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/* qsufsort.c
Copyright 1999, N. Jesper Larsson, all rights reserved.
This file contains an implementation of the algorithm presented in "Faster
Suffix Sorting" by N. Jesper Larsson ( and Kunihiko
Sadakane (
This software may be used freely for any purpose. However, when distributed,
the original source must be clearly stated, and, when the source code is
distributed, the copyright notice must be retained and any alterations in
the code must be clearly marked. No warranty is given regarding the quality
of this software.*/
#include <limits.h>
#include "suffixSort.h"
static integer *I, /* group array, ultimately suffix array.*/
*V, /* inverse array, ultimately inverse of I.*/
r, /* number of symbols aggregated by transform.*/
h; /* length of already-sorted prefixes.*/
#define KEY(p) (V[*(p)+(h)])
#define SWAP(p, q) (tmp=*(p), *(p)=*(q), *(q)=tmp)
#define MED3(a, b, c) (KEY(a)<KEY(b) ? \
(KEY(b)<KEY(c) ? (b) : KEY(a)<KEY(c) ? (c) : (a)) \
: (KEY(b)>KEY(c) ? (b) : KEY(a)>KEY(c) ? (c) : (a)))
/* Subroutine for select_sort_split and sort_split. Sets group numbers for a
group whose lowest position in I is pl and highest position is pm.*/
static void update_group(integer *pl, integer *pm)
integer g;
g=pm-I; /* group number.*/
V[*pl]=g; /* update group number of first position.*/
if (pl==pm)
*pl=-1; /* one element, sorted group.*/
do /* more than one element, unsorted group.*/
V[*++pl]=g; /* update group numbers.*/
while (pl<pm);
/* Quadratic sorting method to use for small subarrays. To be able to update
group numbers consistently, a variant of selection sorting is used.*/
static void select_sort_split(integer *p, integer n) {
integer *pa, *pb, *pi, *pn;
integer f, v, tmp;
pa=p; /* pa is start of group being picked out.*/
pn=p+n-1; /* pn is last position of subarray.*/
while (pa<pn) {
for (pi=pb=pa+1, f=KEY(pa); pi<=pn; ++pi)
if ((v=KEY(pi))<f) {
f=v; /* f is smallest key found.*/
SWAP(pi, pa); /* place smallest element at beginning.*/
pb=pa+1; /* pb is position for elements equal to f.*/
} else if (v==f) { /* if equal to smallest key.*/
SWAP(pi, pb); /* place next to other smallest elements.*/
update_group(pa, pb-1); /* update group values for new group.*/
pa=pb; /* continue sorting rest of the subarray.*/
if (pa==pn) { /* check if last part is single element.*/
*pa=-1; /* sorted group.*/
/* Subroutine for sort_split, algorithm by Bentley & McIlroy.*/
static integer choose_pivot(integer *p, integer n) {
integer *pl, *pm, *pn;
integer s;
pm=p+(n>>1); /* small arrays, middle element.*/
if (n>7) {
if (n>40) { /* big arrays, pseudomedian of 9.*/
pl=MED3(pl, pl+s, pl+s+s);
pm=MED3(pm-s, pm, pm+s);
pn=MED3(pn-s-s, pn-s, pn);
pm=MED3(pl, pm, pn); /* midsize arrays, median of 3.*/
return KEY(pm);
/* Sorting routine called for each unsorted group. Sorts the array of integeregers
(suffix numbers) of length n starting at p. The algorithm is a ternary-split
quicksort taken from Bentley & McIlroy, "Engineering a Sort Function",
Software -- Practice and Experience 23(11), 1249-1265 (November 1993). This
function is based on Program 7.*/
static void sort_split(integer *p, integer n)
integer *pa, *pb, *pc, *pd, *pl, *pm, *pn;
integer f, v, s, t, tmp;
if (n<7) { /* multi-selection sort smallest arrays.*/
select_sort_split(p, n);
v=choose_pivot(p, n);
while (1) { /* split-end partition.*/
while (pb<=pc && (f=KEY(pb))<=v) {
if (f==v) {
SWAP(pa, pb);
while (pc>=pb && (f=KEY(pc))>=v) {
if (f==v) {
SWAP(pc, pd);
if (pb>pc)
SWAP(pb, pc);
if ((s=pa-p)>(t=pb-pa))
for (pl=p, pm=pb-s; s; --s, ++pl, ++pm)
SWAP(pl, pm);
if ((s=pd-pc)>(t=pn-pd-1))
for (pl=pb, pm=pn-s; s; --s, ++pl, ++pm)
SWAP(pl, pm);
if (s>0)
sort_split(p, s);
update_group(p+s, p+n-t-1);
if (t>0)
sort_split(p+n-t, t);
/* Bucketsort for first iteration.
Input: x[0...n-1] holds integeregers in the range 1...k-1, all of which appear
at least once. x[n] is 0. (This is the corresponding output of transform.) k
must be at most n+1. p is array of size n+1 whose contents are disregarded.
Output: x is V and p is I after the initial sorting stage of the refined
suffix sorting algorithm.*/
static void bucketsort(integer *x, integer *p, integer n, integer k)
integer *pi, i, c, d, g;
for (pi=p; pi<p+k; ++pi)
*pi=-1; /* mark linked lists empty.*/
for (i=0; i<=n; ++i) {
x[i]=p[c=x[i]]; /* insert in linked list.*/
for (pi=p+k-1, i=n; pi>=p; --pi) {
d=x[c=*pi]; /* c is position, d is next in list.*/
x[c]=g=i; /* last position equals group number.*/
if (d>=0) { /* if more than one element in group.*/
p[i--]=c; /* p is permutation for the sorted x.*/
do {
d=x[c=d]; /* next in linked list.*/
x[c]=g; /* group number in x.*/
p[i--]=c; /* permutation in p.*/
} while (d>=0);
} else
p[i--]=-1; /* one element, sorted group.*/
/* Transforms the alphabet of x by attempting to aggregate several symbols integero
one, while preserving the suffix order of x. The alphabet may also be
compacted, so that x on output comprises all integeregers of the new alphabet
with no skipped numbers.
Input: x is an array of size n+1 whose first n elements are positive
integeregers in the range l...k-1. p is array of size n+1, used for temporary
storage. q controls aggregation and compaction by defining the maximum value
for any symbol during transformation: q must be at least k-l; if q<=n,
compaction is guaranteed; if k-l>n, compaction is never done; if q is
integer_MAX, the maximum number of symbols are aggregated integero one.
Output: Returns an integereger j in the range 1...q representing the size of the
new alphabet. If j<=n+1, the alphabet is compacted. The global variable r is
set to the number of old symbols grouped integero one. Only x[n] is 0.*/
static integer transform(integer *x, integer *p, integer n, integer k, integer l, integer q)
integer b, c, d, e, i, j, m, s;
integer *pi, *pj;
for (s=0, i=k-l; i; i>>=1)
++s; /* s is number of bits in old symbol.*/
e=integer_MAX>>s; /* e is for overflow checking.*/
for (b=d=r=0; r<n && d<=e && (c=d<<s|(k-l))<=q; ++r) {
b=b<<s|(x[r]-l+1); /* b is start of x in chunk alphabet.*/
d=c; /* d is max symbol in chunk alphabet.*/
m=(1<<(r-1)*s)-1; /* m masks off top old symbol from chunk.*/
x[n]=l-1; /* emulate zero terminator.*/
if (d<=n) { /* if bucketing possible, compact alphabet.*/
for (pi=p; pi<=p+d; ++pi)
*pi=0; /* zero transformation table.*/
for (pi=x+r, c=b; pi<=x+n; ++pi) {
p[c]=1; /* mark used chunk symbol.*/
c=(c&m)<<s|(*pi-l+1); /* shift in next old symbol in chunk.*/
for (i=1; i<r; ++i) { /* handle last r-1 positions.*/
p[c]=1; /* mark used chunk symbol.*/
c=(c&m)<<s; /* shift in next old symbol in chunk.*/
for (pi=p, j=1; pi<=p+d; ++pi)
if (*pi)
*pi=j++; /* j is new alphabet size.*/
for (pi=x, pj=x+r, c=b; pj<=x+n; ++pi, ++pj) {
*pi=p[c]; /* transform to new alphabet.*/
c=(c&m)<<s|(*pj-l+1); /* shift in next old symbol in chunk.*/
while (pi<x+n) { /* handle last r-1 positions.*/
*pi++=p[c]; /* transform to new alphabet.*/
c=(c&m)<<s; /* shift right-end zero in chunk.*/
} else { /* bucketing not possible, don't compact.*/
for (pi=x, pj=x+r, c=b; pj<=x+n; ++pi, ++pj) {
*pi=c; /* transform to new alphabet.*/
c=(c&m)<<s|(*pj-l+1); /* shift in next old symbol in chunk.*/
while (pi<x+n) { /* handle last r-1 positions.*/
*pi++=c; /* transform to new alphabet.*/
c=(c&m)<<s; /* shift right-end zero in chunk.*/
j=d+1; /* new alphabet size.*/
x[n]=0; /* end-of-string symbol is zero.*/
return j; /* return new alphabet size.*/
/* Makes suffix array p of x. x becomes inverse of p. p and x are both of size
n+1. Contents of x[0...n-1] are integeregers in the range l...k-1. Original
contents of x[n] is disregarded, the n-th symbol being regarded as
end-of-string smaller than all other symbols.*/
void suffixSort(integer *x, integer *p, integer n, integer k, integer l,integer preffixSize)
integer *pi, *pk;
integer i, j, s, sl;
V=x; /* set global values.*/
if (n>=k-l) { /* if bucketing possible,*/
j=transform(V, I, n, k, l, n);
bucketsort(V, I, n, j); /* bucketsort on first r positions.*/
} else {
transform(V, I, n, k, l, integer_MAX);
for (i=0; i<=n; ++i)
I[i]=i; /* initialize I with suffix numbers.*/
sort_split(I, n+1); /* quicksort on first r positions.*/
h=r; /* number of symbols aggregated by transform.*/
while (*I>=-n && h<preffixSize) {
pi=I; /* pi is first position of group.*/
sl=0; /* sl is negated length of sorted groups.*/
do {
if ((s=*pi)<0) {
pi-=s; /* skip over sorted group.*/
sl+=s; /* add negated length to sl.*/
} else {
if (sl) {
*(pi+sl)=sl; /* combine sorted groups before pi.*/
pk=I+V[s]+1; /* pk-1 is last position of unsorted group.*/
sort_split(pi, pk-pi);
pi=pk; /* next group.*/
} while (pi<=I+n);
if (sl) /* if the array ends with a sorted group.*/
*(pi+sl)=sl; /* combine sorted groups at end of I.*/
h=2*h; /* double sorted-depth.*/
for (i=0; i<=n; ++i) /* reconstruct suffix array from inverse.*/