結果
| 問題 |
No.461 三角形はいくつ？
|
| コンテスト | |
| ユーザー |
 tanzaku
|
| 提出日時 | 2016-12-12 20:54:53 |
| 言語 | Java (openjdk 23) |
| 結果 |
AC
|
| 実行時間 | 3,313 ms / 5,000 ms |
| コード長 | 13,136 bytes |
| コンパイル時間 | 5,076 ms |
| コンパイル使用メモリ | 93,376 KB |
| 実行使用メモリ | 41,468 KB |
| 最終ジャッジ日時 | 2024-11-29 17:55:08 |
| 合計ジャッジ時間 | 77,629 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 41 |
ソースコード
import java.io.*;
import java.math.*;
import java.util.*;
import static java.util.Arrays.*;
public class _461 {
private static final int mod = (int)1e9+7;
final Random random = new Random(0);
final IOFast io = new IOFast();
final double eps = 1e-12;
/// MAIN CODE
public void run() throws IOException {
if (true) { tle(); return; }
// int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
int TEST_CASE = 1;
while(TEST_CASE-- != 0) {
int n = io.nextInt();
int[][] qs = io.nextIntArray2D(n, 3);
long ans = 1;
for (int i = 0; i < n; i++) {
ans++;
for (int j = 0; j < i; j++) {
int c1 = cross(qs[i], qs[j]);
if (c1 == -1) continue;
if (c1 == 1) ans++;
for (int k = 0; k < j; k++) {
if (qs[i][0] == qs[k][0]) continue;
if (qs[j][0] == qs[k][0]) continue;
if (degenerated(qs[i], qs[j], qs[k])) continue;
if (triangle(qs[i], qs[j], qs[k])) ans++;
}
}
}
io.out.println(ans);
}
}
// p[i] = q[i][1] / (q[i][1] + q[i][2])
// p[i] + p[j] - 1 + p[j] + p[k] - 1 = p[j]
// p[i] + p[j] + p[k] = 2
int cross(int[] q1, int[] q2) {
if (q1[0] == q2[0]) return -1;
long r1 = q1[1] + q1[2];
long r2 = q2[1] + q2[2];
// long cmp = q1[1] / (q1[1] + q1[2]) + q2[1] / (q2[1] + q2[2]) > 1;
long cmp = q1[1] * r2 + q2[1] * r1 - r1 * r2;
return cmp > 0 ? 1 : cmp < 0 ? -1 : 0;
}
boolean triangle(int[] q1, int[] q2, int[] q3) {
long r1 = q1[1] + q1[2];
long r2 = q2[1] + q2[2];
long r3 = q3[1] + q3[2];
return
q1[1] * r2 + q2[1] * r1 >= r1 * r2 &&
q1[1] * r3 + q3[1] * r1 >= r1 * r3 &&
q2[1] * r3 + q3[1] * r2 >= r2 * r3;
}
boolean degenerated(int[] q1, int[] q2, int[] q3) {
long r1 = q1[1] + q1[2];
long r2 = q2[1] + q2[2];
long r3 = q3[1] + q3[2];
return q1[1] * r2 * r3 + q2[1] * r1 * r3 + q3[1] * r1 * r2 == 2 * r1 * r2 * r3;
}
void mistake() throws IOException {
int n = io.nextInt();
int[][] qs = io.nextIntArray2D(n, 3);
double[] p = new double[n];
List<Double> y = new ArrayList<>();
long ans = n + 1;
for (int i = 0; i < n; i++) {
p[i] = (double)qs[i][1] / (qs[i][1] + qs[i][2]);
if (qs[i][0] == 0) {
y.add(p[i]);
}
}
Collections.sort(y);
for (int i = 0; i < n; i++) {
for (int j = 0; j < i; j++) if (qs[i][0] != qs[j][0]) {
if (p[i] + p[j] - eps > 1) {
ans++;
}
if (qs[i][0] == 0 || qs[j][0] == 0) continue;
// dump(p[i] + p[j]);
if (p[i] + p[j] + eps < 1) continue;
double p1 = Math.min(p[i], p[j]);
double p2 = 2 - p[i] - p[j];
// p3 >= 1-min(p1,p2)
ans += query(y, 1 - p1);
// degenerated : p1 + p2 + p3 == 2
ans -= find(y, p2);
// dump(i, j, query(y, p1), find(y, p2));
}
}
io.out.println(ans);
}
long find(List<Double> y, double key) {
int idx = Collections.binarySearch(y, key - eps);
if (idx < 0) idx = -idx - 1;
if (idx >= y.size()) return 0;
return Math.abs(y.get(idx) - key) <= eps ? 1 : 0;
}
long query(List<Double> y, double key) {
int idx = Collections.binarySearch(y, key - eps);
if (idx < 0) idx = -idx - 1;
// else idx--;
return y.size() - idx;
// return idx;
}
void tle() throws IOException {
int n = io.nextInt();
int[][] qs = io.nextIntArray2D(n, 3);
RationalLong[] p = new RationalLong[n];
List<RationalLong> y = new ArrayList<>();
long ans = n + 1;
for (int i = 0; i < n; i++) {
p[i] = new RationalLong(qs[i][1], qs[i][1] + qs[i][2]);
if (qs[i][0] == 0) {
y.add(p[i]);
}
}
Collections.sort(y);
RationalLong two = RationalLong.ONE.mul(2);
RationalLong pij = new RationalLong();
RationalLong p2 = new RationalLong();
RationalLong p3 = new RationalLong();
for (int i = 0; i < n; i++) {
for (int j = 0; j < i; j++) if (qs[i][0] != qs[j][0]) {
pij.add(p[i], p[j]);
if (pij.compareTo(RationalLong.ONE) > 0) {
ans++;
}
if (pij.compareTo(RationalLong.ONE) < 0) continue;
if (qs[i][0] == 0 || qs[j][0] == 0) continue;
RationalLong p1 = RationalLong.min(p[i], p[j]);
p2.sub(two, pij);
p3.sub(RationalLong.ONE, p1);
// p3 >= 1-min(p1,p2)
ans += query(y, p3);
// degenerated : p1 + p2 + p3 == 2
ans -= find(y, p2);
// dump(i, j, query(y, p3), find(y, p2));
}
}
io.out.println(ans);
}
long find(List<RationalLong> y, RationalLong key) {
int idx = Collections.binarySearch(y, key);
if (idx < 0) return 0;
return 1;
}
long query(List<RationalLong> y, RationalLong key) {
int idx = Collections.binarySearch(y, key);
if (idx < 0) idx = -idx - 1;
// else idx--;
return y.size() - idx;
// return idx;
}
static class RationalLong implements Comparable<RationalLong> {
private long denominator, numerator;
private static long gcd(long n, long r) { while(r != 0) { final long t = n % r; n = r; r = t; } return n; }
public static RationalLong min(RationalLong r1, RationalLong r2) {
return r1.compareTo(r2) < 0 ? r1 : r2;
}
public static RationalLong ZERO = new RationalLong(0, 1);
public static RationalLong ONE = new RationalLong(1, 1);
public static RationalLong TEN = new RationalLong(10, 1);
public long denominator() { return denominator; }
public long numerator() { return numerator; }
public static RationalLong valueOf(final int x) { return new RationalLong(x); }
public static RationalLong valueOf(final long x) { return new RationalLong(x); }
public RationalLong() {
denominator = 0;
numerator = 1;
}
public RationalLong(long n, long d) {
if(d < 0) { d = -d; n = -n; }
final long x = gcd(Math.abs(n), d);
denominator = d / x;
numerator = n / x;
}
public RationalLong(final RationalLong r) {
denominator = r.denominator;
numerator = r.numerator;
}
public RationalLong(final long x) {
denominator = 1;
numerator = x;
}
private void reduce() {
final long x = gcd(numerator, denominator);
if (x == 0) return;
if(x != 1) {
numerator = numerator / x;
denominator = denominator / x;
}
if(denominator < 0) {
denominator = -denominator;
numerator = -numerator;
}
}
public RationalLong negate() { RationalLong r = new RationalLong(this); r.numerator = -r.numerator; return r; }
public RationalLong add(final long b) { return new RationalLong(denominator() * b + numerator(), denominator()); }
public RationalLong add(final RationalLong b) {
return new RationalLong(
numerator * b.denominator + denominator * b.numerator,
denominator * b.denominator);
}
public void add(final RationalLong a, final RationalLong b) {
this.numerator = a.numerator * b.denominator + a.denominator * b.numerator;
this.denominator = a.denominator * b.denominator;
reduce();
}
public RationalLong sub(final long b) { return add(-b); }
public RationalLong sub(final RationalLong b) { return add(b.negate()); }
public void sub(final RationalLong a, final RationalLong b) {
this.numerator = a.numerator * b.denominator - a.denominator * b.numerator;
this.denominator = a.denominator * b.denominator;
reduce();
}
public RationalLong mul(final long b) { return new RationalLong(b * numerator(), denominator()); }
public RationalLong mul(final RationalLong b) {
return new RationalLong(
numerator * b.numerator,
denominator * b.denominator);
}
public RationalLong div(final long b) { return new RationalLong(numerator(), denominator() * b); }
public RationalLong div(final RationalLong b) {
return new RationalLong(
numerator * b.denominator,
denominator * b.numerator);
}
@Override
public String toString() {
return numerator + "/" + denominator;
}
@Override
public int compareTo(RationalLong o) {
return Long.compare(numerator * o.denominator, denominator * o.numerator);
}
@Override
public boolean equals(Object obj) {
// TODO Auto-generated method stub
return compareTo((RationalLong)obj) == 0;
}
}
/// TEMPLATE
static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }
void printArrayLn(int[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
void printArrayLn(long[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); }
void main() throws IOException {
// IOFast.setFileIO("rle-size.in", "rle-size.out");
try { run(); }
catch (EndOfFileRuntimeException e) { }
io.out.flush();
}
public static void main(String[] args) throws IOException { new _461().main(); }
static class EndOfFileRuntimeException extends RuntimeException {
private static final long serialVersionUID = -8565341110209207657L; }
static
public class IOFast {
private InputStream in = System.in;
private PrintWriter out = new PrintWriter(System.out);
private static int pos, readLen;
private static final byte[] buffer = new byte[1024 * 8];
private static char[] str = new char[500*8*2];
private static boolean[] isDigit = new boolean[256];
private static boolean[] isSpace = new boolean[256];
private static boolean[] isLineSep = new boolean[256];
static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
public byte read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; }
public int nextInt() throws IOException {
byte first = (byte)nextChar();
boolean minus = false;
int res = 0;
if (first == '-') {
minus = true;
} else {
res = first - '0';
}
while (true) {
byte b = read();
if (isSpace[b]) break;
res = res * 10 + b - '0';
}
return minus ? -res : res;
}
public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); }
public String nextString() throws IOException { return new String(next()); }
public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
// public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; }
// public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
public double nextDouble() throws IOException {
double res = nextChar() - '0';
while (true) {
byte c = read();
if (isSpace[c]) return res;
if (c == '.') break;
res = res * 10 + c - '0';
}
double d = 1;
while (true) {
byte c = read();
// dump(c);
if (!isDigit[c]) break;
res = res * 10 + c - '0';
d *= 10;
}
// dump(1);
return res / d;
}
public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
}
}