boolean isEqualLMSSubstring(long pos1, long pos2) {
boolean prevLS = SType;
long offset = 0;
for (; offset < N; ++offset) {
long p1 = (pos1 + offset) % N;
long p2 = (pos2 + offset) % N;
if (T.lookup(p1) == T.lookup(p2) && LS.get(p1) == LS.get(p2)) {
if (prevLS == LType && LS.get(p1) == SType) return true; // equal LMS substring
prevLS = LS.get(p1);
continue;
} else return false;
}
return false;
}
private void induceSA(LSeq SA) {
long[] cursorInBucket = Arrays.copyOf(bucketEnd, bucketEnd.length);
// induce left
for (long i = 0; i < N; ++i) {
long si = SA.lookup(i);
if (si == N) continue;
si = (si - 1 + N) % N;
if (LS.get(si) == LType) SA.set(cursorInBucket[(int) T.lookup(si) - 1]++, si);
}
// induce right
System.arraycopy(bucketEnd, 0, cursorInBucket, 0, bucketEnd.length);
for (long i = N - 1; i >= 0; --i) {
long si = SA.lookup(i);
if (si == N) continue;
si = (si - 1 + N) % N;
if (LS.get(si) == SType) SA.set(--cursorInBucket[(int) T.lookup(si)], si);
}
}
boolean isLMS(long pos) {
return LS.get(pos % N) == SType && LS.get((pos - 1 + N) % N) == LType;
}
public void SAIS(LSeq SA) {
StopWatch timer = new StopWatch();
_logger.info("SAIS: N=" + SA.textSize());
// Determin T[N-1]'s LS-type
// T[i] is SType if T[i,_) < T[i+1,_)
// T[i] is LType if T[i,_) > T[i+1,_)
{
long i = 0;
for (; i < N; ++i) {
long x = T.lookup((N + i - 1) % N);
long y = T.lookup((N + i) % N);
if (x == y) continue;
if (x < y) {
LS.set(N - 1, SType);
break;
} else {
LS.set(N - 1, LType);
break;
}
}
if (i == N) {
// When T = AAAA... , etc.
LS.set(N - 1, LType);
}
}
// T[i] is SType if T[i] < T[i+1] or T[i] = T[i+1] and T[i+1] is S-type
// T[i] is LType if T[i] > T[i+1] or T[i] = T[i+1] and T[i+1] is L-type
// Set the LS type of each character
for (long i = N - 1; i > 0; --i) {
long x = T.lookup(i);
long y = T.lookup(i - 1);
if (x < y) LS.set(i - 1, LType);
else if (x > y) LS.set(i - 1, SType);
else LS.set(i - 1, LS.get(i));
}
// Initialize the buckets.
// A bucket is a container of the suffixes sharing the same first character
{
_logger.trace("Initialize the buckets");
Arrays.fill(bucketEnd, 0);
// Compute the size of each bucket
for (long i = 0; i < N; ++i) {
++bucketEnd[(int) T.lookup(i)];
}
// Accumulate the character counts. The bucketStart holds the pointers to beginning of the
// buckets in SA
for (int i = 1; i < bucketEnd.length; ++i) {
bucketEnd[i] += bucketEnd[i - 1];
}
_logger.trace("Done.");
}
// initialize the suffix array
for (long i = 0; i < N; ++i) SA.set(i, N);
// Step 1: reduce the problem by at least 1/2
// Sort all the S-substrings
// Find LMS characters
long[] cursorInBucket = Arrays.copyOf(bucketEnd, bucketEnd.length);
for (long i = 0; i < N; ++i) {
if (isLMS(i)) SA.set(--cursorInBucket[(int) T.lookup(i)], i);
}
// Induced sorting LMS prefixes
{
_logger.trace(String.format("[N=%,d] induceSA", SA.textSize()));
induceSA(SA);
_logger.trace("Done.");
}
int numLMS = 0;
// Compact all the sorted substrings into the first M items of SA
// 2*M must be not larger than N
for (long i = 0; i < N; ++i) {
long si = SA.lookup(i);
if (si != N && isLMS(si)) SA.set(numLMS++, si);
}
// Initialize the name array buffer
for (long i = numLMS; i < N; ++i) SA.set(i, N);
// Find the lexicographic names of the LMS substrings
_logger.trace("Sorting LMS substrings: N=" + SA.textSize());
int name = 1;
SA.set(numLMS + (SA.lookup(0) / 2), name++);
for (long i = 1; i < numLMS; ++i) {
final long prev = SA.lookup(i - 1);
final long current = SA.lookup(i);
if (!isEqualLMSSubstring(prev, current)) {
name++;
}
SA.set(numLMS + (current / 2), name - 1);
}
for (long i = N - 1, j = N - 1; i >= numLMS; --i) {
if (SA.lookup(i) != N) SA.set(j--, SA.lookup(i) - 1);
}
// Step 2: solve the reduced problem
// Create SA1, a view of SA[0, numLMS-1]
_logger.trace("Solving the reduced problem: N=" + SA.textSize());
LSeq SA1 = new ArrayWrap(SA, 0, numLMS);
LSeq T1 = new ArrayWrap(SA, N - numLMS, numLMS);
if (name - 1 != numLMS) {
new CyclicSAIS(T1, name - 1).SAIS(SA1);
} else {
// When all LMS substrings have unique names
for (long i = 0; i < numLMS; i++) SA1.set(T1.lookup(i), i);
}
// Step 3: Induce SA from SA1
// Construct P1 using T1 buffer
for (long i = 0, j = 0; i < N; ++i) {
if (isLMS(i)) T1.set(j++, i); //
}
// Translate short name into the original index at T
// SA1 now holds the LMS-substring indexes
for (long i = 0; i < numLMS; ++i) {
SA1.set(i, T1.lookup(SA1.lookup(i)));
}
// Step 3-1: Put all the items in SA1 into corresponding S-type buckets of SA
// Clear SA[N1 .. N-1]
for (long i = numLMS; i < N; ++i) {
SA.set(i, N);
}
// Put SA1 contents into S-type buckets of SA
System.arraycopy(bucketEnd, 0, cursorInBucket, 0, bucketEnd.length);
for (int i = numLMS - 1; i >= 0; --i) {
long si = SA1.lookup(i);
SA.set(i, N);
long index = --cursorInBucket[(int) T.lookup(si)];
SA.set(index, si);
}
// SA.set(0, T.textSize() - 1);
// Step 3-2, 3-3
_logger.trace("Inducing SA from SA1: N=" + SA.textSize());
induceSA(SA);
_logger.info(String.format("done. %.2f sec.", timer.getElapsedTime()));
}