K order knapsack ---runtime error
hello @guptarahul3100
ur dp state is wrong.
suppose we have s1and s2 as string and k.
i=0 (for string s1)
j=0(for string s2)
if s1[i]==s2[j]
then ans=1+solvefor(i+1,j+1,k)
if(s1[i]!=s2[j] (we have two options)
- ans=solvefor(i+1,j,k) or solvefor(i,j+1,k) take maximum among them // we did similar thing in lcs
- if k>0 then i can use 1 k to make them equal and lcs in that case will be
ans=1+solvefor(i+1,j+1,k-1) // k-1 because i have used 1 k to make them equal
among those two options whichever will give maximum answe we will consider that.
Define a 3D matrix dp[][][], where dp[i][j][k] defines the Longest Common Subsequence for the first i numbers of first array, first j number of second array when we are allowed to change at max k number in the first array.
Therefore, recursion will look like
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