ali-ghanbari commented on a change in pull request #233:
URL: https://github.com/apache/commons-text/pull/233#discussion_r674469665
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File path:
src/main/java/org/apache/commons/text/similarity/LongestCommonSubsequence.java
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@@ -120,24 +170,72 @@ public CharSequence longestCommonSubsequence(final
CharSequence left, final Char
if (left == null || right == null) {
throw new IllegalArgumentException("Inputs must not be null");
}
- final StringBuilder longestCommonSubstringArray = new
StringBuilder(Math.max(left.length(), right.length()));
- final int[][] lcsLengthArray = longestCommonSubstringLengthArray(left,
right);
- int i = left.length() - 1;
- int j = right.length() - 1;
- int k = lcsLengthArray[left.length()][right.length()] - 1;
- while (k >= 0) {
- if (left.charAt(i) == right.charAt(j)) {
- longestCommonSubstringArray.append(left.charAt(i));
- i = i - 1;
- j = j - 1;
- k = k - 1;
- } else if (lcsLengthArray[i + 1][j] < lcsLengthArray[i][j + 1]) {
- i = i - 1;
- } else {
- j = j - 1;
- }
+ // Find lengths of two strings
+ final int leftSz = left.length();
+ final int rightSz = right.length();
+
+ // Check if we can save even more space
+ if (leftSz < rightSz) {
+ return algorithmC(right, rightSz, left, leftSz);
}
- return longestCommonSubstringArray.reverse().toString();
+ return algorithmC(left, leftSz, right, rightSz);
+ }
+
+ /**
+ * An implementation of "ALG C" from Hirschberg's paper <a
href="https://dl.acm.org/doi/10.1145/360825.360861";>A linear space algorithm
for computing maximal common subsequences</a>.
+ * Assuming the sequence <code>left</code> is of size <code>m</code> and
the sequence <code>right</code> is of size <code>n</code>,
+ * this method returns Longest Common Subsequence (LCS) the two sequences.
+ * As per the paper, this method runs in O(m * n) time and O(m + n) space.
+ *
+ * @param left Left sequence
+ * @param m Length of left sequence
+ * @param right Right sequence
+ * @param n Length of right sequence
+ * @return LCS of <code>left</code> and <code>right</code>
+ */
+ static CharSequence algorithmC(final CharSequence left, final int m,
Review comment:
> ... Algorithm A and Algorithm B are very similar, but I think A
requires O(mn) time and O(mn) space. While Algorithm B requires O(mn) time and
O(m+n) space.
Right, in terms of time complexity, yes, they all are quadratic (O(mn), to
be precise) in the size of input strings.
Algorithm B has O(m+n) space complexity, while Algorithm A has O(mn) space
complexity (it returns an entire DP array; just like the method that we marked
as deprecated).
> And, Algorithm C is the third one in that paper, with O(mn) time...
Thanks for bring this up @kinow. The recurrence does not seem to be easy to
solve for me; I need some time to think about this (end of work day and this
needs a fresh mind:).
Looking at the space analysis proof given in the paper, it looks like the
paper makes assumptions about the storage of substrings. (please correct me if
I am wrong)
Thanks!
> Past midnight here, long time with ...
Thanks @kinow your constructive comments and your hard work! 👍 🥇
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