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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
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);
}
}
}