// http://en.wikipedia.org/wiki/Levenshtein_distance
//
// Although the algorithm is typically described using an m x n
- // array, only two rows are used at a time, so this implementation
- // just keeps two separate vectors for those two rows.
+ // array, only one row plus one element are used at a time, so this
+ // implementation just keeps one vector for the row. To update one entry,
+ // only the entries to the left, top, and top-left are needed. The left
+ // entry is in row[x-1], the top entry is what's in row[x] from the last
+ // iteration, and the top-left entry is stored in previous.
int m = s1.len_;
int n = s2.len_;
- vector<int> previous(n + 1);
- vector<int> current(n + 1);
-
- for (int i = 0; i <= n; ++i)
- previous[i] = i;
+ vector<int> row(n + 1);
+ for (int i = 1; i <= n; ++i)
+ row[i] = i;
for (int y = 1; y <= m; ++y) {
- current[0] = y;
- int best_this_row = current[0];
+ row[0] = y;
+ int best_this_row = row[0];
+ int previous = y - 1;
for (int x = 1; x <= n; ++x) {
+ int old_row = row[x];
if (allow_replacements) {
- current[x] = min(previous[x-1] + (s1.str_[y-1] == s2.str_[x-1] ? 0 : 1),
- min(current[x-1], previous[x])+1);
+ row[x] = min(previous + (s1.str_[y - 1] == s2.str_[x - 1] ? 0 : 1),
+ min(row[x - 1], row[x]) + 1);
}
else {
- if (s1.str_[y-1] == s2.str_[x-1])
- current[x] = previous[x-1];
+ if (s1.str_[y - 1] == s2.str_[x - 1])
+ row[x] = previous;
else
- current[x] = min(current[x-1], previous[x]) + 1;
+ row[x] = min(row[x - 1], row[x]) + 1;
}
- best_this_row = min(best_this_row, current[x]);
+ previous = old_row;
+ best_this_row = min(best_this_row, row[x]);
}
if (max_edit_distance && best_this_row > max_edit_distance)
return max_edit_distance + 1;
-
- current.swap(previous);
}
- return previous[n];
+ return row[n];
}