hdu1087 - Super Jumping! Jumping! Jumping! (dp 求递增子序列的最大和)

Super Jumping! Jumping! Jumping!

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 20915    Accepted Submission(s): 9133

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

3 1 3 24 1 2 3 44 3 3 2 10

 

Sample Output

4103

 

Author

lcy

 

 

            参考博客：http://qianmacao.blog.163.com/blog/static/203397180201221074949474/

            这道题开始做的时候我总想着把最长序列放入f[i]，这样肯定做不出来，查阅资料后，才知道，原来f[i]不一定非代表最长序列，如这道题就是开辟数组记录其子序列最大和。

 

 

/********************************************* *   acm:   hdu-1087* *   title: Super Jumping! Jumping! Jumping! * *   time:  2014.6.17 * *********************************************/  //考察dp 最长有序子序列问题：求子序列的最大和/*思路：dp方程 dp[i] = max{dp[j] + a[i]} (o <=j<i)其中dp[i]表示第i个元素的最长递增子序列和.e.g:序列： 1 3 7  5 2 3 4数组a：1 3 7  5 2 3 4数组s：1 4 11 9 3 6 10so: max = 11*/#include <stdio.h>#define MAXSIZE 1001int a[MAXSIZE];int s[MAXSIZE];int main(){int i, j, N;int max_t;   //局部序列最大和int max;     //当前序列的最大和while (scanf("%d", &N), N){for (i = 0; i < N; i++){scanf("%d", &a[i]);}s[0] = a[0];max = s[0];for (i = 1; i < N; i++){max_t = 0;for (j = 0; j < i; j++){if (a[i] > a[j] && s[j] > max_t){max_t = s[j];}}s[i] = a[i] + max_t;if (s[i] > max){max = s[i];}}printf("%d\n", max);}return 0;}