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svanidz1's blog

Minimum Xor subsequence
By svanidz1, 13 years ago, In English

Does there exist an algorithm, for a given sequence to find a sub-sequence with minimum possible xor? Or at least an algorithm finding a subsequence of xor==0?

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13 years ago, hide # |
 
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which asymptotic are you interesting about? For instance, one can use Meet-in-the-middle for second problem...

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13 years ago, hide # |
 
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First thought: you can treat numbers like binary vectors and construct a matrix, where each row is a binary vector, corresponding to a particular number in sequence. Then you can perfrom Gaussian elimination modulo 2 on this matrix and if you have at least one all-zeroes row you can get xor == 0. If for each row R you also save indexes of rows interacted with row R during Gaussian elimination you can restore the corresponding subsequence.

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13 years ago, hide # |
 
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http://codeforces.me/blog/entry/1201
http://apps.topcoder.com/forums/;jsessionid=27C509BC366B5418E52684946CBFC0DF?module=Thread&threadID=704255&start=0&mc=5#1393888

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