每日三题-Day2-C（HDU 1087 Super Jumping! Jumping! Jumping! 最大上升子序列和）

原题地址

Super Jumping! Jumping! Jumping!

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 37302 Accepted Submission(s): 17041

[align=left]Problem Description[/align]
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.

[align=left]Input[/align]
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.

[align=left]Output[/align]
For each case, print the maximum according to rules, and one line one case.

[align=left]Sample Input[/align]

3 1 3 2
4 1 2 3 4
4 3 3 2 1
0

[align=left]Sample Output[/align]

4
10
3

题意：

给你n个数，求其递增的子序列的最大的和。

思路：

dp[i]代表从0~i的序列里，以第i个数结尾的（包含第i个数）最大上升子序列和。

那么dp[i+1] = max(dp[ 0~i ]) + num[ i+1 ]   其中0~i的数里，必须小于第i+1个数才参与比较。

AC代码：

#include<cstdio>
#include<cstring>
#include<algorithm>
#define INF 0x3f3f3f3f
using namespace std;

int dp[1010];
int a[1010];
int main()
{
int n;
while(~scanf("%d",&n))
{
if(n==0)break;
int ans=0;
for(int i=0;i<n;i++)
{
scanf("%d",&a[i]);
}
dp[0]=a[0];
ans=a[0];
for(int i=1;i<n;i++)
{
int maxa=a[i];
for(int j=0;j<i;j++)
{
if(a[i]>a[j])
{
maxa=max(dp[j]+a[i],maxa);
}
}
dp[i]=maxa;
ans=max(dp[i],ans);
}
printf("%d\n",ans);
}
return 0;
}