;
20     
21     return 0;
22 }