Problem Statement:

We have N points in a complete graph where each node represents a point with (x, y) coordinates. We must start at point 1 and visit all other points exactly once, minimizing the total energy cost required to travel between points.

We are given:

An N × N cost matrix where cost[i][j] represents the energy consumption to travel from point i to point j.

The constraints allow N ≤ 45, meaning an exact approach is possible but needs optimization.

Key Questions:

What is the best order of visiting the points to minimize energy?

How can we efficiently solve this problem for N up to 45?

Are there any optimizations beyond the standard TSP with DP + Bitmasking?