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社区首页 >专栏 >POJ 刷题系列:2151. Check the difficulty of problems

POJ 刷题系列:2151. Check the difficulty of problems

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发布2019-05-26 07:51:53
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发布2019-05-26 07:51:53
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文章被收录于专栏:机器学习入门机器学习入门

版权声明:本文为博主原创文章,未经博主允许不得转载。 https://cloud.tencent.com/developer/article/1434487

POJ 刷题系列:2151. Check the difficulty of problems

传送门:2151. Check the difficulty of problems

题意:

ACM比赛中,共M道题,T个队,pij表示第i队解出第j题的概率,问每队至少解出一题且冠军队至少解出N道题的概率。

思路:

数学题,答案为:每个队至少解决1道题的概率P1 - 每个队至少解决(1 ~ N-1)题的概率P2

代码语言:javascript
复制
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Map;
import java.util.StringTokenizer;

public class Main{

    String INPUT = "./data/judge/201801/P2151.txt";

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    void read() {
        while(true) {
            int m = ni();
            int t = ni();
            int k = ni();
            if (m + t + k == 0) break;

            double[][] pij = new double[t][m];
            for (int i = 0; i < t; ++i) {
                for (int j = 0; j < m; ++j) {
                    double p = nd();
                    pij[i][j] = p;
                }
            }

            // 第t个队, 前m到题,做对k道题的概率
            double[][][] f = new double[t + 16][m + 16][m + 16];

            for (int i = 0; i < t; ++i) {
                f[i][0][0] = 1;

                // 答对0题的概率
                for (int j = 0; j < m; ++j) {
                    f[i][j + 1][0] = f[i][j][0] * (1 - pij[i][j]);
                }
                for (int j = 0; j < m; ++j) {
                    for (int l = 1; l <= m; ++l) {
                        f[i][j + 1][l] = f[i][j][l - 1] * pij[i][j] + f[i][j][l] * (1 - pij[i][j]);
                    }
                }
            }
            // 每个队 答对 k道题的概率
            double[][] s = new double[t + 16][m + 16];
            for (int i = 0; i < t; ++i) {
                s[i][0] = f[i][m][0];
                for (int j = 1; j <= m; ++j) {
                    s[i][j] = s[i][j - 1] +  f[i][m][j];
                }
            }

            double P1 = 1.0; // 所有队至少答对一题的概率
            for (int i = 0; i < t; ++i) {
                P1 = P1 * (s[i][m] - s[i][0]);
            }
            double P2 = 1.0; // 所有队至少答对1~k-1题的概率
            for (int i = 0; i < t; ++i) {
                P2 = P2 * (s[i][k - 1] - s[i][0]);
            }

            out.printf("%.3f\n", P1 - P2);
        }
    }

    FastScanner in;
    PrintWriter out;

    void run() throws IOException {
        boolean oj;
        try {
            oj = ! System.getProperty("user.dir").equals("F:\\oxygen_workspace\\Algorithm");
        } catch (Exception e) {
            oj = System.getProperty("ONLINE_JUDGE") != null;
        }

        InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));
        in = new FastScanner(is);
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        read();
        out.flush();
        if (!oj){
            System.out.println("[" + (System.currentTimeMillis() - s) + "ms]");
        }
    }

    public boolean more(){
        return in.hasNext();
    }

    public int ni(){
        return in.nextInt();
    }

    public long nl(){
        return in.nextLong();
    }

    public double nd(){
        return in.nextDouble();
    }

    public String ns(){
        return in.nextString();
    }

    public char nc(){
        return in.nextChar();
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        boolean hasNext;

        public FastScanner(InputStream is) throws IOException {
            br = new BufferedReader(new InputStreamReader(is));
            hasNext = true;
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    hasNext = false;
                    return "##";
                }
            }
            return st.nextToken();
        }

        String next = null;
        public boolean hasNext(){
            next = nextToken();
            return hasNext;
        }

        public int nextInt() {
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return Integer.parseInt(more);
        }

        public long nextLong() {
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return Long.parseLong(more);
        }

        public double nextDouble() {
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return Double.parseDouble(more);
        }

        public String nextString(){
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return more;
        }

        public char nextChar(){
            if (next == null){
                hasNext();
            }
            String more = next;
            next = null;
            return more.charAt(0);
        }
    }

    static class D{

        public static void pp(int[][] board, int row, int col) {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < row; ++i) {
                for (int j = 0; j < col; ++j) {
                    sb.append(board[i][j] + (j + 1 == col ? "\n" : " "));
                }
            }
            System.out.println(sb.toString());
        }

        public static void pp(char[][] board, int row, int col) {
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < row; ++i) {
                for (int j = 0; j < col; ++j) {
                    sb.append(board[i][j] + (j + 1 == col ? "\n" : " "));
                }
            }
            System.out.println(sb.toString());
        }
    }

    static class ArrayUtils {

        public static void fill(int[][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                Arrays.fill(f[i], value);
            }
        }

        public static void fill(int[][][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                fill(f[i], value);
            }
        }

        public static void fill(int[][][][] f, int value) {
            for (int i = 0; i < f.length; ++i) {
                fill(f[i], value);
            }
        }
    }

    static class Num{
        public static <K> void inc(Map<K, Integer> mem, K k) {
            if (!mem.containsKey(k)) mem.put(k, 0);
            mem.put(k, mem.get(k) + 1);
        }
    }
}
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原始发表:2018年01月16日,如有侵权请联系 cloudcommunity@tencent.com 删除

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