GATE CSE
First time here? Checkout the FAQ!
x
0 votes
11 views

An automatic spelling checker works as follows. Given a word $w$, first check if $w$ is found in the dictionary. If $w$ is not in the dictionary, compute a dictionary entry that is close to $w$. For instance if the user types $\mathsf{ocurrance}$, the spelling checker should suggest $\mathsf{occurence}$, which belongs to the dictionary. Similarity between words such as $\mathsf{occurrence}$ and $\mathsf{occurrance}$ is quantified in terms of $alignment$.

An alignment between two strings $w1$ and $w2$ (over the alphabet $\{ \mathsf{a, b, c, ...., z} \}$) is obtained by inserting hyphens in the two strings such that the modified strings $align$ (i.e.,the modified strings are of equal length, and at each position, either both strings have the same letter or one of the strings has a hyphen).

here are three examples of alignments. The first is between $\mathsf{ocurrance}$ and $\mathsf{occurrence}$ and the second and third are between $\mathsf{ctatg}$ and $\mathsf{ttaagc}$.

(1)

oc-urr-ance

occurre-nce

(2)

ct-at-g-

-tta-agc

(3)

ctat---g-

---ttaagc

A $mismatch$ in an alignment is a position where one of modified strings has  a hyphen and the other does not. There are three mismatches in the first alignment given above, five mismatches in the second, and seven mismatches in the third.

use dynamic programming to give an efficient algorithm that takes two strings $x$ and $y$ (over teh alphabet $\{ \mathsf{a, b, c, ... , z} \}$ as its input, and computes the minimum number of mismatches among all alignments of $x$ and $y$. What is the running time of your algorithm (in terms of the lengths of $x$ and $y$)?

asked in Others by Veteran (76.3k points)   | 11 views

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.


Top Users Apr 2017
  1. akash.dinkar12

    3660 Points

  2. Divya Bharti

    2576 Points

  3. Deepthi_ts

    2040 Points

  4. rude

    1966 Points

  5. Tesla!

    1768 Points

  6. Debashish Deka

    1614 Points

  7. Shubham Sharma 2

    1610 Points

  8. Arunav Khare

    1464 Points

  9. Arjun

    1440 Points

  10. Kapil

    1426 Points

Monthly Topper: Rs. 500 gift card

22,084 questions
28,059 answers
63,275 comments
24,158 users