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.

Awall of 0.5m thickness is to be constructed from a material which has average thermal conductivity of 1.4 w/mk. the wall is to be insulated with a material having an average thermal conductivity of 0.35 w/mk so that heat loss per square meter shall not exceed 1450 w. assume inner wall surface temperature of 1200°c and outer surface temperature of the insulation to be 15°c. calculate the thickness of insulation required.