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Duff's device provides a compact loop unrolling by using the case keyword both inside and outside the loop. This is unusual because the contents of a case statement are traditionally thought of as a block of code nested inside the case statement, and a reader would typically expect it to end before the next case statement.
Algorithms to which the Method of Four Russians may be applied include: computing the transitive closure of a graph, Boolean matrix multiplication, edit distance calculation, sequence alignment, index calculation for binary jumbled pattern matching. In each of these cases it speeds up the algorithm by one or two logarithmic factors.
In the simple case, the loop control is merely an administrative overhead that arranges the productive statements. The loop itself contributes nothing to the results desired, merely saving the programmer the tedium of replicating the code a hundred times which could have been done by a pre-processor generating the replications, or a text editor.
This can speed up the swap using temporary variables and give it an edge over other algorithms. For example, the XOR swap algorithm requires sequential execution of three instructions. However, using two temporary registers, two processors executing in parallel can swap two variables in two clock cycles:
Instead, when superflip is composed with the "four-dot" or "four-spot" position, in which four faces have their centres exchanged with the centres on the opposite face, the resulting position requires 26 moves under QTM. [3] Under STM, the superflip requires at least 16 moves (as shown by the third algorithm).
The simplest pancake sorting algorithm performs at most 2n − 3 flips. In this algorithm, a kind of selection sort, we bring the largest pancake not yet sorted to the top with one flip; take it down to its final position with one more flip; and repeat this process for the remaining pancakes.
To work around this limitation, the flip-flop operator would have to be modeled as an abstract data type, parameterized with: a predicate that tells whether to switch the flip-flop on, a predicate that tells whether to switch the flip-flop off. This flip-flop data type would provide a function that queries and updates its state at the same time.
They start by randomly assigning values to each variable and then traverse the given Boolean expression to identify which variables to flip to minimize the number of unsatisfied clauses. They may randomly select a variable to flip or select a new random variable assignment to escape local maxima, much like a simulated annealing algorithm.