2022.11.22Longest Ordered Subsequence POJ - 2533

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

7
1 7 3 5 9 4 8

4

 原题链接：传送门

题意求最长上升子序列

刚开始题意没看清写成a[j] <= a[i]了wa了好几发，上升子序列就不需要等于

#include
using namespace std;
const int N = 1001;
int a[N], dp[N]; 
int main(){
  int n;
  cin >> n;
  int ans = 1;
  for(int i = 1; i <= n; i++)  cin>>a[i];	
  for(int i = 1; i <= n; i++){
    dp[i] = 1;
	for(int j = 1; j < i; j++){
      if(a[j] < a[i] && dp[j] + 1 > dp[i]){
        dp[i] = dp[j] + 1;	
      }	
	}
	if(dp[i] > ans) ans = dp[i];
  }
  cout << ans << endl;
  return 0;
}