For each of the following problems: design a greedy algorithm that solves the problem; describe your algorithm with clear pseudocode; and prove the time efficiency class of your algorithm.

2-coloring input: an undirected graph G (V, E) output: a sequence coloring-((u, c)IE V and ce(1,2) such that each V appears exactly once in colors , and no adjacent vertices are assigned the same color

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?