hdu1087 最大上升子序列模板

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.



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 that 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

题意就是要求最大上升子序列的和，这个算法和最长上升子序列有点类似，条件都是a[i]>a[j]这就是限定上升条件，转移方程dp[i]=max(dp[i],dp[j]+a[i])方程的意思就是如果第i个接在第j个后面的最大值，dp[i]就是前i个的最大上升子序列和的值，再一直更新最大值就可以了。

#include <iostream>
#include <cstdio>
#include <algorithm>

using namespace std;
int a[100009];
int dp[100009];
int main()
{
    int i,j,k,n,maxx;
    while(~scanf("%d",&n))
    {
        if(n==0) break;
        for(i=0; i<=n-1; i++)
        {
            scanf("%d",&a[i]);
        }
        maxx=0;
        for(i=0; i<=n-1; i++)
        {
            dp[i]=a[i];
            for(j=0; j<=i-1; j++)
            {
                if(a[i]>a[j])
                dp[i]=max(dp[i],dp[j]+a[i]);
            }
            maxx=max(dp[i],maxx);
        }
        printf("%d\n",maxx);
    }
}