From 8b387d36b57689ca2ffed86e5022820adab976a9 Mon Sep 17 00:00:00 2001 From: Heng Li Date: Fri, 19 Aug 2011 18:08:48 -0400 Subject: [PATCH] Constructing suffix array for multi-sentinel str. --- ksa.c | 242 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 242 insertions(+) create mode 100644 ksa.c diff --git a/ksa.c b/ksa.c new file mode 100644 index 0000000..18f686d --- /dev/null +++ b/ksa.c @@ -0,0 +1,242 @@ +/* + * Copyright (c) 2008 Yuta Mori All Rights Reserved. + * 2011 Attractive Chaos + * + * Permission is hereby granted, free of charge, to any person + * obtaining a copy of this software and associated documentation + * files (the "Software"), to deal in the Software without + * restriction, including without limitation the rights to use, + * copy, modify, merge, publish, distribute, sublicense, and/or sell + * copies of the Software, and to permit persons to whom the + * Software is furnished to do so, subject to the following + * conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES + * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND + * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT + * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, + * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING + * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR + * OTHER DEALINGS IN THE SOFTWARE. + */ + +/* This is a library for constructing the suffix array for a string containing + * multiple sentinels with sentinels all represented by 0. The last symbol in + * the string must be a sentinel. The library is modified from an early version + * of Yuta Mori's SAIS library, but is slower than the lastest SAIS by about + * 30%, partly due to the recent optimization Yuta has applied and partly due + * to the extra comparisons between sentinels. This is not the first effort in + * supporting multi-sentinel strings, but is probably the easiest to use. */ + +#include + +#ifdef _KSA64 +#include +typedef int64_t saint_t; +#define SAINT_MAX INT64_MAX +#define SAIS_CORE ksa_core64 +#define SAIS_BWT ksa_bwt64 +#define SAIS_MAIN ksa_sa64 +#else +#include +typedef int saint_t; +#define SAINT_MAX INT_MAX +#define SAIS_CORE ksa_core +#define SAIS_BWT ksa_bwt +#define SAIS_MAIN ksa_sa +#endif + +/* T is of type "const unsigned char*". If T[i] is a sentinel, chr(i) takes a negative value */ +#define chr(i) (cs == sizeof(saint_t) ? ((const saint_t *)T)[i] : (T[i]? (saint_t)T[i] : i - SAINT_MAX)) + +/** Count the occurrences of each symbol */ +static void getCounts(const unsigned char *T, saint_t *C, saint_t n, saint_t k, int cs) +{ + saint_t i; + for (i = 0; i < k; ++i) C[i] = 0; + for (i = 0; i < n; ++i) { + saint_t c = chr(i); + ++C[c > 0? c : 0]; + } +} + +/** + * Find the end of each bucket + * + * @param C occurrences computed by getCounts(); input + * @param B start/end of each bucket; output + * @param k size of alphabet + * @param end compute the end of bucket if true; otherwise compute the end + */ +static inline void getBuckets(const saint_t *C, saint_t *B, saint_t k, saint_t end) +{ + saint_t i, sum = 0; + if (end) for (i = 0; i < k; ++i) sum += C[i], B[i] = sum; + else for (i = 0; i < k; ++i) sum += C[i], B[i] = sum - C[i]; +} + +/** Induced sort */ +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) +{ + saint_t *b, i, j; + saint_t c0, c1; + /* left-to-right induced sort (for L-type) */ + if (C == B) getCounts(T, C, n, k, cs); + getBuckets(C, B, k, 0); /* find starts of buckets */ + for (i = 0, b = 0, c1 = -1; i < n; ++i) { + j = SA[i], SA[i] = ~j; + if (0 < j) { /* >0 if j-1 is L-type; <0 if S-type; ==0 undefined */ + --j; + if ((c0 = chr(j)) != c1) { + B[c1 > 0? c1 : 0] = b - SA; + c1 = c0; + b = SA + B[c1 > 0? c1 : 0]; + } + *b++ = (0 < j && chr(j - 1) < c1) ? ~j : j; + } + } + /* right-to-left induced sort (for S-type) */ + if (C == B) getCounts(T, C, n, k, cs); + getBuckets(C, B, k, 1); /* find ends of buckets */ + for (i = n - 1, b = 0, c1 = -1; 0 <= i; --i) { + if (0 < (j = SA[i])) { /* the prefix is S-type */ + --j; + if ((c0 = chr(j)) != c1) { + B[c1 > 0? c1 : 0] = b - SA; + c1 = c0; + b = SA + B[c1 > 0? c1 : 0]; + } + if (c0 > 0) *--b = (j == 0 || chr(j - 1) > c1) ? ~j : j; + } else SA[i] = ~j; /* if L-type, change the sign */ + } +} + +/** + * Recursively construct the suffix array for a string containing multiple + * sentinels. NULL is taken as the sentinel. + * + * @param T NULL terminated input string (there can be multiple NULLs) + * @param SA output suffix array + * @param fs working space available in SA (typically 0 when first called) + * @param n length of T, including the trailing NULL + * @param k size of the alphabet (typically 256 when first called) + * @param cs # bytes per element in T; 1 or sizeof(saint_t) (typically 1 when first called) + * + * @return 0 upon success + */ +int SAIS_CORE(const unsigned char *T, saint_t *SA, saint_t fs, saint_t n, saint_t k, int cs) +{ + saint_t *C, *B; + saint_t i, j, c, m, q, qlen, name; + saint_t c0, c1; + + /* STAGE I: reduce the problem by at least 1/2 sort all the S-substrings */ + if (k <= fs) C = SA + n, B = (k <= fs - k) ? C + k : C; + else { + if ((C = (saint_t*)malloc(k * (1 + (cs == 1)) * sizeof(saint_t))) == NULL) return -2; + B = cs == 1? C + k : C; + } + getCounts(T, C, n, k, cs); + getBuckets(C, B, k, 1); /* find ends of buckets */ + for (i = 0; i < n; ++i) SA[i] = 0; + /* mark L and S (the t array in Nong et al.), and keep the positions of LMS in the buckets */ + for (i = n - 2, c = 1, c1 = chr(n - 1); 0 <= i; --i, c1 = c0) { + if ((c0 = chr(i)) < c1 + c) c = 1; /* c1 = chr(i+1); c==1 if in an S run */ + else if (c) SA[--B[c1 > 0? c1 : 0]] = i + 1, c = 0; + } + induceSA(T, SA, C, B, n, k, cs); + if (fs < k) free(C); + /* pack all the sorted LMS into the first m items of SA + 2*m must be not larger than n (see Nong et al. for the proof) */ + for (i = 0, m = 0; i < n; ++i) { + saint_t p = SA[i]; + if (p == n - 1) SA[m++] = p; + else if (0 < p && chr(p - 1) > (c0 = chr(p))) { + for (j = p + 1; j < n && c0 == (c1 = chr(j)); ++j); + if (j < n && c0 < c1) SA[m++] = p; + } + } + for (i = m; i < n; ++i) SA[i] = 0; /* init the name array buffer */ + /* store the length of all substrings */ + for (i = n - 2, j = n, c = 1, c1 = chr(n - 1); 0 <= i; --i, c1 = c0) { + if ((c0 = chr(i)) < c1 + c) c = 1; /* c1 = chr(i+1) */ + else if (c) SA[m + ((i + 1) >> 1)] = j - i - 1, j = i + 1, c = 0; + } + /* find the lexicographic names of all substrings */ + for (i = 0, name = 0, q = n, qlen = 0; i < m; ++i) { + saint_t p = SA[i], plen = SA[m + (p >> 1)], diff = 1; + if (plen == qlen) { + for (j = 0; j < plen && chr(p + j) == chr(q + j); j++); + if (j == plen) diff = 0; + } + if (diff) ++name, q = p, qlen = plen; + SA[m + (p >> 1)] = name; + } + + /* STAGE II: solve the reduced problem; recurse if names are not yet unique */ + if (name < m) { + saint_t *RA = SA + n + fs - m - 1; + for (i = n - 1, j = m - 1; m <= i; --i) + if (SA[i] != 0) RA[j--] = SA[i]; + RA[m] = 0; // add a sentinel; in the resulting SA, SA[0]==m always stands + if (SAIS_CORE((unsigned char *)RA, SA, fs + n - m * 2 - 2, m + 1, name + 1, sizeof(saint_t)) != 0) return -2; + for (i = n - 2, j = m - 1, c = 1, c1 = chr(n - 1); 0 <= i; --i, c1 = c0) { + if ((c0 = chr(i)) < c1 + c) c = 1; + else if (c) RA[j--] = i + 1, c = 0; /* get p1 */ + } + for (i = 0; i < m; ++i) SA[i] = RA[SA[i+1]]; /* get index */ + } + + /* STAGE III: induce the result for the original problem */ + if (k <= fs) C = SA + n, B = (k <= fs - k) ? C + k : C; + else { + if ((C = (saint_t*)malloc(k * (1 + (cs == 1)) * sizeof(saint_t))) == NULL) return -2; + B = cs == 1? C + k : C; + } + /* put all LMS characters into their buckets */ + getCounts(T, C, n, k, cs); + getBuckets(C, B, k, 1); /* find ends of buckets */ + for (i = m; i < n; ++i) SA[i] = 0; /* init SA[m..n-1] */ + for (i = m - 1; 0 <= i; --i) { + j = SA[i], SA[i] = 0; + c = chr(j); + SA[--B[c > 0? c : 0]] = j; + } + induceSA(T, SA, C, B, n, k, cs); + if (fs < k) free(C); + return 0; +} + +/** + * Construct the suffix array for a NULL terminated string possibly containing + * multiple sentinels (NULLs). + * + * @param T[0..n-1] NULL terminated input string + * @param SA[0..n-1] output suffix array + * @param n length of the given string, including NULL + * @param k size of the alphabet including the sentinel; no more than 256 + * @return 0 upon success + */ +int SAIS_MAIN(const unsigned char *T, saint_t *SA, saint_t n, int k) +{ + if (T == NULL || SA == NULL || T[n - 1] != '\0' || n <= 0) return -1; + if (k < 0 || k > 256) k = 256; + return SAIS_CORE(T, SA, 0, n, (saint_t)k, 1); +} + +int SAIS_BWT(unsigned char *T, saint_t n, int k) +{ + saint_t *SA, i; + int ret; + if ((SA = malloc(n * sizeof(saint_t))) == 0) return -1; + if ((ret = SAIS_MAIN(T, SA, n, k)) != 0) return ret; + for (i = 0; i < n; ++i) + if (SA[i]) SA[i] = T[SA[i] - 1]; // if SA[i]==0, SA[i]=0 + for (i = 0; i < n; ++i) T[i] = SA[i]; + free(SA); + return 0; +}