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Space-Time Tradeoffs and Efficiency

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A lot of computer science is about efficiency. For instance, one frequently used mechanism for measuring the theoretical speed of algorithms is Big-O notation. What most people don't realize, however, is that often there is a trade-off between speed and memory: or, as I like to call it, a tradeoff between space and time.
Think of space efficiency and time efficiency as two opposite ends on a band (a continuum). Every point in between the two ends has a certain time and space efficiency. The more time efficiency you have, the less space efficiency you have, and vice versa. The picture below illustrates this in a simple fashion:

Algorithms like Mergesort are exceedingly fast, but require lots of space to do the operations. On the other side of the spectrum, Bubble Sort is exceedingly slow, but takes up the minimum of space.  more...

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