Let us say that a graph G = (V, E) is a near-tree if it is connected and has at most n + 8 edges, where n = |V|. Give an algorithm with running time O(n) that takes a near-tree G with costs onits edges and returns a minimum spanning tree of G. You may assume that all of the edge costsare distinct.

In a unit cell of fcc structure, indicate the position of one of the tetrahedral interstitial sites by plotting the corresponding tetrahedron. do the same for one of the octahedral interstitial sites (in a separate fcc unit cell). mark the positions of all the tetrahedral and octahedral interstitial sites in the unit cells. how many equivalent tetrahedral sites and how many equivalent octahedral sites are contained in a fcc unit cell, respectively. what is the coordination number for a tetrahedral site and what is the coordination number for an octahedral site?