Exercises

[wjholden]

• Construct a regular polygon using repeated global transformations and then drawing v=(0,1).
• Solve wings problem using dynamic programming.
• Define a generating function for A002378 given sum identity. Now define the same thing recursively: f(x)=f(x-1)+2x for x>0 and f(0)=0.
• Use Floyd-Warshall to find routing loop in digraph with asymmetric cost handshakes.

[wjholden]

• Apply Prime Number Theorem to difficulty of brute-force cracking RSA with 1024-bit key.
• Apply Master Theorem to Merge Sort.
• Empirically measure performance of Quick Sort by adding r-l to a counter. See how you can influence the performance of Quick Sort by biasing the input.
• Make up your own PRNG and then apply any of Knuth's methods to assess it's strength?
• Write a program to compute a summary route for IPv4 prefixes.
• Use only AND, OR, and NOT operations to construct a four-bit adder with overflow.

[wjholden]

• Find the ratio F(n+1)/F(n) for some Fibonacci-like sequence where F(1) and F(2) are either or both ≠1 but still F(n)=F(n-1)+F(n-2).

[wjholden]

• Polynomial parentheses matching.

[wjholden]

Wings, Fibonacci, parentheses, fractals, and routing loops.