Given the size of board (n) and the position of the queen (r,c) how can we calculate the total number of squares which can be controlled by the queen?


closed as off-topic by elias, Glorfindel, Mithrandir, Beastly Gerbil, Rubio Jan 29 '17 at 22:23

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  • 4
    $\begingroup$ You can count them! :D $\endgroup$ – boboquack Jan 29 '17 at 8:29

Assuming the queen controls its own square and 0-based indexing, we have:

  • $1$ - its own square
  • $2n-2$ - the rows and columns without its own square
  • $n-1-|r+c-n+1|$ - the number of squares on one diagonal
  • $n-1-|r-c|$ - the number of squares on the other diagonal

Add them all up and we have:



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