DA05 - B.B Karki LSU 0.1 CSC 3102 Nonrecursive Algorithms...

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Unformatted text preview: B.B. Karki, LSU 0.1 CSC 3102 Nonrecursive Algorithms B.B. Karki, LSU 0.2 CSC 3102 Definition and Examples Nonrecursive algorithm: Executed only once to solve the problem. Examples Largest element in a list of numbers Element uniqueness problem Matrix operations: addition, multiplication, and transpose Digits in binary representation Recursive algorithm invokes (makes reference to) itself B.B. Karki, LSU 0.2 CSC 3102 Definition and Examples Nonrecursive algorithm: Executed only once to solve the problem. Examples Largest element in a list of numbers Element uniqueness problem Matrix operations: addition, multiplication, and transpose Digits in binary representation Recursive algorithm invokes (makes reference to) itself repeatedly until a certain condition matches. B.B. Karki, LSU 0.3 CSC 3102 Analyzing Efficiency of Nonrecursive Algorithms Steps in mathematical analysis of nonrecursive algorithms: Decide on parameter n indicating input size Identify algorithm’s basic operation Determine worst, average, and best case for input of size n if the basic operation count depends not only on n Set up summation for C ( n ) reflecting algorithm’s loop structure Express the number of times the algorithm’s basic operation is executed Simplify summation using standard formulas and rules of sum manipulation (see Appendix A) Find a closed-form formula for the count and/or establish it’s order of growth. B.B. Karki, LSU 0.4 CSC 3102 Example 1: Maximum Element Algorithm MaxElement ( A[0.. n - 1] ) //Determines the value of the largest element in a given array //Input: An array A[0.. n - 1] of real numbers //Output: The value of the largest element in A maxval ← A[0] for i ← 1 to n - 1 do if A[i] > maxval maxval ← A[i] return maxval B.B. Karki, LSU 0.5 CSC 3102 Example 1: Maximum Element (Cont.) Input size = n , the number of elements in the array Algorithm’s basic operation is “comparison” It is executed on each repetition of the loop Formula for the basic operation count: Sum is simply 1 repeated by n- 1 times....
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DA05 - B.B Karki LSU 0.1 CSC 3102 Nonrecursive Algorithms...

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