merging-triplets

A set of files for solving the problem listed here: http://stackoverflow.com/questions/22222994/optimal-merging-of-triplets

Usage

merge_triplets.py

• ./merge_triplets.py < triplets will merge triplets listed in the file triplets with lookahead 3 and output the size of the resulting set.
• ./merge_triplets.py -v < triplets will output information on every step of the algorithm, visualizing recursion.
• ./merge_triplets.py 0 < triplets will use zero lookahead, a.k.a. the blind algorithm as discussed on StackOverflow.
• ./merge_triplets.py 1 < triplets will use the simple heuristic, a.k.a Level 1: Greedy.
• ./merge_triplets.py 2 < triplets also for any argument larger than 1, this will use the recursive lookahead algorithm a.k.a. Level 2: Very greedy

random_triplets.py

• ./random_triplets.py n will generate n triplets on stdout, with maximum element value about base-3 logarithm of n
• ./random_triplets.py | ./merge_triplets.py is a convinient way of combining the two scripts

find_diff.sh

• ./find_diff.sh n l1 l2 will repeatedly generate sets of n triplets, and compare the results of merges with lookaheads l1 and l2 to find differences. When a difference is found, the script prints details of the event as well as the triplets that caused it and exits. Default values for n, l1 and l2 are 10, 2 and 3 respectively.

stat_diff.sh

• ./stat_diff.sh n l1 l2 will do the same thing as ./find_diff.sh n l1 l2 except that instead of exiting, it will keep track of differences and continue running with new datasets. Sending an interrupt (Ctrl-C) will cause the script to print the statistics so far and exit. The script will leave behind last_better[12]_triplets files (so long the corresponding datasets have been found) so that they can be analyzed after the script has finished.

proof* files

• These files are examples of triplets which cause different results for different lookaheads, as found by the find_diff.sh script.