This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Analysis of Algorithm 2 60 [CS1102C AY0708S2 Lecture 5] Lecture Outline ยก What is an algorithm? ยก What is analysis of algorithm? ยก How to analyze an algorithm ยก BigO notation ยก Examples 3 60 [CS1102C AY0708S2 Lecture 5] You are expected to know ยก Operations on logarithm function ยก Arithmetic and geometric progressions ยข Their sums ยก Linear, Quadratic, Cubic, Polynomial ยก Ceiling, Floor, Absolute Value 4 60 [CS1102C AY0708S2 Lecture 5] Algorithm and Analysis ยก Algorithm: ยข A stepbystep procedure for solving a problem ยก Analysis of Algorithm: ยข To evaluate rigorously the resources (time and space) needed by an algorithm and represent the result of the evaluation with a formula ยข We focus more on time requirement in our analysis ยข The time requirement of an algorithm is also called the time complexity of the algorithm 5 60 [CS1102C AY0708S2 Lecture 5] Limitation of exact running time ยก We can measure the exact running time of a program ยข Use wall clock time or code inserted into program ยก To compute the exact running time needed by an algorithm, the analysis will depend on : ยข Language in which the algorithm is coded ยข Data set : input to the algorithm ยข Computer that the algorithm is executed on ยก Such analysis will make it difficult to compare 2 algorithms ยก It is useful to know the behavior of the algorithm before it is coded / executed ยข Poorly designed algorithm may take very long to finish execution 6 60 [CS1102C AY0708S2 Lecture 5] How to Analyze an Algorithm? ยก Instead of measure the exact timing ยข Count the number of operations needed ยก Operations: Arithmetic, Assignment, Comparison etc ยข Usually choose the โdominantโ operations ยก Example: for (int i=1; i<=n; i++) { perform 100 operations; // A for (int j=1; j<=n; j++) perform 2 operations; // B } Total Ops = A + B = ฮฃ {i = 1,n}100 + ฮฃ {i = 1,n} ( ฮฃ {j = 1,n} 2) = 100n + ฮฃ {i = 1,n} (2n) = 100n + 2n 2 = 2n 2 + 100n 7 60 [CS1102C AY0708S2 Lecture 5] Time Requirement ยก Knowing the number of operations required for an algorithm A, we can state that: ยข E.g. Algorithm A takes 2n 2 + 100n operations to solve problem of size n ยก If the time t needed for one operation is known, then we can state: ยข E.g. Algorithm A takes (2n 2 + 100n)*t time units ยก However, time t is a directly dependent on the factors mentioned earlier: ยข Computer and Programming Language ยก Instead of typing the analysis to actual time t, we can state: ยข Algorithm A takes time that is proportional to 2n 2 + 100n for solving problem of size n 8 60 [CS1102C AY0708S2 Lecture 5] Approximation of Analysis Results ยก Suppose the complexity of ยข Algorithm A is found to be 3n 2 + 2n + log n + 1/4n ยข Algorithm B is found to be 0.39n 3 + n ยก Intuitively, we know Algorithm A will outperform B ยข when solving larger problem i.e. larger n when solving larger problem i....
View
Full Document
 Spring '11
 dunnowho
 Analysis of algorithms, Analysis of Algorithm, CS1102C AY0708S2 Lecture

Click to edit the document details