HDOJ_1087_Super Jumping! Jumping! Jumping! 【DP】

HDOJ_1087_Super Jumping! Jumping! Jumping! 【DP】

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 44670 Accepted Submission(s): 20693

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

Sample Output

4
10
3

题意
寻找最长上升子序列，输出其和

思路
如果一个数组的最后一个元素大于前面的某一个元素，那么这个数组的最长上升子序列和就等于前面的那一个元素到开头组成的数组的最长上升子序列和 + 这个数组元素的值

AC代码

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <cstring>
#include <map>
#include <stack>
#include <set>
#include <cstdlib>
#include <ctype.h>
#include <numeric>
#include <sstream>
using namespace std;

typedef long long LL;
const double PI = 3.14159265358979323846264338327;
const double E = 2.718281828459;
const double eps = 1e-6;
const int MAXN = 0x3f3f3f3f;
const int MINN = 0xc0c0c0c0;
const int maxn = 1e3 + 5;
const int MOD = 1e9 + 7;
int arr[maxn], dp[maxn];

int main()
{
    int n;
    while (cin >> n && n)
    {
        int i, j;
        for (i = 0; i < n; i++)
            scanf("%d", &arr[i]);
        memset(dp, 0, sizeof(dp));
        LL ans = 0;
        for (i = 0; i < n; i++)
        {
            dp[i] = arr[i];
            for (j = i - 1; j >= 0; j--)
            {
                if (arr[i] > arr[j])
                    dp[i] = max(dp[i], dp[j] + arr[i]);
            }
            if (dp[i] > ans)
                ans = dp[i];
        }
        cout << ans << endl;
    }
}