AtCoder Beginner Contest 011 D: 大ジャンプ
解法
水平方向に飛ばなければならない回数を H 、垂直方向に飛ばなければならない回数を V とする。
垂直方向に飛ぶ回数を v とすると、垂直方向に戻る回数は v-V、 水平方向に飛ぶ回数 h=(N-v-v+V-H)/2+H、水平方向に戻る回数は h-H となる。この時ゴールに辿り着く確率は
である。これを各 v について計算すれば良い。
コード
import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintWriter; import java.util.NoSuchElementException; public class Main { private static class Task { void solve(FastScanner in, PrintWriter out) { int N = in.nextInt(); int D = in.nextInt(); int X = Math.abs(in.nextInt()); int Y = Math.abs(in.nextInt()); if (X % D != 0 || Y % D != 0) { out.println(0.0); return; } int V = X / D; int H = Y / D; double ans = 0.0; for (int v = V; v <= N; v++) { int antiV = v - V; int rest = N - v - antiV - H; if (rest < 0) continue; if (rest % 2 != 0) continue; int h = rest / 2 + H; int antiH = rest / 2; assert h + v + antiV + antiH == N; double tmp = 1.0; long n = 1; for (int i = 1; i <= h; i++, n++) { tmp *= n; tmp /= i; tmp /= 4.0; } for (int i = 1; i <= antiH; i++, n++) { tmp *= n; tmp /= i; tmp /= 4.0; } for (int i = 1; i <= v; i++, n++) { tmp *= n; tmp /= i; tmp /= 4.0; } for (int i = 1; i <= antiV; i++, n++) { tmp *= n; tmp /= i; tmp /= 4.0; } assert n == N; ans += tmp; } out.println(ans); } } /** * ここから下はテンプレートです。 */ public static void main(String[] args) { OutputStream outputStream = System.out; FastScanner in = new FastScanner(); PrintWriter out = new PrintWriter(outputStream); Task solver = new Task(); solver.solve(in, out); out.close(); } private static class FastScanner { private final InputStream in = System.in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int bufferLength = 0; private boolean hasNextByte() { if (ptr < bufferLength) { return true; } else { ptr = 0; try { bufferLength = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } if (bufferLength <= 0) { return false; } } return true; } private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1; } private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126; } private void skipUnprintable() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; } boolean hasNext() { skipUnprintable(); return hasNextByte(); } public String next() { if (!hasNext()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while (isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } long nextLong() { if (!hasNext()) throw new NoSuchElementException(); long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } if (b < '0' || '9' < b) { throw new NumberFormatException(); } while (true) { if ('0' <= b && b <= '9') { n *= 10; n += b - '0'; } else if (b == -1 || !isPrintableChar(b)) { return minus ? -n : n; } else { throw new NumberFormatException(); } b = readByte(); } } double nextDouble() { return Double.parseDouble(next()); } double[] nextDoubleArray(int n) { double[] array = new double[n]; for (int i = 0; i < n; i++) { array[i] = nextDouble(); } return array; } double[][] nextDoubleMap(int n, int m) { double[][] map = new double[n][]; for (int i = 0; i < n; i++) { map[i] = nextDoubleArray(m); } return map; } public int nextInt() { return (int) nextLong(); } public int[] nextIntArray(int n) { int[] array = new int[n]; for (int i = 0; i < n; i++) array[i] = nextInt(); return array; } public long[] nextLongArray(int n) { long[] array = new long[n]; for (int i = 0; i < n; i++) array[i] = nextLong(); return array; } public String[] nextStringArray(int n) { String[] array = new String[n]; for (int i = 0; i < n; i++) array[i] = next(); return array; } public char[][] nextCharMap(int n) { char[][] array = new char[n][]; for (int i = 0; i < n; i++) array[i] = next().toCharArray(); return array; } } }