programming-examples/java/Data_Structures/ThreeSumFast.java

 

/*************************************************************************
 *  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;

import edu.princeton.cs.introcs.In;
import edu.princeton.cs.introcs.StdOut;

/**
 *  The  ThreeSumFast  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).
 *   
 *  This implementation uses sorting and binary search and takes time 
 *  proportional to N^2 log N, where N is the number of integers.
 *   
 *  For additional documentation, see <a href="http://algs4.cs.princeton.edu/14analysis">Section 1.4</a> of
 *   Algorithms, 4th Edition  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);
    } 
}