edu.princeton.cs.algs4.Inversions Maven / Gradle / Ivy
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/******************************************************************************
* Compilation: javac Inversions.java
* Execution: java Inversions < input.txt
* Dependencies: StdIn.java StdOut.java
*
* Read array of n integers and count number of inversions in n log n time.
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code Inversions} class provides static methods to count the
* number of inversions in either an array of integers or comparables.
* An inversion in an array {@code a[]} is a pair of indicies {@code i} and
* {@code j} such that {@code i < j} and {@code a[i] > a[j]}.
*
* This implementation uses a generalization of mergesort. The count
* operation takes time proportional to n log n,
* where n is the number of keys in the array.
*
* For additional documentation, see Section 2.2
* of Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class Inversions {
// do not instantiate
private Inversions() { }
// merge and count
private static long merge(int[] a, int[] aux, int lo, int mid, int hi) {
long inversions = 0;
// copy to aux[]
for (int k = lo; k <= hi; k++) {
aux[k] = a[k];
}
// merge back to a[]
int i = lo, j = mid+1;
for (int k = lo; k <= hi; k++) {
if (i > mid) a[k] = aux[j++];
else if (j > hi) a[k] = aux[i++];
else if (aux[j] < aux[i]) { a[k] = aux[j++]; inversions += (mid - i + 1); }
else a[k] = aux[i++];
}
return inversions;
}
// return the number of inversions in the subarray b[lo..hi]
// side effect b[lo..hi] is rearranged in ascending order
private static long count(int[] a, int[] b, int[] aux, int lo, int hi) {
long inversions = 0;
if (hi <= lo) return 0;
int mid = lo + (hi - lo) / 2;
inversions += count(a, b, aux, lo, mid);
inversions += count(a, b, aux, mid+1, hi);
inversions += merge(b, aux, lo, mid, hi);
assert inversions == brute(a, lo, hi);
return inversions;
}
/**
* Returns the number of inversions in the integer array.
* The argument array is not modified.
* @param a the array
* @return the number of inversions in the array. An inversion is a pair of
* indicies {@code i} and {@code j} such that {@code i < j}
* and {@code a[i] > a[j]}.
*/
public static long count(int[] a) {
int[] b = new int[a.length];
int[] aux = new int[a.length];
for (int i = 0; i < a.length; i++)
b[i] = a[i];
long inversions = count(a, b, aux, 0, a.length - 1);
return inversions;
}
// merge and count (Comparable version)
private static > long merge(Key[] a, Key[] aux, int lo, int mid, int hi) {
long inversions = 0;
// copy to aux[]
for (int k = lo; k <= hi; k++) {
aux[k] = a[k];
}
// merge back to a[]
int i = lo, j = mid+1;
for (int k = lo; k <= hi; k++) {
if (i > mid) a[k] = aux[j++];
else if (j > hi) a[k] = aux[i++];
else if (less(aux[j], aux[i])) { a[k] = aux[j++]; inversions += (mid - i + 1); }
else a[k] = aux[i++];
}
return inversions;
}
// return the number of inversions in the subarray b[lo..hi]
// side effect b[lo..hi] is rearranged in ascending order
private static > long count(Key[] a, Key[] b, Key[] aux, int lo, int hi) {
long inversions = 0;
if (hi <= lo) return 0;
int mid = lo + (hi - lo) / 2;
inversions += count(a, b, aux, lo, mid);
inversions += count(a, b, aux, mid+1, hi);
inversions += merge(b, aux, lo, mid, hi);
assert inversions == brute(a, lo, hi);
return inversions;
}
/**
* Returns the number of inversions in the comparable array.
* The argument array is not modified.
* @param a the array
* @param the inferred type of the elements in the array
* @return the number of inversions in the array. An inversion is a pair of
* indicies {@code i} and {@code j} such that {@code i < j}
* and {@code a[i].compareTo(a[j]) > 0}.
*/
public static > long count(Key[] a) {
Key[] b = a.clone();
Key[] aux = a.clone();
long inversions = count(a, b, aux, 0, a.length - 1);
return inversions;
}
// is v < w ?
private static > boolean less(Key v, Key w) {
return (v.compareTo(w) < 0);
}
// count number of inversions in a[lo..hi] via brute force (for debugging only)
private static > long brute(Key[] a, int lo, int hi) {
long inversions = 0;
for (int i = lo; i <= hi; i++)
for (int j = i + 1; j <= hi; j++)
if (less(a[j], a[i])) inversions++;
return inversions;
}
// count number of inversions in a[lo..hi] via brute force (for debugging only)
private static long brute(int[] a, int lo, int hi) {
long inversions = 0;
for (int i = lo; i <= hi; i++)
for (int j = i + 1; j <= hi; j++)
if (a[j] < a[i]) inversions++;
return inversions;
}
/**
* Reads a sequence of integers from standard input and
* prints the number of inversions to standard output.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
int[] a = StdIn.readAllInts();
int n = a.length;
Integer[] b = new Integer[n];
for (int i = 0; i < n; i++)
b[i] = a[i];
StdOut.println(Inversions.count(a));
StdOut.println(Inversions.count(b));
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.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.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.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.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/