E - Super Jumping! Jumping! Jumping! 【DP||类LCS】

Nowadays, a kind of chess game called “Super Jumping! Jumping! Jumping!” is very popular in HDU. Maybe you are a good boy, and know little about this game, so I introduce it to you now.

start——>1——>3——>2——>end

The game can be played by two or more than two players. It consists of a chessboard（棋盘）and some chessmen（棋子）, and all chessmen are marked by a positive integer or “start” or “end”. The player starts from start-point and must jumps into end-point finally. In the course of jumping, the player will visit the chessmen in the path, but everyone must jumps from one chessman to another absolutely bigger (you can assume start-point is a minimum and end-point is a maximum.). And all players cannot go backwards. One jumping can go from a chessman to next, also can go across many chessmen, and even you can straightly get to end-point from start-point. Of course you get zero point in this situation. A player is a winner if and only if he can get a bigger score according to his jumping solution. Note that your score comes from the sum of value on the chessmen in you jumping path.
Your task is to output the maximum value according to the given chessmen list.
Input
Input contains multiple test cases. Each test case is described in a line as follow:
N value_1 value_2 …value_N
It is guarantied tat N is not more than 1000 and all value_i are in the range of 32-int.
A test case starting with 0 terminates the input and this test case is not to be processed.
Output
For each case, print the maximum according to rules, and one line one case.
Sample Input
3 1 3 2
4 1 2 3 4
4 3 3 2 1
0
Sample Output
4
10
3

题意：在一个序列中，找出一个严格递增的子序列，要求这个子序列各项的和最大并输出。

一顿操作猛如虎，就是不能nlogn 有点不甘心！

#include<iostream>
#include<cstring>
#include<algorithm>
#include<iomanip>
#include<cstdio>
#include<functional>
using namespace std;
#define ll long long int 
#define INF 0x3f3f3f3f
#define JNF 0x7fffffff
const int maxn = 1e3 + 10;
#define Irish_Moonshine main
int a[maxn];
int vis[maxn];
int dp[maxn];
int N;
//这题难道不能nlogn？ 这就很生气
int Irish_Moonshine()
{
    while (~scanf("%d", &N) && N)
    {
        int ans = 0;
        memset(vis, 0, sizeof(vis));
        memset(dp, 0, sizeof(dp));
        for (int i = 0; i < N; i++)
        {
            scanf("%d", &a[i]);
        }
        for (int i = 0; i < N; i++)
        {
            for (int j = 0; j < i; j++)
            {
                if (a[j] < a[i])
                {
                    dp[i] = max(dp[i], dp[j] + a[i]);
                }
            }
            dp[i] = max(dp[i], a[i]);
            ans = max(ans, dp[i]);
        }
        printf("%d\n", ans);
    }
    return 0;
}