Karatsuba Multiplication

Internal

• Algorithms | Divide and Conquer

TODO

• problem statement
• naïve solution
• Gauss trick
• complexity
• Karatsuba: explain the key idea – apply the master theorem to demonstrate that the complexity is still O(n2). The key insight for Karatsuba algorithm is the Gauss’ trick to reduce four sub-parts recursive multiplications to 3, and the complexity is ?

Overview

Apply the Gauss' trick and end up with three recursive calls instead of four. This yields a O(n*logn) complexity. It if was four, the recursive complexity it would have been O(n²).

TODO

Playground

https://github.com/ovidiuf/playground/tree/master/learning/stanford-algorithms-specialization/01-karatsuba

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