Medium | Strategy |

Suppose you have a hotel which has one floor with infinite number of rooms in a row and all of them are occupied.

1) A new customer wants to check in, how will you accommodate her?

2) What if infinite number of people want to check in, how will you accommodate them?

3) Suppose infinite number of buses arrive at the hotel, each having infinite number of people, how will you accommodate them?

1) A new customer wants to check in, how will you accommodate her?

2) What if infinite number of people want to check in, how will you accommodate them?

3) Suppose infinite number of buses arrive at the hotel, each having infinite number of people, how will you accommodate them?

Hint

Define Infinity ;)

Solution

1) Since there are infinite number of rooms and infinite+1= infinite

Just ask person in room k to move to k+1, thus making the first room vacant. :)

2) In the other case, since infinite+infinite = infinite

asking person in room k to move to 2k solves the problem.

3) Since NxN is countable set. We can get a 1-1 mapping from N to NxN

Hence, we can accommodate (infinite people X infinite buses) in the hotel.

Relevant article:

http://en.wikipedia.org/wiki/Cantor_pairing_function

Just ask person in room k to move to k+1, thus making the first room vacant. :)

2) In the other case, since infinite+infinite = infinite

asking person in room k to move to 2k solves the problem.

3) Since NxN is countable set. We can get a 1-1 mapping from N to NxN

Hence, we can accommodate (infinite people X infinite buses) in the hotel.

Relevant article:

http://en.wikipedia.org/wiki/Cantor_pairing_function

Source: CSEblog

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