Why does this recursion method work? I have explored it for a day or two, and I cannot figure out why
Problem Statement: I have a tree with node values ( i , j ) where i , j < 1. The children of each node take on the values (i - 1, j), (i - 1, j - 1), and (i, j - 1) respectively. Now, i and j have ...
Algorithm to generate all sets of m points in n x n x n cubic lattice which are unique under symmetry
I am implementing an algorithm which is going to be quite computationally complex, and want to try to make sure I'm not doing unnecessary work. There is an n x n x n cubic lattice, e.g. if n=2 this ...
I have a requirement to allow my end users to input formula much like a spreadsheet. I have an array like this: $table = array( 1=>array( "id"=>1, ...
Given the following recurrence: T(n) = T(n-1) + n^2 How can I prove it to be O(n^3) with the substitution method? The O(n^3) guess derives from the fact that at every step of the recursion we pay ...
Here are given two functions that calculate the sum of elements in a list. The proof should be done using induction. The hypothesis is: sum(as) = sum1(as, 0) def sum( as : List [ Int ] ) : Int = as ...