some simple algorithms and data structures merge sort is prototypical divide-and-conquer algorithm it was invented in by john von neumannand is still widely used like many divide-andconquer algorithms it is most easily described recursively if the list is of length or it is already sorted if the list has more than one elementsplit the list into two listsand use merge sort to sort each of them merge the results the key observation made by von neumann is that two sorted lists can be efficiently merged into single sorted list the idea is to look at the first element of each listand move the smaller of the two to the end of the result list when one of the lists is emptyall that remains is to copy the remaining items from the other list considerfor examplemerging the two lists [ , , , , , and [ , , , ]left in list [ , , , , , [ , , , , [ , , , , [ , , , , [ , , , , [ , , , [ , , [ , , [left in list result [ , , , [ , , , [ , , [ , [ [ [ [[[[ [ , [ , , [ , , , [ , , , , [ , , , , , [ , , , , , , [ , , , , , , , , , what is the complexity of the merge processit involves two constant-time operationscomparing the values of elements and copying elements from one list to another the number of comparisons is (len( ))where is the longer of the two lists the number of copy operations is (len( len( ))because each element gets copied exactly once thereforemerging two sorted lists is linear in the length of the lists figure contains an implementation of the merge sort algorithm notice that we have made the comparison operator parameter of the mergesort function the parameter' default value is the lt operator defined in the standard python module named operator this module defines set of functions corresponding to the built-in operators of python (for example for numbersin section we will exploit this flexibility