1451 合法三角形

萌萌哒的传送门

这道题很明显，可以通过算出有多少个三元组在一条线上，总的结果减去就行。这个可以通过枚举每一个点，算出

数组其它的点跟这个点的斜率，如果斜率相同的，就意味着在同一条线上。然后就直接搞了

弱写的代码:

//package xdlove_acmer;

import java.util.*;
import java.io.*;
import java.math.*;

public class Main {

	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve() {
		int n = ni();
		long ans = 1L * n * (n - 1) * (n - 2) / 6;
		int[] x = new int[n],y = new int[n];
		Map<Double, Integer> mp = new HashMap<Double, Integer>();
		for(int i = 0; i < n; i++) {
			x[i] = ni(); y[i] = ni();  
		}
		for(int i = 0; i < n; i++) {
			mp.clear();
			for(int j = i + 1; j < n; j++) {
				if(i != j) {
					int nx = x[j] - x[i];
					int ny = y[j] - y[i];
					double k;
					if(nx == 0) k = 10000;
					else k = 1.0 * ny / nx + 1e-8;
					int num = 0;
					if(mp.containsKey(k)) {
						num = mp.get(k);
					}
					mp.put(k, num + 1);
				}
			}
			Iterator<Double> itr = mp.keySet().iterator();
			while(itr.hasNext()) {
				int t = mp.get(itr.next());
				ans -= 1L * t * (t - 1) / 2;
			}
		}
		out.println(ans);
	}
	
	public static void main(String[] args) throws Exception {
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(
				INPUT.getBytes());
		out = new PrintWriter(System.out);
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G - S + "ms");
	}

	private static boolean eof() {
		if (lenbuf == -1)
			return true;
		int lptr = ptrbuf;
		while (lptr < lenbuf)
			if (!isSpaceChar(inbuf[lptr++]))
				return false;

		try {
			is.mark(1000);
			while (true) {
				int b = is.read();
				if (b == -1) {
					is.reset();
					return true;
				} else if (!isSpaceChar(b)) {
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}

	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;

	private static int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private static boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private static int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private static double nd() {
		return Double.parseDouble(ns());
	}

	private static char nc() {
		return (char) skip();
	}

	private static String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b !=
									// ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private static char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private static char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}
	
	private static int[] copy_int(int a[]) {
		int[] b = new int[a.length];
		for(int i = 0; i < a.length; i++)
			b[i] = a[i];
		return b;
	}
	
	private static int[] unique(int a[]) {
		int nl = 1;
		int[] c;
		for(int i = 1; i < a.length; i++) {
			if(a[i] != a[nl - 1]) a[nl++] = a[i];
		}
		c = new int[nl];
		for(int i = 0; i < nl; i++) 
			c[i] = a[i]; 
		return c;
	}

	private static int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private static long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private static void tr(Object... o) {
		if (INPUT.length() != 0)
			System.out.println(Arrays.deepToString(o));
	}

}