HDU-1087最大上升子序列和

最大上升子序列和算法

最新推荐文章于 2020-04-25 13:27:22 发布

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本文介绍了一种求解最大上升子序列和的算法问题，通过动态规划的方法找到给定序列中符合规则的最大子序列之和。具体实现包括初始化dp数组、遍历输入序列并更新dp数组以记录最优解。

Super Jumping! Jumping! Jumping!

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 47907 Accepted Submission(s): 22173

Problem Description

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

Sample Output

4
10
3

题意：就是最大上升子序列和.......

思路：用一个数组dp[i]储存到i的时候的最大子序列和

坑点：无

AC代码：

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
int dp[1100],num[1100];
int main()
{
    int n,i,j,Max;
    while (cin>>n&&n)
        {
            memset(dp,0,sizeof(dp));
            memset(num,0,sizeof(num));
            for (i=1;i<=n;i++)
                cin>>num[i];
            for (i=1;i<=n;i++)
                {
                    dp[i]=num[i];            //数组一开始的值是num[i]
                    for (j=1;j<i;j++)
                        if (num[i]>num[j])
                            dp[i]=max(dp[j]+num[i],dp[i]);        //当前面有比num[i]小的数字，求最大
                }
            Max=-1;
            for (i=1;i<=n;i++)                        //找出最大的子序列和
                Max=max(Max,dp[i]);
            cout<<Max<<endl;
        }
    return 0;
}