HDU 1087 Super Jumping! Jumping! Jumping!

Posted 2020-09-16 Dysania_l

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

 

题意分析：

求最大递增序列之和 状态转移方程为： ans = max(ans,dp[j]);

ans为以j结尾的最大递增子序列的和；其中用dp[]储存以i为结尾的最大递增序列的和，

dp[i] = ans + a[i];

注意由于需要考虑是所有的和，所以循环应为

for(i=1;i<=m;i++) for(j=0;j<i;j++)

最后只要比较以各个位置为结点的dp[i]的值便可。

 

综上，实现代码为：

#include<bits/stdc++.h>
using namespace std;
int main()
{
    int i,j,m,a[1005],dp[1005];
    while(cin>>m&&m)
    {
        for(i=1;i<=m;i++)
            cin>>a[i];
        memset(dp,0,sizeof(dp)); 
        for(i=1;i<=m;i++)
        {
            int ans = -10000000;
            for(j=0;j<i;j++)  //求出以各个位置为节点的最大值
            {
                if(a[i]>a[j])
                    ans = max(ans,dp[j]);
            }
            dp[i] = ans + a[i];
        }
        int ans = -10000000;
        for(i=1;i<=m;i++)  //取各个节点的最大值，即为最大递增序列之和
        {
            if(ans<dp[i])
                ans = dp[i];
        }
        cout<<ans<<endl;
    }
    return 0;
}