To implement the described algorithm, we'll use an iterative approach where we first calculate the closest triangles for both the beginning and ending points of each tract and then choose the subset of tracts that maximize the mesh coverage and area dispersion. For this, we will create helper functions to find the closest triangle, calculate dispersion, and select the subset of tracts.
Include the necessary headers:
#include <iostream>
#include <vector>
#include <algorithm>
#include <limits>
#include <tuple>