Algorithm to efficiently determine the [n][n] element in a matrix

Question

This is a question regarding a piece of coursework so would rather you didn\'t fully answer the question but rather give tips to improve the run time complexity of my curren

Answer 1

If the question is about how to output all values of the function for 0<=i, 0<=j, here is a solution in time O(N²) and space O(N). The time behavior is optimal.

Use a temporary array T of N numbers and set it to all ones, except for the first element.

Then row by row,

    use a temporary element TT and set it to 1,
    then column by column, assign simultaneously T[I-1], TT = TT, (TT + T[I-1] + T[I])/3.