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Computer Science Warmups

Computers encrypt digital information and allow people to collaborate across the globe. Computer science studies the theory behind mechanisms like these and the practical details needed to build them. See more

Level 1

         

Pantha du Prince sends you a secret message hidden within a string of nonsense. You know that the real message is periodic within the garbage and that he's partial to the number three.

Find Pantha's hidden message to you by taking periodic substrings.

panthas_message = "Tkxhwbiscscu vfbmwlgzirlsnysqr"

Government surveillance agencies have a tendency to accumulate strange new powers during times of panic. The US National Security Agency (NSA) now has the ability to monitor the communications of suspected individuals as well as the communications of people within some number of hops of any suspect. In the communication network above, which person is connected to the greatest number of people through 1 hop or less?

Notes and assumptions

  • Each dot represents a person.
  • Each line represents communication between the people on either end .
  • If X communicates with Y, and Y communicates with Z, we say X and Z have a 1-hop connection, and that X has a 0-hop connection with Y.

Each edge in the binary tree has length 1. What is the minimum distance that the squirrel must travel to collect all 8 acorns?

One day you decide to sort data on your old INTEL 8008 computer. If a mergesort algorithm in worst case takes 84 seconds to sort an input of size 256.

Which of the following closely approximates the maximum input size that can be sorted by the computer in a worst case runtime of 7 minutes?

Robots are used to prepare bags of sliced apples. One particularly bad robot gets tired as his power starts to run low, so making the \(k\)th bag takes the robot \(k+4\) actions.

For example, the robot can make the 1st bag with just 5 actions, but by the 100th bag, it takes the robot 104 actions. The total number of actions needed to make \(n\) bags of sliced apples (for large \(n\)) is:

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