silent_sky's blog

How to find the xor of numbers in a range
By silent_sky, history, 6 years ago, In English

Given two integers $$$A$$$ and $$$B$$$, find $$$A$$$ $$$\oplus$$$ $$$($$$ $$$A$$$ $$$+$$$ $$$1$$$ $$$)$$$ $$$\oplus$$$ $$$($$$ $$$A$$$ $$$+$$$ $$$2$$$ $$$)$$$ $$$\oplus$$$ $$$\dots$$$ $$$\oplus$$$ $$$B$$$ where $$$A$$$ $$$<=$$$ $$$B$$$

No, not in linear time

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6 years ago, # |
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You can use a trick, that 1 xor 2 xor .. xor (4 * x — 1) = 0.

And A xor A + 1 xor .. xor B = (1 xor 2 xor .. xor (A — 1)) xor (1 xor 2 .. xor B)

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6 years ago, # |
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https://mirror.codeforces.com/blog/entry/2154

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6 years ago, # |
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The XOR sum of numbers from 1 to m equals:

m   if m%4 is 0
1   if m%4 is 1
m+1 if m%4 is 2
0   if m%4 is 3
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