博客
关于我
HDU - 4597 Play Game (博弈 + 区间dp)
阅读量:284 次
发布时间:2019-03-01

本文共 2083 字,大约阅读时间需要 6 分钟。

Alice and Bob are playing a game. There are two piles of cards. There are N cards in each pile, and each card has a score. They take turns to pick up the top or bottom card from either pile, and the score of the card will be added to his total score. Alice and Bob are both clever enough, and will pick up cards to get as many scores as possible. Do you know how many scores can Alice get if he picks up first?

Input

The first line contains an integer T (T≤100), indicating the number of cases. 

Each case contains 3 lines. The first line is the N (N≤20). The second line contains N integer ai(1≤ai≤10000). The third line contains N integer bi (1≤bi≤10000).

Output

For each case, output an integer, indicating the most score Alice can get.

Sample Input

2  1 23 53  3 10 100 20 2 4 3

Sample Output

53 105

题意:Alice和Bob轮流在两个数组中取数字,每次只能取走一个数组的第一个或最后一个数字,问Alice取走数字的最大和

思路:dp[i][j][p][q] 表示第一个数组剩余 [i, j] ,第二个数组剩余 [p, q] 时,执行下一步的人可以获得的最大价值,它可以由上一步对方的最大值转移过来,4种转移方式:数组一的第一个、数组一的最后一个、数组二的第一个、数组二的最后一个。

for循环着实不好写,还是记忆化搜索8

#include 
using namespace std;typedef long long ll;const int inf = 0x3f3f3f3f;const int N = 25;int a[N], b[N], dp[N][N][N][N], n;int dfs(int i, int j, int p, int q, int sum) { if(i > j && p > q) return 0; if(dp[i][j][p][q]) return dp[i][j][p][q]; if(i <= j) { dp[i][j][p][q] = max(dp[i][j][p][q], sum - dfs(i + 1, j, p, q, sum - a[i])); dp[i][j][p][q] = max(dp[i][j][p][q], sum - dfs(i, j - 1, p, q, sum - a[j])); } if(p <= q) { dp[i][j][p][q] = max(dp[i][j][p][q], sum - dfs(i, j, p + 1, q, sum - b[p])); dp[i][j][p][q] = max(dp[i][j][p][q], sum - dfs(i, j, p, q - 1, sum - b[q])); } return dp[i][j][p][q];}int main(){// freopen("in.txt", "r", stdin); int t; scanf("%d", &t); while(t--) { scanf("%d", &n); int sum = 0; for(int i = 1; i <= n; ++i) { scanf("%d", &a[i]); sum += a[i]; } for(int i = 1; i <= n; ++i) { scanf("%d", &b[i]); sum += b[i]; } memset(dp, 0, sizeof(dp)); printf("%d\n", dfs(1, n, 1, n, sum)); } return 0;}

 

转载地址:http://kcio.baihongyu.com/

你可能感兴趣的文章
mysql创建数据库指定字符集
查看>>
MySql创建数据表
查看>>
MySQL创建新用户以及ERROR 1396 (HY000)问题解决
查看>>
MySQL创建用户与授权
查看>>
MySQL创建用户报错:ERROR 1396 (HY000): Operation CREATE USER failed for 'slave'@'%'
查看>>
MySQL创建索引时提示“Specified key was too long; max key length is 767 bytes”
查看>>
mysql初始密码错误问题
查看>>
mysql判断某一张表是否存在的sql语句以及方法
查看>>
mysql加入安装策略_一键安装mysql5.7及密码策略修改方法
查看>>
mysql加强(1)~用户权限介绍、分别使用客户端工具和命令来创建用户和分配权限
查看>>
mysql加强(3)~分组(统计)查询
查看>>
mysql加强(4)~多表查询:笛卡尔积、消除笛卡尔积操作(等值、非等值连接),内连接(隐式连接、显示连接)、外连接、自连接
查看>>
mysql加强(5)~DML 增删改操作和 DQL 查询操作
查看>>
mysql加强(6)~子查询简单介绍、子查询分类
查看>>
mysql加强(7)~事务、事务并发、解决事务并发的方法
查看>>
mysql千万级大数据SQL查询优化
查看>>
MySQL千万级大表优化策略
查看>>
MySQL单实例或多实例启动脚本
查看>>
MySQL压缩包方式安装,傻瓜式教学
查看>>
MySQL原理、设计与应用全面解析
查看>>