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// Copyright Vespa.ai. Licensed under the terms of the Apache 2.0 license. See LICENSE in the project root.
// Levenshtein distance algorithm is based off Java implementation from apache commons-text library licensed under the Apache 2.0 license.
#include "levenshtein_distance.h"
#include <cassert>
#include <limits>
#include <vector>
namespace vespalib {
std::optional<uint32_t>
LevenshteinDistance::calculate(std::span<const uint32_t> left, std::span<const uint32_t> right,
uint32_t threshold, bool prefix_match)
{
assert(left.size() <= static_cast<size_t>(INT32_MAX));
assert(right.size() <= static_cast<size_t>(INT32_MAX));
threshold = std::min(threshold, static_cast<uint32_t>(std::numeric_limits<int32_t>::max()));
uint32_t n = left.size();
uint32_t m = right.size();
if (!prefix_match) {
// These optimizations are only valid when matching with target/source string symmetry.
// Correctness of the main matrix calculation loop should not depend on these.
if (n > m) {
return calculate(right, left, threshold, false);
}
// if one string is empty, the edit distance is necessarily the length
// of the other.
if (n == 0) {
return m <= threshold ? std::optional(m) : std::nullopt;
}
if (m == 0) {
return n <= threshold ? std::optional(n) : std::nullopt;
}
// the edit distance cannot be less than the length difference
if (m - n > threshold) {
return std::nullopt;
}
} else {
// A source (right) cannot be transformed into a target prefix (left) if doing
// so would require inserting more than max edits number of characters.
if ((n > m) && (n - m > threshold)) {
return std::nullopt;
}
}
std::vector<uint32_t> p(n+1); // 'previous' cost array, horizontally
std::vector<uint32_t> d(n+1); // cost array, horizontally
const uint32_t boundary = std::min(n, threshold) + 1;
for (uint32_t i = 0; i < boundary; ++i) {
p[i] = i;
}
// these fills ensure that the value above the rightmost entry of our
// stripe will be ignored in following loop iterations
for (uint32_t i = boundary; i < p.size(); ++i) {
p[i] = std::numeric_limits<uint32_t>::max();
}
for (uint32_t i = 0; i < d.size(); ++i) {
d[i] = std::numeric_limits<uint32_t>::max();
}
// iterates through t
uint32_t min_edits = n; // prefix matching: worst-case to transform to target
for (uint32_t j = 1; j <= m; ++j) {
uint32_t rightJ = right[j - 1]; // jth character of right
d[0] = j;
int32_t min = std::max(1, static_cast<int32_t>(j) - static_cast<int32_t>(threshold));
uint32_t max = j > std::numeric_limits<uint32_t>::max() - threshold ?
n : std::min(n, j + threshold);
// ignore entry left of leftmost
if (min > 1) {
assert(static_cast<size_t>(min) <= d.size());
d[min - 1] = std::numeric_limits<uint32_t>::max();
}
uint32_t lowerBound = std::numeric_limits<uint32_t>::max();
for (uint32_t i = min; i <= max; ++i) {
if (left[i - 1] == rightJ) {
// diagonally left and up
d[i] = p[i - 1];
} else {
// 1 + minimum of cell to the left, to the top, diagonally
// left and up
d[i] = 1 + std::min(std::min(d[i - 1], p[i]), p[i - 1]);
}
lowerBound = std::min(lowerBound, d[i]);
}
if (lowerBound > threshold) {
if (!prefix_match) {
return std::nullopt; // Cannot match
} else {
break; // May already have matched via min_edits
}
}
std::swap(p, d);
// For prefix matching:
// By definition, the Levenshtein matrix cell at row `i`, column `j`
// provides the minimum number of edits required to transform a prefix of
// source string S (up to and including length `i`) into a prefix of target
// string T (up to and including length `j`). Since we want to match against
// the entire target (prefix query) string with length `n`, the problem is
// reduced to finding the minimum value of the `n`th column that is `<= k`
// (aggregated here and checked after the loop).
min_edits = std::min(p[n], min_edits);
}
if (prefix_match) {
return ((min_edits <= threshold) ? std::optional<uint32_t>{min_edits} : std::nullopt);
} else if (p[n] <= threshold) {
return {p[n]};
}
return std::nullopt;
}
std::optional<uint32_t>
LevenshteinDistance::calculate(std::span<const uint32_t> left, std::span<const uint32_t> right, uint32_t threshold)
{
return calculate(left, right, threshold, false);
}
} // vespalib
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