Edit Distance Problem

Source: http://people.csail.mit.edu/bdean/6.046/dp/

Problem: 
Given two text strings A of length n and B of length m, you want to transform A into B with a minimum number of operations of the following types: delete a character from A, insert a character into A, or change some character in A into a new character. The minimal number of such operations required to transform A into B is called the edit distance between A and B.

Given two strings A and B, what is the path from A to B with minimum edit distance?


Comments

  1. Apurva1:14 AM, July 26, 2013

    I think it will be Levenshtein distance if the distance for insertion is same for all character pairs[replacing A with B has same cost as replacing A with G] else Dynamic Time Warp Distance.

    ReplyDelete
  2. Goyal10:51 AM, July 26, 2013

    This comment has been removed by the author.

    ReplyDelete
  3. nick4:34 PM, July 27, 2013

    Initial Condition: Edit distance for m = 0 , n= 0 is 0 ie (0,0) = 0
    for each (i,j) where i belongs to m and j belongs to n
    check = min { i.(i - 1 , j- 1) + cost of replacement of ith and jth element(here if a[i] == b[j] then the cost will be zero)
    ii.(i,j-1) + cost of insertion of the jth element
    iii.(i-1,j) + cost of the insertion of the ith element
    }
    This problem if solved recursively will take exponential time however can be done in O(m*n) by using dynamic programming with additional O(m*n) spaces.

    eg: APPLE and CAPE
    Considering the cost of addition, deletion or replacement is each 1.
    A P P L E
    C 1 2 3 4 5
    A 1 2 3 4 5
    P 2 1 2 3 4
    E 3 3 2 3 3

    Space Optimization:
    The problem can be further optimized for space by using only the last array. Thus, only additional space required will be 2* min(m,n).

    ReplyDelete

Post a Comment

Popular posts from this blog

Fraction Brainteaser

Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20 out of 28 Geometry questions.  In total, Siddhant scores 25 out of 34.  Vaibhav writes another Maths test and correctly answers 20 out of 25 Arithmetic questions and 6 out of 9 Geometry questions. in total, Vaibhav scores 26 out of 34. Note that a) Vaibhav scores more than Siddhant b) Siddhant score better than Vaibhav in both individual topics -  5/6 > 20/25 and 20/28 > 6/9 How is it possible? 
Read more

Buying Dimsums

Source: Alok Goyal (Stellaris VP, Ex-Helion VC) puzzle blog Problem: A fast food restaurant sells dimsums in boxes of 7 and 3. What’s the greatest number of dimsums a person cannot buy. Generalize it for p and q where p and q are relatively prime. I loved the puzzle. Hope you enjoy it too.
Read more

Consecutive Heads

Let's say A keep tossing a fair coin, until he get 2 consecutive heads, define X to be the number of tosses for this process; B keep tossing another fair coin, until he get 3 consecutive heads, define Y to be the number of the tosses for this process. 1) Calculate P{X>Y} 2) What's the expected value of X 3) What's the expected value of Y This is probably the hardest puzzle I have ever put on my blog. Hence, I will post its solution in the post directly rather than on comment. Solution: 1) (Solved by me finally after 13 months :)) Make a state diagram. Let the state be (a,b) where a is the number of consecutive heads streak "A" is on currently and b is the number of consecutive heads streak "B" is on currently. So, (0,3) (1,3) are final accepted states and (2,0) (2,1) (2,2) (2,3) are failure states. If you get tails, your contribution to the state reaches to "0" f(State) = P(X>Y | "State" configuration initially)
Read more