Algorithms Problem 1:

Problem 1. a) Show that if f(n) is O(g(n)) and d(n) is O(h(n)), then f(n) d(n) is O(g(n) h(n)).

b) Show that 3(n + 1)^5 + 2n^3 log n is O(n^5).

c) Algorithm A executes 10n^2 log n operations, while algorithm B executes n^3 operations.

Determine the minimum integer value n0 such that A executes fewer operations than B for n n0.