uva 10149 - Yahtzee（DP）

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本文介绍了一种计算Yahtzee游戏最佳可能得分的算法实现。通过动态规划方法，文章详细展示了如何针对每轮投掷的五枚骰子，在13种计分类别中选择最优得分策略，同时考虑了额外的奖励分数条件。

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Problem A - Yahtzee

The game of Yahtzee involves 5 dice, which are thrown in 13 rounds. A score card contains 13 categories; each round may be scored in a category of the player's choosing, but each category may be scored only once in the game. The 13 categores are scored as follows:

ones - sum of all ones thrown
twos - sum of all twos thrown
threes - sum of all threes thrown
fours - sum of all fours thrown
fives - sum of all fives thrown
sixes - sum of all sixes thrown
chance - sum of all dice
three of a kind - sum of all dice, provided at least three have same value
four of a kind - sum of all dice, provided at least four have same value
five of a kind - 50 points, provided all five dice have same value
short straight - 25 points, provided four of the dice form a sequence (that is, 1,2,3,4 or 2,3,4,5 or 3,4,5,6)
long straight - 35 points, provided all dice form a sequence (1,2,3,4,5 or 2,3,4,5,6)
full house - 40 points, provided three of the dice are equal and the other two dice are also equal. (for example, 2,2,5,5,5)

Each of the last six categories may be scored as 0 if the criteria are not met.

The score for the game is the sum of all 13 categories plus a bonus of 35 points if the sum of the first six categores (ones to sixes) is 63 or greater.

Your job is to compute the best possible score for a sequence of rounds.

The Input

Each line of input contains 5 integers between 1 and 6, indicating the values of the five dice thrown in each round. There are 13 such lines for each game, and there may be any number of games in the input data.

The Output

Your output should consist of a single line for each game containing 15 numbers: the score in each category (in the order given), the bonus score (0 or 35), and the total score. If there is more than categorization that yields the same total score, any one will do.

Sample Input

Output for Sample Input

1 2 3 4 5 0 15 0 0 0 25 35 0 0 90
3 6 9 12 15 30 21 20 26 50 25 35 40 35 327

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

const int maxn = 10000;
int dp[maxn] , sum[maxn][20] , bonues , total , dice[20][5];

void initial(){
    for(int i = 0; i < maxn; i++){
        dp[i] = -1;
    }
    memset(sum , 0 , sizeof sum);
    total = 0;
    bonues = 0;
}

void readcase(){
    for(int i = 1; i < 13; i++){
        for(int j = 0; j < 5; j++){
            scanf("%d" , &dice[i][j]);
        }
    }
}

int get_sum(int k , int d){
    k++;
    int t = 0 , appear[8] = {0};
    if(k <= 6){
        for(int i = 0; i < 5; i++){
            if(dice[d][i] == k) t += k;
        }
        return t;
    }
    for(int i = 0; i < 5; i++){
        t += dice[d][i];
        appear[dice[d][i]]++;
    }
    if(k == 7){
        return t;
    }
    if(k == 8 || k == 9){
        for(int i = 1; i < 7; i++){
            if(appear[i] >= k-5) return t;
        }
        return 0;
    }
    if(k == 10){
        for(int i = 1; i < 7; i++){
            if(appear[i] >= 5) return 50;
        }
        return 0;
    }
    if(k == 11){
        if(appear[1] && appear[2] && appear[3] && appear[4]) return 25;
        if(appear[5] && appear[2] && appear[3] && appear[4]) return 25;
        if(appear[5] && appear[6] && appear[3] && appear[4]) return 25;
        return 0;
    }
    if(k == 12){
        if(appear[1] && appear[2] && appear[3] && appear[4] && appear[5]) return 35;
        if(appear[6] && appear[2] && appear[3] && appear[4] && appear[5]) return 35;
        return 0;
    }
    if(k == 13){
        for(int i = 1; i < 7; i++){
            if(appear[i] == 3){
                for(int j = 1; j < 7; j++){
                    if(appear[j] == 2){
                        return 40;
                    }
                }
            }
        }
        return 0;
    }
    return 0;
}

int DP(int k , int category){
    if(k < 0) return 0;
    if(dp[category] != -1) return dp[category];
    int ans = 0;
    for(int i = 0; i < 13; i++){
        if(category&(1<<i)){
            int tsum = get_sum(k , i);
            if(ans < tsum+DP(k-1 , category-(1<<i))){
                ans = tsum+DP(k-1 , category-(1<<i));
                sum[category][k] = i;
            }
        }
    }
    if(k == 5 && ans >= 63){
        ans += 35;
    }
    return dp[category] = ans;
}

void output(int k , int category){
    if(k == 0){
        printf("%d " , get_sum(k , sum[category][k]));
        return;
    }
    output(k-1 , category-(1<<sum[category][k]));
    printf("%d " , get_sum(k , sum[category][k]));
    if(k == 5 && DP(k , category) >= 63) bonues = 35;
}

void computing(){
    int category = 0;
    for(int i = 0; i < 13; i++){
        category += (1<<i);
    }
    total = DP(12 , category);
    output(12 , category);
    printf("%d %d\n" , bonues , total);
}

int main(){
    while(scanf("%d%d%d%d%d" , &dice[0][0], &dice[0][1], &dice[0][2], &dice[0][3], &dice[0][4]) != EOF){
        initial();
        readcase();
        computing();
    }
    return 0;
}