package edu.princeton.cs.algs4.ch14;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* Compilation: javac ThreeSumFast.java
* Execution: java ThreeSumFast input.txt
* Dependencies: StdOut.java In.java Stopwatch.java
* Data files: http://algs4.cs.princeton.edu/14analysis/1Kints.txt
* http://algs4.cs.princeton.edu/14analysis/2Kints.txt
* http://algs4.cs.princeton.edu/14analysis/4Kints.txt
* http://algs4.cs.princeton.edu/14analysis/8Kints.txt
* http://algs4.cs.princeton.edu/14analysis/16Kints.txt
* http://algs4.cs.princeton.edu/14analysis/32Kints.txt
* http://algs4.cs.princeton.edu/14analysis/1Mints.txt
*
* A program with N^2 log N running time. Read in N integers
* and counts the number of triples that sum to exactly 0.
*
* Limitations
* -----------
* - we ignore integer overflow
* - doesn't handle case when input has duplicates
*
*
* % java ThreeSumFast 1Kints.txt
* 70
*
* % java ThreeSumFast 2Kints.txt
* 528
*
* % java ThreeSumFast 4Kints.txt
* 4039
*
* % java ThreeSumFast 8Kints.txt
* 32074
*
* % java ThreeSumFast 16Kints.txt
* 255181
*
* % java ThreeSumFast 32Kints.txt
* 2052358
*
*************************************************************************/
import java.util.Arrays;
/**
* The <tt>ThreeSumFast</tt> class provides static methods for counting
* and printing the number of triples in an array of distinct integers that
* sum to 0 (ignoring integer overflow).
* <p>
* This implementation uses sorting and binary search and takes time
* proportional to N^2 log N, where N is the number of integers.
* <p>
* For additional documentation, see <a href="http://algs4.cs.princeton.edu/14analysis">Section 1.4</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class ThreeSumFast {
// returns true if the sorted array a[] contains any duplicated integers
private static boolean containsDuplicates(int[] a) {
for (int i = 1; i < a.length; i++)
if (a[i] == a[i-1]) return true;
return false;
}
/**
* Prints to standard output the (i, j, k) with i < j < k such that a[i] + a[j] + a[k] == 0.
* @param a the array of integers
* @throws IllegalArgumentException if the array contains duplicate integers
*/
public static void printAll(int[] a) {
int N = a.length;
Arrays.sort(a);
if (containsDuplicates(a)) throw new IllegalArgumentException("array contains duplicate integers");
for (int i = 0; i < N; i++) {
for (int j = i+1; j < N; j++) {
int k = Arrays.binarySearch(a, -(a[i] + a[j]));
if (k > j) StdOut.println(a[i] + " " + a[j] + " " + a[k]);
}
}
}
/**
* Returns the number of triples (i, j, k) with i < j < k such that a[i] + a[j] + a[k] == 0.
* @param a the array of integers
* @return the number of triples (i, j, k) with i < j < k such that a[i] + a[j] + a[k] == 0
*/
public static int count(int[] a) {
int N = a.length;
Arrays.sort(a);
if (containsDuplicates(a)) throw new IllegalArgumentException("array contains duplicate integers");
int cnt = 0;
for (int i = 0; i < N; i++) {
for (int j = i+1; j < N; j++) {
int k = Arrays.binarySearch(a, -(a[i] + a[j]));
if (k > j) cnt++;
}
}
return cnt;
}
/**
* Reads in a sequence of distinct integers from a file, specified as a command-line argument;
* counts the number of triples sum to exactly zero; prints out the time to perform
* the computation.
*/
public static void main(String[] args) {
In in = new In(args[0]);
int[] a = in.readAllInts();
int cnt = count(a);
StdOut.println(cnt);
}
}
/*************************************************************************
* Copyright 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4-package.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4-package.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with algs4-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/