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SuffixArray.cc
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SuffixArray.cc
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#include <vector>
#include <algorithm>
#include <string>
#include <cstring>
using namespace std;
// BEGIN
// A prefix-doubling suffix array construction implementation.
#define FOR(v,l,u) for( size_t v = l; v < u; ++v )
typedef vector<size_t> VI;
typedef pair<int, int> II;
#define MAX_N 100010
int RA[MAX_N], tempRA[MAX_N];
int SA[MAX_N], tempSA[MAX_N];
int c[MAX_N];
// uses Radix Sort as a subroutine to sort in O(n)
void CountingSort(int n, int k) {
int i, sum, maxi = max(300, n);
memset(c, 0, sizeof c);
for (i = 0; i < n; i++)
c[i+k < n ? RA[i+k] : 0]++;
for (i = sum = 0; i < maxi; i++) {
int t = c[i]; c[i] = sum; sum += t;
}
for (i = 0; i < n; i++)
tempSA[c[SA[i]+k < n ? RA[SA[i]+k] : 0]++] = SA[i];
for (i = 0; i < n; i++)
SA[i] = tempSA[i];
}
// Construct SA in O(n log n) time. Solves UVa Online Judge "Glass Beads" in .5 seconds
void ConstructSA(string T) {
int i, k, r, n = T.size();
for (i = 0; i < n; i++) RA[i] = T[i];
for (i = 0; i < n; i++) SA[i] = i;
for (k = 1; k < n; k <<= 1) {
CountingSort(n, k);
CountingSort(n, 0);
tempRA[SA[0]] = r = 0;
for (i = 1; i < n; i++)
tempRA[SA[i]] =
(RA[SA[i]] == RA[SA[i-1]] && RA[SA[i]+k] == RA[SA[i-1]+k]) ? r : ++r;
for (i = 0; i < n; i++)
RA[i] = tempRA[i];
if (RA[SA[n-1]] == n-1) break;
}
}
// Given a "string" w, and suffix array SA, compute the array LCP for which
// the suffix starting at SA[i] matches SA[i+1] for exactly LCP[i] characters
// It is assumed that the last character of w is the unique smallest-rank
// character in w. Runs in O(n).
void LongestCommonPrefix( const string &w, VI &LCP ) {
const size_t N = w.size(); VI rk(N);
FOR(i,0,N) rk[ SA[i] ] = i;
LCP = VI(N-1); size_t k = 0;
FOR(i,0,N) {
if( rk[i] == N-1 ) continue;
size_t j = SA[ rk[i]+1 ];
while( w[ i+k ] == w[ j+k ] ) ++k;
LCP[ rk[i] ] = k;
if( k > 0 ) --k;
}
}
// Finds the smallest and largest i such that the prefix of suffix SA[i] matches
// the pattern string P. Returns (-1, -1) if P is not found in T. Runs in O(m log n).
II StringMatching(const string &T, const string P) {
int n = T.size(), m = P.size();
int lo = 0, hi = n-1, mid = lo;
while (lo < hi) {
mid = (lo + hi) / 2;
int res = T.compare(SA[mid], m, P);
if (res >= 0) hi = mid;
else lo = mid+1;
}
if (T.compare(SA[lo], m, P) != 0) return II(-1, -1);
II ans; ans.first = lo;
lo = 0; hi = n-1; mid = lo;
while (lo < hi) {
mid = (lo + hi) / 2;
int res = T.compare(SA[mid], m, P);
if (res > 0) hi = mid;
else lo = mid+1;
}
if (T.compare(SA[hi], m, P)) hi--;
ans.second = hi;
return ans;
}
// END
#include <iostream>
bool cmp_suffixes( string arry, size_t a, size_t b ) {
if( a == b ) return false;
while( max(a,b) < arry.size() && arry[a] == arry[b] ) { ++a; ++b; }
if( a == arry.size() ) return true;
if( b == arry.size() ) return false;
return arry[a] < arry[b];
}
void test_suffix_array_correct() {
cerr << "test suffix array correctness" << endl;
{
string s = "1213112542";
ConstructSA(s);
FOR(i,0,9) {
if( !cmp_suffixes(s,SA[i],SA[i+1]) ) {
cerr << "suffixes " << SA[i] << " and " << SA[i+1] << " out of order." << endl;
}
}
VI lcp; LongestCommonPrefix( s, lcp );
VI rk(s.size()); FOR(i,0,s.size()) rk[ SA[i] ] = i;
if( lcp[ rk[0] ] != 2 ) {
cerr << "suffixes 0.. and " << SA[rk[0]+1] << ".. have bad lcp (exp. 2, got " << lcp[rk[0]] << "):" << endl;
cerr << "\t"; FOR(i,0,s.size()) cerr << s[i]; cerr << endl;
cerr << "\t"; FOR(i,SA[rk[0]+1],s.size()) cerr << s[i]; cerr << endl;
}
if( lcp[ rk[8] ] != 0 ) {
cerr << "suffixes 8.. and " << SA[rk[8]+1] << ".. have bad lcp (exp. 0, got " << lcp[rk[8]] << "):" << endl;
cerr << "\t"; FOR(i,8,s.size()) cerr << s[i]; cerr << endl;
cerr << "\t"; FOR(i,SA[rk[8]+1],s.size()) cerr << s[i]; cerr << endl;
}
string T = "GATAGACA$";
ConstructSA(T);
II ans = StringMatching(T, "GA");
if (ans.first != 6 || ans.second != 7) {
cerr << "string matching not finding match" << endl;
}
II ans2 = StringMatching(T, "asdf");
if (ans2.first != -1 || ans2.second != -1) {
cerr << "string match returned false positive on query" << endl;
}
}
}
int main() {
test_suffix_array_correct();
return 0;
}