Algorithms For Dummies

 

»

Gauss’s complex multiplication algorithm

 

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Karatsuba multiplication

 

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Toom-Cook

 

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Fourier transform methods

Even though many of the methods currently available produce acceptable results, 

they all take time, and when you have a lot of calculations to perform, the time 

problem can become critical. Consequently, large number multiplication is one of 

those problems that requires a better solution than those available today.

Dividing a Resource Equally

Dividing resources equally may not seem hard, but humans, being the envious 

sort, might see the resource as being unequally divided unless you can find a way 

to assure everyone that the division is indeed fair. This is the envy-free cake-

cutting problem. Of course, when you cut a cake, no matter how fairly you attempt 

to do it, there is always the perception that the division is unfair. Creating a fair 

division of resources is important in daily life to minimize strife between stake-

holders in any organization, making everyone more efficient.

Two solutions already exist for the envy-free cake-cutting problem with a specific 

number of people, but no general solution exists. When there are two people 

involved, the first cuts the cake and the second chooses the first piece. In this way, 

both parties are assured of an equal division. The problem becomes harder with 

three people, but you can find the Selfridge-Conway solution for the problem at 

https://ochronus.com/cutting-the-pie

 (even though the site discusses pie, 

the process is the same). However, after you get to four people, no solution exists.

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CHAPTER 22