1.intr - Mathematical Foundation CSE 680 Suggested Reading Sections 1.1 1.2 2.1 2.2 3.1 3.2 1 Running Time Analysis of algorithm to estimate the running

# 1.intr - Mathematical Foundation CSE 680 Suggested Reading...

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Mathematical Foundation CSE 680 Suggested Reading: Sections 1.1, 1.2, 2.1, 2.2, 3.1, 3.2. 1 Running Time Analysis of algorithm: to estimate the running time of an algorithm. Elementary operations: – arithmetic and boolean operations: + , - , × , / , mod, div, and, or – comparison: if a < b , if a = b , etc. – branching: go to – assignment: a b – and so on The running time of an algorithm is the number of elementary operations required to excute the algorithm. It depends on the input (instance): – size of the input – content of the input The worst-case running time of an algorithm: T ( n ) = max { running time over all instances of size n } Express T ( n ) in the O , Ω , or Θ notation. These are called asymptotic notations. They describe the behavior of a function f ( n ) when n is sufficiently large. A function f ( n ) is asymptotically positive if f ( n ) is positive for sufficiently large n . A function f ( n ) is asymptotically increasing if f ( n ) is increasing for sufficiently large n .