This is a correction docuement, due to a week of holiday from 2nd to 6 oct the numbering of notes was decremented by 1,

i.e week 8 was denoted as week 7, Sorry for the inconvenience, this will not happen again.

#FLOYD-WARSHALL Algorithm

This is similar to dijistra algorithm but the difference is that dijistra algorithm is single source where as in this we calculate for all the vertices.
In this problem we tend to first fill the matrix 0 with the immediate path value/cost which we get.
then in the next step we fill the first matrix and in this we keep the intermediate point to be 1 and then find the shortest path and if the path is short we keep it otherwise we take it from the previous matrix.
and then we complete the matrix to end and resulting end matrix will be our final solution.
We can do this in O(n^3) time complexity.

#Independent Set in Trees

A subset of nodes S of V is an independent set of graph G = (V,E) if there are no edges between them.
this can be done using dynamic programming via dividing the problem in two cases in which we will calculate the maximum of independent children of w and in the other the grand children of w + 1 and then taking maximum of it and keep on doing it till we get the solution.