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#include "leditdist.hpp"
// The basic algorithm is as follows:
//
// Let A[n] represent the nth character of string n
// A[n..] represent the substring of A starting at n
// if n > length of A then it is considered an empty string
//
// edit_distance(A,B,limit) = ed(A,B,0)
// where ed(A,B,d) = d if A & B is empty.
// = infinity if d > limit
// = ed(A[2..],B[2..], d) if A[1] == B[1]
// = min ( ed(A[2..],B[2..], d+1),
// ed(A, B[2..], d+1),
// ed(A[2..],B, d+1) ) otherwise
//
// However, the code below:
// 1) Also allows for swaps
// 2) Allow weights to be attached to each edit
// 3) Is not recursive, it uses a loop when it is tail recursion
// and a small stack otherwise. The stack will NEVER be larger
// then 2 * limit.
// 4) Is extremely optimized
#define check_rest(a,b,s) \
a0 = a; b0 = b; \
while (*a0 == *b0) { \
if (*a0 == '\0') { \
if (s < min) min = s; \
break; \
} \
++a0; ++b0; \
}
namespace aspeller {
int limit_edit_distance(const char * a, const char * b,
int limit, const EditDistanceWeights & w)
{
limit = limit*w.max;
static const int size = 10;
struct Edit {
const char * a;
const char * b;
int score;
};
Edit begin[size];
Edit * i = begin;
const char * a0;
const char * b0;
int score = 0;
int min = LARGE_NUM;
while (true) {
while (*a == *b) {
if (*a == '\0') {
if (score < min) min = score;
goto FINISH;
}
++a; ++b;
}
if (*a == '\0') {
do {
score += w.del2;
if (score >= min) goto FINISH;
++b;
} while (*b != '\0');
min = score;
} else if (*b == '\0') {
do {
score += w.del1;
if (score >= min) goto FINISH;
++a;
} while (*a != '\0');
min = score;
} else {
if (score + w.max <= limit) {
if (limit*w.min <= w.max*(w.min+score)) {
// if floor(score/max)=limit/max-1 then this edit is only good
// if it makes the rest of the string match. So check if
// the rest of the string matches to avoid the overhead of
// pushing it on then off the stack
// delete a character from a
check_rest(a+1,b,score + w.del1);
// delete a character from b
check_rest(a,b+1,score + w.del2);
if (*a == *(b+1) && *b == *(a+1)) {
// swap two characters
check_rest(a+2,b+2, score + w.swap);
} else {
// substitute one character for another which is the same
// thing as deleting a character from both a & b
check_rest(a+1,b+1, score + w.sub);
}
} else {
// delete a character from a
i->a = a + 1;
i->b = b;
i->score = score + w.del1;
++i;
// delete a character from b
i->a = a;
i->b = b + 1;
i->score = score + w.del2;
++i;
// If two characters can be swapped and make a match
// then the substitution is pointless.
// Also, there is no need to push this on the stack as
// it is going to be imminently removed.
if (*a == *(b+1) && *b == *(a+1)) {
// swap two characters
a = a + 2;
b = b + 2;
score += w.swap;
continue;
} else {
// substitute one character for another which is the same
// thing as deleting a character from both a & b
a = a + 1;
b = b + 1;
score += w.sub;
continue;
}
}
}
}
FINISH:
if (i == begin) return min;
--i;
a = i->a;
b = i->b;
score = i->score;
}
}
#undef check_rest
#define check_rest(a,b,w) \
a0 = a; b0 = b; \
while(*a0 == *b0) { \
if (*a0 == '\0') { \
if (w < min) min = w; \
break; \
} \
++a0; \
++b0; \
} \
if (amax < a0) amax = a0;
#define check2(a,b,w) \
aa = a; bb = b; \
while(*aa == *bb) { \
if (*aa == '\0') { \
if (amax < aa) amax = aa; \
if (w < min) min = w; \
break; \
} \
++aa; ++bb; \
} \
if (*aa == '\0') { \
if (amax < aa) amax = aa; \
if (*bb == '\0') {} \
else if (*(bb+1) == '\0' && w+ws.del2 < min) min = w+ws.del2; \
} else if (*bb == '\0') { \
++aa; \
if (amax < aa) amax = aa; \
if (*aa == '\0' && w+ws.del1 < min) min = w+ws.del1; \
} else { \
check_rest(aa+1,bb,w+ws.del1); \
check_rest(aa,bb+1,w+ws.del2); \
if (*aa == *(bb+1) && *bb == *(aa+1)) { \
check_rest(aa+2,bb+2,w+ws.swap); \
} else { \
check_rest(aa+1,bb+1,w+ws.sub); \
} \
}
EditDist limit1_edit_distance(const char * a, const char * b,
const EditDistanceWeights & ws)
{
int min = LARGE_NUM;
const char * a0;
const char * b0;
const char * amax = a;
while(*a == *b) {
if (*a == '\0')
return EditDist(0, a);
++a; ++b;
}
if (*a == '\0') {
++b;
if (*b == '\0') return EditDist(ws.del2, a);
return EditDist(LARGE_NUM, a);
} else if (*b == '\0') {
++a;
if (*a == '\0') return EditDist(ws.del1, a);
return EditDist(LARGE_NUM, a);
} else {
// delete a character from a
check_rest(a+1,b,ws.del1);
// delete a character from b
check_rest(a,b+1,ws.del2);
if (*a == *(b+1) && *b == *(a+1)) {
// swap two characters
check_rest(a+2,b+2,ws.swap);
} else {
// substitute one character for another which is the same
// thing as deleting a character from both a & b
check_rest(a+1,b+1,ws.sub);
}
}
return EditDist(min, amax);
}
EditDist limit2_edit_distance(const char * a, const char * b,
const EditDistanceWeights & ws)
{
int min = LARGE_NUM;
const char * a0;
const char * b0;
const char * aa;
const char * bb;
const char * amax = a;
while(*a == *b) {
if (*a == '\0')
return EditDist(0, a);
++a; ++b;
}
if (*a == '\0') {
++b;
if (*b == '\0') return EditDist(ws.del2, a);
++b;
if (*b == '\0') return EditDist(2*ws.del2, a);
return EditDist(LARGE_NUM, a);
} else if (*b == '\0') {
++a;
if (*a == '\0') return EditDist(ws.del1, a);
++a;
if (*a == '\0') return EditDist(2*ws.del1, a);
return EditDist(LARGE_NUM, a);
} else {
// delete a character from a
check2(a+1,b,ws.del1);
// delete a character from b
check2(a,b+1,ws.del2);
if (*a == *(b+1) && *b == *(a+1)) {
// swap two characters
check2(a+2,b+2,ws.swap);
} else {
// substitute one character for another which is the same
// thing as deleting a character from both a & b
check2(a+1,b+1,ws.sub);
}
}
return EditDist(min, amax);
}
}
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