this is a pure python implementation of the greedymergesort algorithm reference https www geeksforgeeks orgoptimalfilemergepatterns for doctests run following command python3 m doctest v greedymergesort py objective merge a set of sorted files of different length into a single sorted file we need to find an optimal solution where the resultant file will be generated in minimum time approach if the number of sorted files are given there are many ways to merge them into a single sorted file this merge can be performed pair wise to merge a mrecord file and a nrecord file requires possibly mn record moves the optimal choice being merge the two smallest files together at each step greedy approach function to merge all the files with optimum cost args files list a list of sizes of different files to be merged returns optimalmergecost int optimal cost to merge all those files examples optimalmergepattern2 3 4 14 optimalmergepattern5 10 20 30 30 205 optimalmergepattern8 8 8 8 8 96 consider two files with minimum cost to be merged function to merge all the files with optimum cost args files list a list of sizes of different files to be merged returns optimal_merge_cost int optimal cost to merge all those files examples optimal_merge_pattern 2 3 4 14 optimal_merge_pattern 5 10 20 30 30 205 optimal_merge_pattern 8 8 8 8 8 96 consider two files with minimum cost to be merged
def optimal_merge_pattern(files: list) -> float:
    
    optimal_merge_cost = 0
    while len(files) > 1:
        temp = 0
        
        for _ in range(2):
            min_index = files.index(min(files))
            temp += files[min_index]
            files.pop(min_index)
        files.append(temp)
        optimal_merge_cost += temp
    return optimal_merge_cost


if __name__ == "__main__":
    import doctest

    doctest.testmod()