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Constructing suffix array for multi-sentinel str.
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Heng Li
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ksa.c
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242
ksa.c
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/*
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* Copyright (c) 2008 Yuta Mori All Rights Reserved.
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* 2011 Attractive Chaos <attractor@live.co.uk>
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*
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* Permission is hereby granted, free of charge, to any person
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* obtaining a copy of this software and associated documentation
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* files (the "Software"), to deal in the Software without
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* restriction, including without limitation the rights to use,
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* copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the
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* Software is furnished to do so, subject to the following
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* conditions:
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*
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* The above copyright notice and this permission notice shall be
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* included in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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* OTHER DEALINGS IN THE SOFTWARE.
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*/
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/* This is a library for constructing the suffix array for a string containing
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* multiple sentinels with sentinels all represented by 0. The last symbol in
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* the string must be a sentinel. The library is modified from an early version
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* of Yuta Mori's SAIS library, but is slower than the lastest SAIS by about
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* 30%, partly due to the recent optimization Yuta has applied and partly due
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* to the extra comparisons between sentinels. This is not the first effort in
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* supporting multi-sentinel strings, but is probably the easiest to use. */
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#include <stdlib.h>
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#ifdef _KSA64
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#include <stdint.h>
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typedef int64_t saint_t;
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#define SAINT_MAX INT64_MAX
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#define SAIS_CORE ksa_core64
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#define SAIS_BWT ksa_bwt64
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#define SAIS_MAIN ksa_sa64
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#else
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#include <limits.h>
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typedef int saint_t;
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#define SAINT_MAX INT_MAX
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#define SAIS_CORE ksa_core
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#define SAIS_BWT ksa_bwt
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#define SAIS_MAIN ksa_sa
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#endif
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/* T is of type "const unsigned char*". If T[i] is a sentinel, chr(i) takes a negative value */
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#define chr(i) (cs == sizeof(saint_t) ? ((const saint_t *)T)[i] : (T[i]? (saint_t)T[i] : i - SAINT_MAX))
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/** Count the occurrences of each symbol */
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static void getCounts(const unsigned char *T, saint_t *C, saint_t n, saint_t k, int cs)
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{
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saint_t i;
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for (i = 0; i < k; ++i) C[i] = 0;
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for (i = 0; i < n; ++i) {
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saint_t c = chr(i);
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++C[c > 0? c : 0];
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}
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}
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/**
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* Find the end of each bucket
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*
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* @param C occurrences computed by getCounts(); input
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* @param B start/end of each bucket; output
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* @param k size of alphabet
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* @param end compute the end of bucket if true; otherwise compute the end
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*/
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static inline void getBuckets(const saint_t *C, saint_t *B, saint_t k, saint_t end)
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{
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saint_t i, sum = 0;
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if (end) for (i = 0; i < k; ++i) sum += C[i], B[i] = sum;
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else for (i = 0; i < k; ++i) sum += C[i], B[i] = sum - C[i];
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}
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/** Induced sort */
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static void induceSA(const unsigned char *T, saint_t *SA, saint_t *C, saint_t *B, saint_t n, saint_t k, saint_t cs)
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{
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saint_t *b, i, j;
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saint_t c0, c1;
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/* left-to-right induced sort (for L-type) */
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if (C == B) getCounts(T, C, n, k, cs);
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getBuckets(C, B, k, 0); /* find starts of buckets */
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for (i = 0, b = 0, c1 = -1; i < n; ++i) {
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j = SA[i], SA[i] = ~j;
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if (0 < j) { /* >0 if j-1 is L-type; <0 if S-type; ==0 undefined */
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--j;
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if ((c0 = chr(j)) != c1) {
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B[c1 > 0? c1 : 0] = b - SA;
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c1 = c0;
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b = SA + B[c1 > 0? c1 : 0];
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}
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*b++ = (0 < j && chr(j - 1) < c1) ? ~j : j;
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}
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}
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/* right-to-left induced sort (for S-type) */
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if (C == B) getCounts(T, C, n, k, cs);
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getBuckets(C, B, k, 1); /* find ends of buckets */
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for (i = n - 1, b = 0, c1 = -1; 0 <= i; --i) {
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if (0 < (j = SA[i])) { /* the prefix is S-type */
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--j;
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if ((c0 = chr(j)) != c1) {
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B[c1 > 0? c1 : 0] = b - SA;
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c1 = c0;
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b = SA + B[c1 > 0? c1 : 0];
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}
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if (c0 > 0) *--b = (j == 0 || chr(j - 1) > c1) ? ~j : j;
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} else SA[i] = ~j; /* if L-type, change the sign */
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}
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}
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/**
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* Recursively construct the suffix array for a string containing multiple
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* sentinels. NULL is taken as the sentinel.
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*
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* @param T NULL terminated input string (there can be multiple NULLs)
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* @param SA output suffix array
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* @param fs working space available in SA (typically 0 when first called)
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* @param n length of T, including the trailing NULL
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* @param k size of the alphabet (typically 256 when first called)
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* @param cs # bytes per element in T; 1 or sizeof(saint_t) (typically 1 when first called)
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*
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* @return 0 upon success
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*/
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int SAIS_CORE(const unsigned char *T, saint_t *SA, saint_t fs, saint_t n, saint_t k, int cs)
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{
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saint_t *C, *B;
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saint_t i, j, c, m, q, qlen, name;
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saint_t c0, c1;
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/* STAGE I: reduce the problem by at least 1/2 sort all the S-substrings */
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if (k <= fs) C = SA + n, B = (k <= fs - k) ? C + k : C;
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else {
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if ((C = (saint_t*)malloc(k * (1 + (cs == 1)) * sizeof(saint_t))) == NULL) return -2;
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B = cs == 1? C + k : C;
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}
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getCounts(T, C, n, k, cs);
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getBuckets(C, B, k, 1); /* find ends of buckets */
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for (i = 0; i < n; ++i) SA[i] = 0;
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/* mark L and S (the t array in Nong et al.), and keep the positions of LMS in the buckets */
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for (i = n - 2, c = 1, c1 = chr(n - 1); 0 <= i; --i, c1 = c0) {
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if ((c0 = chr(i)) < c1 + c) c = 1; /* c1 = chr(i+1); c==1 if in an S run */
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else if (c) SA[--B[c1 > 0? c1 : 0]] = i + 1, c = 0;
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}
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induceSA(T, SA, C, B, n, k, cs);
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if (fs < k) free(C);
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/* pack all the sorted LMS into the first m items of SA
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2*m must be not larger than n (see Nong et al. for the proof) */
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for (i = 0, m = 0; i < n; ++i) {
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saint_t p = SA[i];
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if (p == n - 1) SA[m++] = p;
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else if (0 < p && chr(p - 1) > (c0 = chr(p))) {
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for (j = p + 1; j < n && c0 == (c1 = chr(j)); ++j);
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if (j < n && c0 < c1) SA[m++] = p;
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}
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}
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for (i = m; i < n; ++i) SA[i] = 0; /* init the name array buffer */
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/* store the length of all substrings */
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for (i = n - 2, j = n, c = 1, c1 = chr(n - 1); 0 <= i; --i, c1 = c0) {
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if ((c0 = chr(i)) < c1 + c) c = 1; /* c1 = chr(i+1) */
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else if (c) SA[m + ((i + 1) >> 1)] = j - i - 1, j = i + 1, c = 0;
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}
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/* find the lexicographic names of all substrings */
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for (i = 0, name = 0, q = n, qlen = 0; i < m; ++i) {
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saint_t p = SA[i], plen = SA[m + (p >> 1)], diff = 1;
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if (plen == qlen) {
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for (j = 0; j < plen && chr(p + j) == chr(q + j); j++);
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if (j == plen) diff = 0;
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}
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if (diff) ++name, q = p, qlen = plen;
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SA[m + (p >> 1)] = name;
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}
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/* STAGE II: solve the reduced problem; recurse if names are not yet unique */
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if (name < m) {
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saint_t *RA = SA + n + fs - m - 1;
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for (i = n - 1, j = m - 1; m <= i; --i)
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if (SA[i] != 0) RA[j--] = SA[i];
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RA[m] = 0; // add a sentinel; in the resulting SA, SA[0]==m always stands
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if (SAIS_CORE((unsigned char *)RA, SA, fs + n - m * 2 - 2, m + 1, name + 1, sizeof(saint_t)) != 0) return -2;
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for (i = n - 2, j = m - 1, c = 1, c1 = chr(n - 1); 0 <= i; --i, c1 = c0) {
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if ((c0 = chr(i)) < c1 + c) c = 1;
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else if (c) RA[j--] = i + 1, c = 0; /* get p1 */
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}
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for (i = 0; i < m; ++i) SA[i] = RA[SA[i+1]]; /* get index */
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}
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/* STAGE III: induce the result for the original problem */
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if (k <= fs) C = SA + n, B = (k <= fs - k) ? C + k : C;
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else {
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if ((C = (saint_t*)malloc(k * (1 + (cs == 1)) * sizeof(saint_t))) == NULL) return -2;
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B = cs == 1? C + k : C;
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}
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/* put all LMS characters into their buckets */
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getCounts(T, C, n, k, cs);
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getBuckets(C, B, k, 1); /* find ends of buckets */
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for (i = m; i < n; ++i) SA[i] = 0; /* init SA[m..n-1] */
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for (i = m - 1; 0 <= i; --i) {
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j = SA[i], SA[i] = 0;
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c = chr(j);
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SA[--B[c > 0? c : 0]] = j;
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}
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induceSA(T, SA, C, B, n, k, cs);
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if (fs < k) free(C);
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return 0;
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}
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/**
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* Construct the suffix array for a NULL terminated string possibly containing
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* multiple sentinels (NULLs).
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*
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* @param T[0..n-1] NULL terminated input string
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* @param SA[0..n-1] output suffix array
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* @param n length of the given string, including NULL
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* @param k size of the alphabet including the sentinel; no more than 256
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* @return 0 upon success
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*/
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int SAIS_MAIN(const unsigned char *T, saint_t *SA, saint_t n, int k)
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{
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if (T == NULL || SA == NULL || T[n - 1] != '\0' || n <= 0) return -1;
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if (k < 0 || k > 256) k = 256;
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return SAIS_CORE(T, SA, 0, n, (saint_t)k, 1);
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}
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int SAIS_BWT(unsigned char *T, saint_t n, int k)
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{
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saint_t *SA, i;
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int ret;
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if ((SA = malloc(n * sizeof(saint_t))) == 0) return -1;
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if ((ret = SAIS_MAIN(T, SA, n, k)) != 0) return ret;
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for (i = 0; i < n; ++i)
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if (SA[i]) SA[i] = T[SA[i] - 1]; // if SA[i]==0, SA[i]=0
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for (i = 0; i < n; ++i) T[i] = SA[i];
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free(SA);
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return 0;
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}
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