number of increasing strings of length k

dynamic-programming

#1

I am finding it hard that how to find the number of increasing sequences of length k in n numbers. I know it has use of LIS problem and i have to modify it somehow, but now getting how. it’s complexity is O(k*n^2) DP solution. Please give hint and explain me a little bit.


#2

My hint is:

number of inc. seq. of length k in n elements = ( number of inc. seq. of length k - 1 in n - 1 elements ) + ( number of inc. seq. of length k in n - 1 elements )

You simply use or skip first element. Additionally you need to remember last chosen number (you need to select bigger next time) and it makes O(k*n*n) when you normalize elements in sequence to range [0,n).


#3

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#4

You can look through this link and link . Basically the link provides you with pseudo code for @betlista’s idea.

number of inc. seq. of length k in n elements = ( number of inc. seq. of length k - 1 in n - 1 elements ) + ( number of inc. seq. of length k in n - 1 elements )

#5

Can u write that DP* ? that when i have calculated the LIS array, then next what i need to change in that ?