What is the Consider Fibonacci sequence Assignment

Assignment Task

Questions

1. Consider the sequence (si) i∈N where s i is the number of bitstrings of length i that contain three consecutive 0s. Define this sequence recursively.

2. Consider the sequence (ti) i∈N where ti is the number of bitstrings of length i that contain the string 01. Define this sequence recursively.

3. Consider the sequence (UI) i∈Z + , where u i is the number of messages that can be transmitted in microseconds using three different signals: one signal requires 1 microsecond for transmittal, the other two signals require 2 microseconds each for transmittal, and a signal in a message is followed immediately by the next signal. Define this sequence recursively.

4. Using the library provided in Appendix, write in pseudocode the procedure

5. which returns the next n-permutation in lexicographic order after p, where n is the length of p (but p is not necessarily an n-permutation of 1..n). Return the empty string if p is the last n permutation. For example, return (−3,1,11,5) if p=(−3,1,5,11) and return () if p=(11,5,1,−3).

6. Using the procedure above and the library provided in Appendix, write in pseudocode void printPermutations (integer n) which prints ALL the permutations of 1..n. The empty string must be printed first, then the 1-permutations, the 2-permutations, etc.

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