算法导论 Exercise 3.1-3
2011-02-18 20:21
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Explain why the statement, "The running time of algorithm A is at least O(n2)," is meaningless.
Let the running time be T (n). T (n) ≥ O(n2) means that T (n) ≥ f (n) for some
function f (n) in the set O(n2). This statement holds for any running time T (n),
since the function g(n) = 0 for all n is in O(n2), and running times are always
nonnegative. Thus, the statement tells us nothing about the running time.
Let the running time be T (n). T (n) ≥ O(n2) means that T (n) ≥ f (n) for some
function f (n) in the set O(n2). This statement holds for any running time T (n),
since the function g(n) = 0 for all n is in O(n2), and running times are always
nonnegative. Thus, the statement tells us nothing about the running time.
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