In LCS problem, why can’t (len[I][j]=len[I-1][j-1]+1; ) just be len[I][j]=len[I-1][j]+1; ? [dynamic programming]

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 for (int i=1; i<=n1; i++)
        for (int j=1; j<=n2; j++)
            if (s1[i] == s2[j])
                length[i][j] = length[i-1][j-1] + 1;
            else
                length[i][j] = max(length[i-1][j],
                                   length[i][j-1]);
 
  a b g d
e 0 0 0 0
f 0 0 0 0
g 0 0 1 1
d 0 0 1 2

What I have tried:

image of my thoughts
[Dynamic programming]

Posted 25-Sep-20 22:08pm

JacksonSteel

Updated 25-Sep-20 23:06pm

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Richard MacCutchan 26-Sep-20 4:48am

No idea, it's your code. Or perhaps you just copied some random code from the internet.

JacksonSteel 27-Sep-20 2:32am

My code

2 solutions

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OriginalGriff · Answer 1 · 2020-09-25T23:07:00

To work that out, you will need to read and understand the algorithm.
This may help: Longest common subsequence problem - Wikipedia[^]

But ... once you think you do, start with the debugger, and make the change you suggest. Then test it with a variety of test data. Do you get the same results as the unchanged version? Are you identifying the LCS correctly? If you are for all cases, then great! You can write a paper on your simpler solution!
But ... if not then you know that you can't, and it's going to take you quite a bit of digging to work out why not ...

Enjoy the challenge! :thumbsup:

Richard MacCutchan · Answer 2 · 2020-09-25T22:49:00

Solution 1

I suggest you get a copy of The C Programming Language - Wikipedia[^] and spend some time learning the language from the beginning.

Posted 25-Sep-20 22:49pm

Richard MacCutchan