szawinis's blog

Help with problem
By szawinis, history, 9 years ago, In English

You are given two arrays of integers a, b both with length n <= 10^5. For each 0 <= x <= n print the sum of a[i]*b[x-i] for all 0 <= i <= x.

It's obvious this can be done in quadratic time, but can we do any better?

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9 years ago, hide # |
 
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    9 years ago, hide # ^ |
     
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    Thanks for the reply. Your strategy is quite interesting, however that only solves the problem if we want the sum over a[i]*b[x-i] for all x and for all i. The problem was to isolate each x and calculate the sum over a[i]*b[x-i] for all i for this value of x only, then move on to the next value of x. I'm very sorry if this wasn't clear.

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      9 years ago, hide # ^ |
       
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      Oh, I didn't get that. I think that the same strategy works in this case though.

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9 years ago, hide # |
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It seems that the answer will always be equal to . (can't prove it, sorry)
Let p be the partial sum array of a. Then the answer is simply .

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