graph-algorithm

There are N problems numbered 1..N which you need to complete. You've arranged the problems in increasing difficulty order, and the ith problem has estimated difficulty level i. You have also assigned a rating vi to each problem. Problems with similar vi values are similar in nature. On each day, you will choose a subset of the problems and solve them. You've decided that each subsequent problem solved on the day should be tougher than the previous problem you solved on that day. Also, to not make it boring, consecutive problems you solve should differ in their vi rating by at least K. What is

I would like to know what is the problem name for TSP w/o considering the way of going back to starting point and what is the algorithm to solve this. I looked into Shortest path problem but that is not what I am looking for, the problem only find the shortest path from 2 assigned points. But what I am looking for is the problem which we give n points and inputting only 1 starting point. Then, find the shortest path traveling all points exactly once. (end point can be any point.) I also looked into Hamiltonian path problem but it seems not to solve my defined problem but rather find whether

I've been using a little python script I wrote to manage debt amongst my roommates. It works, but there are some missing features, one of which is simplifying unnecessarily complicated debt structures. For example, if the following weighted directed graph represents some people and the arrows represent debts between them (Alice owes Bob $20 and Charlie $5, Bob owes Charlie $10, etc.): It is clear that this graph should be simplified to the following graph: There's no sense in $10 making its way from Alice to Bob and then from Bob to Charlie if Alice could just give it to Charlie directly. The