Python descriptor details

1. Turn on/off lamps

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Imaging that there are N lamps(1,2,3...), and in the first time there are lit:

• The 1st person will turn off all of the N lamps;
• The 2nd person will turn on the 2nd lamps and the multiple of 2 lamps;
• The 3rd person will turn off the 3rd lamps and the multiple of 3 lamps;
  …
• the nth person will turn on/off(reverse operation) the nth lamps and the multiple of nth lamps.

Question: Print the ID of the lamps which are lit in order after the nth person did the reverse operation. E.g., After the 8th operation, the lamps with ID 2 3 5 6 7 8 are lit.

Solution

The core idea of this question is that we only need to take the operation times of lamps into account. For example, if we know the 5th lamps are turned on/off 4 times, then it is still lit. Therefore, the most thing is to know the times of turn on/off operation for each light.

Then note that the i person can only turn on/off the i and the multiple of i lamps. In other words, as for the lamps i, only the person of the submultiple of i can turn on/off the lamps. For example, with respect to the lamp 8, only the 1 2 4 8 person can turn on/off this lamp. Therefore, the number of the submultiple of lamp i is the times of the operations of lamp i.

Given these points, the question can be transfered to find the submultiple for the i lamp.

References

• csdn

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