最长上升子序列模板 hdu 1087 Super Jumping! Jumping! Jumping!

最新推荐文章于 2024-08-02 10:00:00 发布

转载最新推荐文章于 2024-08-02 10:00:00 发布 · 84 阅读

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原文链接：http://www.cnblogs.com/l609929321/p/9015980.html

本文介绍了一种基于棋盘的游戏“SuperJumping!Jumping!Jumping!”的算法实现，玩家需从起点跳跃到终点，经过路径上的棋子数值必须递增。文章详细解释了如何寻找最优解，即获得最大总分的跳跃路径，并提供了C++代码实现，包括最长递增子序列的求解。

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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.

InputInput 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.
OutputFor each case, print the maximum according to rules, and one line one case.
Sample Input

Sample Output

4
10
3

求一串递增的数字总和的最大值

借这里放下最长上升子序列的模板（求最大长度和最大总和的）

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<string>
#include<cmath>
#define debug(a) cout << #a << " " << a << endl
using namespace std;
typedef long long ll;
const int inf = 1e9;
int a[1010], dp[1010], num[1010], n;
int calc( int sign ) { //求最长,nlog(n)
    fill( dp, dp+1010, inf );
    int ans = 0;
    for( int i = 0; i < n; i ++ ) {
        int index = lower_bound( dp, dp+ans, a[i]*sign ) - dp; //lower为求严格递增，upper为求非严格递增
        dp[index] = a[i]*sign;
        ans = max( ans, index + 1 );
    }
    return ans;
}
int lins() {
    return calc(1);
}
int lnds() {
    return calc(-1);
}
int calc_max() { //求最大,n^2
    int ans = 0;
    for( int i = 0; i < n; i ++ ) {
        dp[i] = a[i];
        for( int j = 0; j < i; j ++ ) {
            if( a[j] < a[i] ) {
                dp[i] = max( dp[i], dp[j]+a[i] );
            }
        }
        ans = max( ans, dp[i] );
    }
    return ans;
}
int main() {
    std::ios::sync_with_stdio(false);
    while( cin >> n ) {
        memset( num, 0, sizeof(num) );
        if( !n ) {
            break;
        }
        for( int i = 0; i < n; i ++ ) {
            cin >> a[i];
        }
        cout << calc_max() << endl;
    }
    return 0;
}

转载于:https://www.cnblogs.com/l609929321/p/9015980.html