angelg's blog

How to solve this problem?
By angelg, history, 9 years ago, In English

Let's suppose you have an array A of numbers (0-255). Then, you pick a single variable K (0-255), and you create another array B. Where Bi = Ai ^ K. Is there a way to restore the original array A? If you are not giving A or K.

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9 years ago, # |
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Anyone cares to share the solution if it's so obvious that I'm getting downvotes?

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9 years ago, # |
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255255 has 614 digits.

Are you sure about constraints or is there any modulo involved ?

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    9 years ago, # ^ |
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    It is not a POWER it is XOR

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      9 years ago, # ^ |
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      Thanks for pointing that out. It can confuse some people.

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9 years ago, # |
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if (Ai^K = Bi) then

Ai^K^K = Bi^K, so Ai = Bi^K(because K^K = 0)

Ai^K^Ai = Bi^Ai, so K = Bi^Ai(because Ai^Ai = 0)

That's how we can find Ai, when we have Bi and K or we can find K, when we have Ai and Bi.

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