ABC165E

E - Rotation Matching

• 
• Thoughts.
  • The point is, the difference can’t be the same.
  • No K and N-K either.
  • I don’t know how many assignments would be OK.
    • M must be less than N/2
    • Oh, it says > $M\times 2+1\le N$
  • 
    • Now if N is odd, the rest are even, so they’re all guaranteed to be at different intervals.
  • This doesn’t work when N is even, the rest of the numbers are also odd and covered.
    • Looks good if you shift one half.
    • If M is even, the length taken in the M/2nd and the remaining length match, so we spread 1 there.
    • After that, they will all be even numbers, so they won’t be covered.
  • I’m sure there’s a bug that could cause a discrepancy of 1 or so at the boundary, but it’s better to implement it and squash it with a small test case than to think about it in my head.
• Official Explanation
  • Style that creates both odd-length and even-length clumps
    • The length, not the evenness, prevents overlap.

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