A1012. The Best Rank (25)

本文介绍了一个针对计算机科学专业一年级学生的成绩排名系统实现方法。该系统根据C语言编程、数学及英语三门课程成绩,以及平均分对学生进行排名,并强调每位学生的最佳排名。文章提供了完整的代码实现,展示了如何通过比较不同课程的优先级来确定最佳排名。

A1012

To evaluate the performance of our first year CS majored students, we consider their grades of three courses only: C - C Programming Language, M - Mathematics (Calculus or Linear Algebra), and E - English. At the mean time, we encourage students by emphasizing on their best ranks -- that is, among the four ranks with respect to the three courses and the average grade, we print the best rank for each student.

For example, The grades of C, M, E and A - Average of 4 students are given as the following:

StudentID  C  M  E  A
310101     98 85 88 90
310102     70 95 88 84
310103     82 87 94 88
310104     91 91 91 91

Then the best ranks for all the students are No.1 since the 1st one has done the best in C Programming Language, while the 2nd one in Mathematics, the 3rd one in English, and the last one in average.

Input

Each input file contains one test case. Each case starts with a line containing 2 numbers N and M (<=2000), which are the total number of students, and the number of students who would check their ranks, respectively. Then N lines follow, each contains a student ID which is a string of 6 digits, followed by the three integer grades (in the range of [0, 100]) of that student in the order of C, M and E. Then there are M lines, each containing a student ID.

Output

For each of the M students, print in one line the best rank for him/her, and the symbol of the corresponding rank, separated by a space.

The priorities of the ranking methods are ordered as A > C > M > E. Hence if there are two or more ways for a student to obtain the same best rank, output the one with the highest priority.

If a student is not on the grading list, simply output "N/A".

Sample Input
5 6
310101 98 85 88
310102 70 95 88
310103 82 87 94
310104 91 91 91
310105 85 90 90
310101
310102
310103
310104
310105
999999
Sample Output
1 C
1 M
1 E
1 A
3 A
N/A
利用优先级A>C>M>E的设定,可以将其存入字符数组中,即利用数组下标代替课程,简化程序。

同时,利用全局变量now可以定位需要进行排序的成绩。

AC代码如下:

#include <cstdio>
#include <algorithm>
using namespace std;
struct Per {
    int num;
    int grade[4];
    int rank[4];
};
Per person[2005];
int now;
char course[5] = { 'A','C','M','E' };
bool cmp(Per a, Per b) {
    if (a.grade[now] != b.grade[now])return a.grade[now] > b.grade[now];
    else return a.num < b.num;
}
int main() {
    int n, m;
    scanf("%d %d", &n, &m);
    int pc, pm, pe;
    for (int i = 0; i < n; i++) {
        scanf("%d %d %d %d", &person[i].num, &pc, &pm, &pe);
        person[i].grade[0] = (pc + pe + pm) / 3;
        person[i].grade[1] = pc; person[i].grade[2] = pm; person[i].grade[3] = pe;
    }
    for (now = 0; now < 4; now++) {
        sort(person, person + n, cmp);
        for (int i = 0; i < n; i++) {
            if (i == 0)person[i].rank[now] = 1;
            else {
                if (person[i].grade[now] == person[i - 1].grade[now])
                    person[i].rank[now] = person[i - 1].rank[now];
                else
                    person[i].rank[now] = i + 1;
            }
        }
    }
    int num,info;
    char best;
    bool flag = false;
    for (int i = 0; i < m; i++) {
        flag = false;
        scanf("%d", &num);
        for (int j= 0; j < n; j++) {
            if (num == person[j].num) {
                flag = true;
                info = j;
                break;
            }
        }
        if (!flag)
            printf("N/A");
        else {
            int max = 3000;
            for (int k = 0; k < 4; k++) {
                if (max > person[info].rank[k]) {
                    max = person[info].rank[k];
                    now = k;
                }
            }
            printf("%d %c", max, course[now]);
        }
        if (i != m - 1)
            printf("\n");
    }
    return 0;
}




To determine the number of distinct sets of 13 cards for which Player A can guarantee a win in a poker game where each player selects 5 cards and Player B wins on ties, the problem revolves around combinatorics and game theory. ### Problem Interpretation: - A standard deck has 52 cards. - Player A selects 13 cards as their hand. - From these 13 cards, Player A must be able to choose a 5-card poker hand that beats any 5-card poker hand that Player B could form from the remaining 39 cards. - If both players have the same rank of hand (e.g., both have a flush), Player B wins by default. - The objective is to count how many such 13-card combinations exist where Player A can always select a 5-card hand strictly better than any 5-card hand Player B could choose. ### Key Observations: - There are $\binom{52}{13}$ total possible 13-card hands. - Not all of these hands will allow Player A to guarantee a win. - The solution involves evaluating the strength of all possible 5-card combinations from the 13-card set and ensuring that none of the 5-card combinations from the remaining 39 cards can tie or beat them. ### Strategy to Solve: 1. **Understand Poker Hand Rankings**: The ranking of poker hands from highest to lowest is: Royal Flush, Straight Flush, Four of a Kind, Full House, Flush, Straight, Three of a Kind, Two Pair, One Pair, High Card. 2. **Generate All 13-Card Hands**: The number of ways to choose 13 cards from 52 is $\binom{52}{13}$, which is approximately $6.35 \times 10^{11}$. 3. **Evaluate Each 13-Card Hand**: - For each 13-card hand, generate all $\binom{13}{5} = 1287$ possible 5-card combinations. - Determine the best possible 5-card hand from these combinations. - From the remaining 39 cards, generate all $\binom{39}{5} = 575757$ possible 5-card combinations for Player B. - Check if any of Player B’s hands can tie or beat Player A’s best hand. 4. **Count Winning Hands for Player A**: - If Player A’s best 5-card hand beats all possible 5-card hands from the remaining 39 cards, count that 13-card set as a winning hand. - This requires a poker hand evaluator to compare the strength of hands. 5. **Implement Efficient Comparison**: - Use a precomputed lookup table for poker hand strengths. - Implement a fast comparison algorithm to avoid redundant computations. - Parallelize the computation to handle the large search space. 6. **Optimize with Pruning**: - Discard 13-card hands early if their best 5-card hand cannot beat the minimum possible strength of Player B’s hands. - For example, if Player A’s best hand is a high card, and Player B can form a pair, discard that 13-card set. 7. **Final Count**: - After evaluating all possible 13-card combinations and filtering out those where Player A cannot guarantee a win, the remaining count is the desired answer. ### Computational Complexity: This problem is computationally intensive due to the large number of combinations. It is not feasible to compute manually and would require: - Efficient poker hand evaluation code. - Distributed computing or GPU acceleration. - Optimization techniques such as memoization and pruning. Here is a simplified version of the code in Python: ```python from itertools import combinations import random # Simplified poker hand evaluator (placeholder) def evaluate_hand(hand): # This would be replaced with a full poker hand evaluator return random.randint(1, 1000000) # Generate a deck of 52 cards deck = list(range(52)) # Placeholder for counting winning hands winning_hands_count = 0 # Iterate over all possible 13-card hands (this is computationally infeasible to complete in full) for hand_A in combinations(deck, 13): remaining_cards = list(set(deck) - set(hand_A)) best_hand_A = max(combinations(hand_A, 5), key=evaluate_hand) # Check if best_hand_A beats all possible 5-card hands from the remaining 39 cards player_B_hands = combinations(remaining_cards, 5) if all(evaluate_hand(best_hand_A) > evaluate_hand(hand_B) for hand_B in player_B_hands): winning_hands_count += 1 print(f"Number of winning 13-card hands: {winning_hands_count}") ``` ### Conclusion: The exact number of such 13-card hands is not trivial to compute and would require a dedicated program with optimized algorithms. However, the framework for solving the problem involves evaluating all possible combinations and comparing poker hand strengths.
评论 1
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值