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import itertools def break_rings(connections): remain_rings = lambda L: set(itertools.chain(*L)) remain_links = lambda r, L: [x for x in L if r not in x] rings = remain_rings(connections) count = 0 while True: rings_after_break, links_after_break = len(rings), len(connections) next_break = None for r in rings: check = len(remain_rings(remain_links(r, connections))) # break the ring that reduces number of rings best if check < rings_after_break: rings_after_break = check next_break = r # if there are rings that reduce same number, # break the most connected ring elif check == rings_after_break: check = len(remain_links(r, connections)) if check < links_after_break: links_after_break = check next_break = r connections = remain_links(next_break, connections) rings = remain_rings(connections) count += 1 if len(rings) == 0: break return count if __name__ == '__main__': # These "asserts" using only for self-checking and not necessary for auto-testing assert break_rings(({1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {4, 6})) == 3, "example" assert break_rings(({1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4})) == 3, "All to all" assert break_rings(({5, 6}, {4, 5}, {3, 4}, {3, 2}, {2, 1}, {1, 6})) == 3, "Chain" assert break_rings(({8, 9}, {1, 9}, {1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {8, 7})) == 5, "Long chain" |