chap limits to computation the problem in the sense of finding the smallest set of vertices that forms vertex cover implement knapsack (see section measure its running time on number of inputs what is the largest practical input size for this problem implement an approximation of traveling salesmanthat isgiven graph with costs for all edgesfind the cheapest cycle that visits all vertices in try various heuristics to find the best approximations for wide variety of input graphs write program thatgiven positive integer as inputprints out the collatz sequence for that number what can you say about the types of integers that have long collatz sequenceswhat can you say about the length of the collatz sequence for various types of integers