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Unformatted text preview: Recursively solve the subproblems “Patch up” the solutions to the subproblems for the final solution Improvements on a smaller scale Greedy algorithms: exponential poly time (Typical) Divide and Conquer: O(n 2 ) asymptotically smaller running time Multiplying two numbers Given two numbers a and b in binary a=(a n1 ,..,a ) and b = (b n1 ,…,b ) Compute c = a x b Running time of primary school algorithm? Running time of primary school algorithm? The current algorithm scheme Mult over n bits Mult over n bits Multiplication over n/2 bit inputs Multiplication over n/2 bit inputs Shift by O(n) bits Shift by O(n) bits Adding O(n) bit numbers Adding O(n) bit numbers T(n) ≤ 4 T(n/2) + cn T(1) ≤ c T(n) is O(n 2 ) T(n) is O(n 2 )...
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 Fall '11
 RUDRA
 Algorithms, Recursion, Sort, Divide and conquer algorithm

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