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113 lines (94 loc) · 3.15 KB
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package atcoder.educational_dp;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;
public final class I {
public static void main(String[] args) {
final FastScanner fs = new FastScanner();
final int n = fs.nextInt();
final double[] prob = new double[n];
for (int i = 0; i < n; i++) {
prob[i] = Double.parseDouble(fs.next());
}
System.out.println(dfs(prob, 0, 0, new Double[n][n]));
}
private static double dfs(double[] prob, int idx, int heads, Double[][] dp) {
if (idx == prob.length) {
return heads > prob.length / 2 ? 1 : 0;
}
if (dp[idx][heads] != null) {
return dp[idx][heads];
}
return dp[idx][heads] = (1 - prob[idx]) * dfs(prob, idx + 1, heads, dp) +
prob[idx] * dfs(prob, idx + 1, heads + 1, dp);
}
static final class Utils {
public static void shuffleSort(int[] arr) {
shuffle(arr);
Arrays.sort(arr);
}
public static void shuffleSort(long[] arr) {
shuffle(arr);
Arrays.sort(arr);
}
public static void shuffle(int[] arr) {
final Random r = new Random();
for (int i = 0; i <= arr.length - 2; i++) {
final int j = i + r.nextInt(arr.length - i);
swap(arr, i, j);
}
}
public static void shuffle(long[] arr) {
final Random r = new Random();
for (int i = 0; i <= arr.length - 2; i++) {
final int j = i + r.nextInt(arr.length - i);
swap(arr, i, j);
}
}
public static void swap(int[] arr, int i, int j) {
final int t = arr[i];
arr[i] = arr[j];
arr[j] = t;
}
public static void swap(long[] arr, int i, int j) {
final long t = arr[i];
arr[i] = arr[j];
arr[j] = t;
}
private Utils() {}
}
static class FastScanner {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
StringTokenizer st = new StringTokenizer("");
private String next() {
while (!st.hasMoreTokens()) {
try {
st = new StringTokenizer(br.readLine());
} catch (IOException e) {
//noinspection CallToPrintStackTrace
e.printStackTrace();
}
}
return st.nextToken();
}
int nextInt() {
return Integer.parseInt(next());
}
long nextLong() {
return Long.parseLong(next());
}
int[] nextIntArray(int n) {
final int[] a = new int[n];
for (int i = 0; i < n; i++) { a[i] = nextInt(); }
return a;
}
long[] nextLongArray(int n) {
final long[] a = new long[n];
for (int i = 0; i < n; i++) { a[i] = nextLong(); }
return a;
}
}
}