package edu.princeton.cs.algs4;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* Compilation: javac SuffixArrayX.java
* Execution: java SuffixArrayX < input.txt
*
* A data type that computes the suffix array of a string using 3-way
* radix quicksort.
*
* % java SuffixArrayX < abra.txt
* i ind lcp rnk select
* ---------------------------
* 0 11 - 0 !
* 1 10 0 1 A!
* 2 7 1 2 ABRA!
* 3 0 4 3 ABRACADABRA!
* 4 3 1 4 ACADABRA!
* 5 5 1 5 ADABRA!
* 6 8 0 6 BRA!
* 7 1 3 7 BRACADABRA!
* 8 4 0 8 CADABRA!
* 9 6 0 9 DABRA!
* 10 9 0 10 RA!
* 11 2 2 11 RACADABRA!
*
*
*************************************************************************/
/**
* The <tt>SuffixArrayX</tt> class represents a suffix array of a string of
* length <em>N</em>.
* It supports the <em>selecting</em> the <em>i</em>th smallest suffix,
* getting the <em>index</em> of the <em>i</em>th smallest suffix,
* computing the length of the <em>longest common prefix</em> between the
* <em>i</em>th smallest suffix and the <em>i</em>-1st smallest suffix,
* and determining the <em>rank</em> of a query string (which is the number
* of suffixes strictly less than the query string).
* <p>
* This implementation uses 3-way radix quicksort to sort the array of suffixes.
* For a simpler (but less efficient) implementations of the same API, see
* {@link SuffixArray}.
* The <em>index</em> and <em>length</em> operations takes constant time
* in the worst case. The <em>lcp</em> operation takes time proportional to the
* length of the longest common prefix.
* The <em>select</em> operation takes time proportional
* to the length of the suffix and should be used primarily for debugging.
* <p>
* This implementation uses '\0' as a sentinel and assumes that the charater
* '\0' does not appear in the text.
* <p>
* In practice, this algorithm runs very fast. However, in the worst-case
* it can be very poor (e.g., a string consisting of N copies of the same
* character. We do not shuffle the array of suffixes before sorting because
* shuffling is relatively expensive and a pathologial input for which
* the suffixes start out in a bad order (e.g., sorted) is likely to be
* a bad input for this algorithm with or without the shuffle.
* <p>
* For additional documentation, see <a href="http://algs4.cs.princeton.edu/63suffix">Section 6.3</a> of
* <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
*/
public class SuffixArrayX {
private static final int CUTOFF = 5; // cutoff to insertion sort (any value between 0 and 12)
private final char[] text;
private final int[] index; // index[i] = j means text.substring(j) is ith largest suffix
private final int N; // number of characters in text
/**
* Initializes a suffix array for the given <tt>text</tt> string.
* @param text the input string
*/
public SuffixArrayX(String text) {
N = text.length();
text = text + '\0';
this.text = text.toCharArray();
this.index = new int[N];
for (int i = 0; i < N; i++)
index[i] = i;
sort(0, N-1, 0);
}
// 3-way string quicksort lo..hi starting at dth character
private void sort(int lo, int hi, int d) {
// cutoff to insertion sort for small subarrays
if (hi <= lo + CUTOFF) {
insertion(lo, hi, d);
return;
}
int lt = lo, gt = hi;
char v = text[index[lo] + d];
int i = lo + 1;
while (i <= gt) {
char t = text[index[i] + d];
if (t < v) exch(lt++, i++);
else if (t > v) exch(i, gt--);
else i++;
}
// a[lo..lt-1] < v = a[lt..gt] < a[gt+1..hi].
sort(lo, lt-1, d);
if (v > 0) sort(lt, gt, d+1);
sort(gt+1, hi, d);
}
// sort from a[lo] to a[hi], starting at the dth character
private void insertion(int lo, int hi, int d) {
for (int i = lo; i <= hi; i++)
for (int j = i; j > lo && less(index[j], index[j-1], d); j--)
exch(j, j-1);
}
// is text[i+d..N) < text[j+d..N) ?
private boolean less(int i, int j, int d) {
if (i == j) return false;
i = i + d;
j = j + d;
while (i < N && j < N) {
if (text[i] < text[j]) return true;
if (text[i] > text[j]) return false;
i++;
j++;
}
return i > j;
}
// exchange index[i] and index[j]
private void exch(int i, int j) {
int swap = index[i];
index[i] = index[j];
index[j] = swap;
}
/**
* Returns the length of the input string.
* @return the length of the input string
*/
public int length() {
return N;
}
/**
* Returns the index into the original string of the <em>i</em>th smallest suffix.
* That is, <tt>text.substring(sa.index(i))</tt> is the <em>i</em> smallest suffix.
* @param i an integer between 0 and <em>N</em>-1
* @return the index into the original string of the <em>i</em>th smallest suffix
* @throws java.lang.IndexOutOfBoundsException unless 0 ≤ <em>i</em> < <Em>N</em>
*/
public int index(int i) {
if (i < 0 || i >= N) throw new IndexOutOfBoundsException();
return index[i];
}
/**
* Returns the length of the longest common prefix of the <em>i</em>th
* smallest suffix and the <em>i</em>-1st smallest suffix.
* @param i an integer between 1 and <em>N</em>-1
* @return the length of the longest common prefix of the <em>i</em>th
* smallest suffix and the <em>i</em>-1st smallest suffix.
* @throws java.lang.IndexOutOfBoundsException unless 1 ≤ <em>i</em> < <em>N</em>
*/
public int lcp(int i) {
if (i < 1 || i >= N) throw new IndexOutOfBoundsException();
return lcp(index[i], index[i-1]);
}
// longest common prefix of text[i..N) and text[j..N)
private int lcp(int i, int j) {
int length = 0;
while (i < N && j < N) {
if (text[i] != text[j]) return length;
i++;
j++;
length++;
}
return length;
}
/**
* Returns the <em>i</em>th smallest suffix as a string.
* @param i the index
* @return the <em>i</em> smallest suffix as a string
* @throws java.lang.IndexOutOfBoundsException unless 0 ≤ <em>i</em> < <Em>N</em>
*/
public String select(int i) {
if (i < 0 || i >= N) throw new IndexOutOfBoundsException();
return new String(text, index[i], N - index[i]);
}
/**
* Returns the number of suffixes strictly less than the <tt>query</tt> string.
* We note that <tt>rank(select(i))</tt> equals <tt>i</tt> for each <tt>i</tt>
* between 0 and <em>N</em>-1.
* @param query the query string
* @return the number of suffixes strictly less than <tt>query</tt>
*/
public int rank(String query) {
int lo = 0, hi = N - 1;
while (lo <= hi) {
int mid = lo + (hi - lo) / 2;
int cmp = compare(query, index[mid]);
if (cmp < 0) hi = mid - 1;
else if (cmp > 0) lo = mid + 1;
else return mid;
}
return lo;
}
// is query < text[i..N) ?
private int compare(String query, int i) {
int M = query.length();
int j = 0;
while (i < N && j < M) {
if (query.charAt(j) != text[i]) return query.charAt(j) - text[i];
i++;
j++;
}
if (i < N) return -1;
if (j < M) return +1;
return 0;
}
/**
* Unit tests the <tt>SuffixArrayx</tt> data type.
*/
public static void main(String[] args) {
String s = StdIn.readAll().replaceAll("\n", " ").trim();
SuffixArrayX suffix = new SuffixArrayX(s);
SuffixArray suffixReference = new SuffixArray(s);
boolean check = true;
for (int i = 0; check && i < s.length(); i++) {
if (suffixReference.index(i) != suffix.index(i)) {
StdOut.println("suffixReference(" + i + ") = " + suffixReference.index(i));
StdOut.println("suffix(" + i + ") = " + suffix.index(i));
String ith = "\"" + s.substring(suffix.index(i), Math.min(suffix.index(i) + 50, s.length())) + "\"";
String jth = "\"" + s.substring(suffixReference.index(i), Math.min(suffixReference.index(i) + 50, s.length())) + "\"";
StdOut.println(ith);
StdOut.println(jth);
check = false;
}
}
// StdOut.println("rank(" + args[0] + ") = " + suffix.rank(args[0]));
StdOut.println(" i ind lcp rnk select");
StdOut.println("---------------------------");
for (int i = 0; i < s.length(); i++) {
int index = suffix.index(i);
String ith = "\"" + s.substring(index, Math.min(index + 50, s.length())) + "\"";
int rank = suffix.rank(s.substring(index));
assert s.substring(index).equals(suffix.select(i));
if (i == 0) {
StdOut.printf("%3d %3d %3s %3d %s\n", i, index, "-", rank, ith);
}
else {
// int lcp = suffix.lcp(suffix.index(i), suffix.index(i-1));
int lcp = suffix.lcp(i);
StdOut.printf("%3d %3d %3d %3d %s\n", i, index, lcp, rank, ith);
}
}
}
}
/*************************************************************************
* 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.
*************************************************************************/