usaco3.3.5 A Game

双人游戏问题  有如下一个双人游戏:N个正整数的序列放在一个游戏平台上,两个人轮流从序列的两端取数,取数后该数字被去掉并累加到本玩家的得分中,当数取尽时,游戏结束,以最终的分多者为胜利。编写一个执行最优策略的程序,最优策略就是使得自己能在当前情况下得到最优策略。要求程序要始终为第二位玩家执行最优策略。 该题目的动态规划方程是: 设sum(s,t)为区间s,t中的数字和,gain(s,t)为按照最优策略能获得... 阅读详情

一 原题

A Game
IOI'96 - Day 1

Consider the following two-player game played with a sequence of N positive integers (2 <= N <= 100) laid onto a 1 x N game board. Player 1 starts the game. The players move alternately by selecting a number from either the left or the right end of the gameboar. That number is then deleted from the board, and its value is added to the score of the player who selected it. A player wins if his sum is greater than his opponents.

Write a program that implements the optimal strategy. The optimal strategy yields maximum points when playing against the "best possible" opponent. Your program must further implement an optimal strategy for player 2.

PROGRAM NAME: game1

INPUT FORMAT

Line 1:N, the size of the board
Line 2-etc:N integers in the range (1..200) that are the contents of the game board, from left to right

SAMPLE INPUT (file game1.in)

6
4 7 2 9
5 2

OUTPUT FORMAT

Two space-separated integers on a line: the score of Player 1 followed by the score of Player 2.

SAMPLE OUTPUT (file game1.out)

18 11


二 分析

动态规划。dp[i][j]表示在区间[i, j]内先手能获得的最高分数。


三 代码

运行结果:
USER: Qi Shen [maxkibb3]
TASK: game1
LANG: C++

Compiling...
Compile: OK

Executing...
   Test 1: TEST OK [0.000 secs, 4264 KB]
   Test 2: TEST OK [0.000 secs, 4264 KB]
   Test 3: TEST OK [0.000 secs, 4264 KB]
   Test 4: TEST OK [0.000 secs, 4264 KB]
   Test 5: TEST OK [0.000 secs, 4264 KB]
   Test 6: TEST OK [0.000 secs, 4264 KB]
   Test 7: TEST OK [0.000 secs, 4264 KB]
   Test 8: TEST OK [0.000 secs, 4264 KB]
   Test 9: TEST OK [0.000 secs, 4264 KB]
   Test 10: TEST OK [0.000 secs, 4264 KB]
   Test 11: TEST OK [0.000 secs, 4264 KB]
   Test 12: TEST OK [0.000 secs, 4264 KB]
   Test 13: TEST OK [0.000 secs, 4264 KB]
   Test 14: TEST OK [0.000 secs, 4264 KB]
   Test 15: TEST OK [0.000 secs, 4264 KB]
   Test 16: TEST OK [0.000 secs, 4264 KB]

All tests OK.

Your program ('game1') produced all correct answers! This is your submission #2 for this problem. Congratulations!


AC代码:
/*
ID:maxkibb3
LANG:C++
PROG:game1
*/

#include<cstdio>
#include<algorithm>
using namespace std;

const int MAXN = 105;

int n;
int a[MAXN];
int sum[MAXN][MAXN];
int dp[MAXN][MAXN];

int main() {
    freopen("game1.in", "r", stdin);
    freopen("game1.out", "w", stdout);
    scanf("%d", &n);
    for(int i = 0; i < n; i++) {
        scanf("%d", &a[i]);
        sum[i][i] = a[i];
        dp[i][i] = a[i];
    }
    for(int i = 0; i < n; i++) {
        for(int j = i + 1; j < n; j++) {
            sum[i][j] = sum[i][j - 1];
            sum[i][j] += a[j];
        }
    }
    for(int i = 1; i < n; i++) {
        for(int j = 0; j < n - i; j++) {
            dp[j][j + i] = max(a[j] + sum[j + 1][j + i] - dp[j + 1][j + i],
                           a[j + i] + sum[j][j + i - 1] - dp[j][j + i - 1]);
        }
    }
    printf("%d %d\n", dp[0][n - 1], sum[0][n - 1] - dp[0][n - 1]);
    return 0;
}


取数对弈(算法) 取数对弈游戏问题: 取数游戏是一个 2 人对策游戏。游戏开始时将 n 个数在棋盘上从左到右排成一行。 甲乙双方轮流在这一行数的左右两端取数,直至全部取完 n 个数。每人所取得的数的总和为其得分值。 最后双方得分多者获胜。(游戏规定由甲方先取数。) 这里,甲乙双方都采用如下最优策略: 1)甲每次取都希望取到的这个数使自己得分最高 2)乙每次取都希望取到的这个数令甲的得分最低 请编程实现:在甲乙双方都采用最优策略的前提下,计算甲方先取数时双方的最后得分。 输入格式 对于每组输入数据,输入数据的第 1 行有 1 个正整数 n (1<=n<=100),表示有 n 个数在棋盘上从左到右排成一行。 接下来的 n 个数表示在棋盘上依次排列的 n 个数。 输出格式 在甲乙双方都采用最优策略的前提下,输出计算出的双方的最后得分。甲方得分在前,乙方得分在后。 输入样例 6 4 7 2 9 5 2 输出样例 18 11 立即下载

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深度学习工具包Deprecation notice.-----This toolbox is outdated and no longer maintained.There are much better tools available for deep learning than this toolbox, e.g. [Theano](http://deeplearning.net/software/theano/), [torch](http://torch.ch/) or [tensorflow](http://www.tensorflow.org/)I would suggest you use one of the tools mentioned above rather than use this toolbox.Best, Rasmus.DeepLearnToolbox================A Matlab toolbox for Deep Learning.Deep Learning is a new subfield of machine learning that focuses on learning deep hierarchical models of data.It is inspired by the human brain&#39;s apparent deep (layered, hierarchical) architecture.A good overview of the theory of Deep Learning theory is[Learning Deep Architectures for AI](http://www.iro.umontreal.ca/~bengioy/papers/ftml_book.pdf)For a more informal introduction, see the following videos by Geoffrey Hinton and Andrew Ng.* [The Next Generation of Neural Networks](http://www.youtube.com/watch?v=AyzOUbkUf3M) (Hinton, 2007)* [Recent Developments in Deep Learning](http://www.youtube.com/watch?v=VdIURAu1-aU) (Hinton, 2010)* [Unsupervised Feature Learning and Deep Learning](http://www.youtube.com/watch?v=ZmNOAtZIgIk) (Ng, 2011)If you use this toolbox in your research please cite [Prediction as a candidate for learning deep hierarchical models of data](http://www2.imm.dtu.dk/pubdb/views/publication_details.php?id=6284)```@MASTERSTHESIS\{IMM2012-06284, author = "R. 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% Dropout fraction opts.numepochs = 1; % Number of full sweeps through dataopts.batchsize = 100; % Take a mean gradient step over this many samplesnn = nntrain(nn, train_x, train_y, opts);[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, &#39;Too big error&#39;);%% ex4 neural net with sigmoid activation functionrand(&#39;state&#39;,0)nn = nnsetup([784 100 10]);nn.activation_function = &#39;sigm&#39;; % Sigmoid activation functionnn.learningRate = 1; % Sigm require a lower learning rateopts.numepochs = 1; % Number of full sweeps through dataopts.batchsize = 100; % Take a mean gradient step over this many samplesnn = nntrain(nn, train_x, train_y, opts);[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, &#39;Too big error&#39;);%% ex5 plotting functionalityrand(&#39;state&#39;,0)nn = nnsetup([784 20 10]);opts.numepochs = 5; % Number of full sweeps through datann.output = &#39;softmax&#39;; % use softmax outputopts.batchsize = 1000; % Take a mean gradient step over this many samplesopts.plot = 1; % enable plottingnn = nntrain(nn, train_x, train_y, opts);[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, &#39;Too big error&#39;);%% ex6 neural net with sigmoid activation and plotting of validation and training error% split training data into training and validation datavx = train_x(1:10000,:);tx = train_x(10001:end,:);vy = train_y(1:10000,:);ty = train_y(10001:end,:);rand(&#39;state&#39;,0)nn = nnsetup([784 20 10]); nn.output = &#39;softmax&#39;; % use softmax outputopts.numepochs = 5; % Number of full sweeps through dataopts.batchsize = 1000; % Take a mean gradient step over this many samplesopts.plot = 1; % enable plottingnn = nntrain(nn, tx, ty, opts, vx, vy); % nntrain takes validation set as last two arguments (optionally)[er, bad] = nntest(nn, test_x, test_y);assert(er < 0.1, &#39;Too big error&#39;);```[![Bitdeli Badge](https://d2weczhvl823v0.cloudfront.net/rasmusbergpalm/deeplearntoolbox/trend.png)](https://bitdeli.com/free "Bitdeli Badge")

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【问题描述】   有如下一个双人游戏:   N个正整数的序列放在一个游戏平台上,游戏由玩家1开始,两人轮流从序列的两端取数,取数后该数字被去掉并累加到本玩家的得分中,当数取尽时,游戏结束。以最终得分多者为胜。   编一个执行最优策略的程序,最优策略就是使自己能得到在当前情况下最大的可能的总分的策略。你的程序要始终为两位玩家执行最优策略。【输入格式】 第一行: 正整数N, 表示序列中正整数

天地皆逆旅,你我本行人。 593

A Game (game1)[USACO 3.3.5]

看不懂啊,貌似用到了博弈论的知识,还是太弱了……{ ID:lstlst12 PROG:game1 LANG:PASCAL } program game1; var n:longint; f,sum:array [-1..100,-1..100] of longint; a

175

动规——【USACO3.3.5】A Game游戏 IOI'96

Description 有如下一个双人游戏:N(2 编一个执行最优策略的程序,最优策略就是使玩家在与最好的对手对弈时,能得到的在当前情况下最大的可能的总分的策略。你的程序要始终为第二位玩家执行最优策略。  状态:f[i][j]表示第i个数到第j个数先手可以获得的最大得分。 决策:先手可以取第i个数,那么剩下的i+1到j个数就等价于后手的情况,反之亦然。 代码如下: #includ

INCINCIBLE的博客 1217

A Game (game1)[USACO 3.3.5] 题解

{ ID:lstlst12 PROG:game1 LANG:PASCAL } program game1; var n:longint; f,sum:array [-1..100,-1..100] of longint; a:array [0..100] of longi

132

A Game (game1)[USACO 3.3.5] 代码

{ ID:lstlst12 PROG:game1 LANG:PASCAL } program game1; var n:longint; f,sum:array [-1..100,-1..100] of longint; a:array [0..100] of longi

234

A Game (game1)[USACO 3.3.5]解题报告

{ ID:lstlst12 PROG:game1 LANG:PASCAL } program game1; var n:longint; f,sum:array [-1..100,-1..100] of longint;//sum[i,j]表示从i到j这段范围内的数字总和,

185

USACO Section 3.3 A Game pascal

描述 Description 有如下一个双人游戏:N(2 <= N <= 100)个正整数的序列放在一个游戏平台上,两人轮流从序列的两端取数,取数后该数字被去掉并累加到本玩家的得分中,当数取尽时,游戏结束。以最终得分多者为胜。 编一个执行最优策略的程序,最优策略就是使自己能得到在当前情况下最大的可能的总分的策略。你的程序要始终为第二位玩家执行最优策略。 输入格式 Input

叫我小雷雷就好 1380
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