3-sum问题平方对数级别算法

港控/mmm° 2021-07-24 19:58 414阅读 0赞

# 一 代码 #

/******************************************************************************
     *  Compilation:  javac ThreeSumFast.java
     *  Execution:    java ThreeSumFast input.txt
     *  Dependencies: StdOut.java In.java Stopwatch.java
     *  Data files:   https://algs4.cs.princeton.edu/14analysis/1Kints.txt
     *                https://algs4.cs.princeton.edu/14analysis/2Kints.txt
     *                https://algs4.cs.princeton.edu/14analysis/4Kints.txt
     *                https://algs4.cs.princeton.edu/14analysis/8Kints.txt
     *                https://algs4.cs.princeton.edu/14analysis/16Kints.txt
     *                https://algs4.cs.princeton.edu/14analysis/32Kints.txt
     *                https://algs4.cs.princeton.edu/14analysis/1Mints.txt
     *
     *  A program with n^2 log n running time. Reads 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
     *
     ******************************************************************************/
    
    package common;
    
    import java.util.Arrays;
    
    /**
     * The {@code 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).
     * <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="https://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 {
    
        // Do not instantiate.
        private 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 {@code i < j < k}
         * such that {@code 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 {@code i < j < k}
         * such that {@code a[i] + a[j] + a[k] == 0}.
         *
         * @param a the array of integers
         * @return the number of triples (i, j, k) with {@code i < j < k}
         * such that {@code 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 count = 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) count++;
                }
            }
            return count;
        }
    
        /**
         * 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.
         *
         * @param args the command-line arguments
         */
        public static void main(String[] args) {
            In in = new In(args[0]);
            int[] a = in.readAllInts();
            int count = count(a);
            StdOut.println(count);
        }
    }

# 二 测试 #

F:\Algorithm\target\classes>java common.ThreeSumFast 1Kints.txt
    70
    
    F:\Algorithm\target\classes>java common.ThreeSumFast 2Kints.txt
    528
    
    F:\Algorithm\target\classes>java common.ThreeSumFast 4Kints.txt
    4039
    
    F:\Algorithm\target\classes>java common.ThreeSumFast 8Kints.txt
    32074
    
    F:\Algorithm\target\classes>java common.ThreeSumFast 16Kints.txt
    255181
    
    F:\Algorithm\target\classes>java common.ThreeSumFast 32Kints.txt
    2052358

# 三 测试说明 #

该算法是平方对数级别算法。