1 / 17

Algorithms

The Project for the Establishing the Korea ㅡ Vietnam College of Technology in Bac Giang. Algorithms. April-May 2013. Dr. Youn-Hee Han. Professor/Lecturers. Name : Youn-Hee Han Department: Computer Science and Engineering Contact: 010-3912-0900

cael
Download Presentation

Algorithms

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Project for the Establishing the Korea ㅡ Vietnam College of Technology in BacGiang Algorithms April-May 2013 Dr. Youn-Hee Han

  2. Professor/Lecturers Name: Youn-Hee Han Department: Computer Science and Engineering Contact: 010-3912-0900 E-mail:yhhan@koreatech.ac.kr • <Education Background> • 1992 ~ 1996: B.S. in mathematics, Korea University • 1996 ~ 1998: M.S. in Computer Science and Engineering, Korea University • 1998 ~ 2002: Ph.D. in Computer Science and Engineering, Korea University • <Working Experience> • 2002 ~ 2006: Senior Researcher, Samsung Advanced Institute of Technology • 2006 ~ Current: Prof., Korea University of Technology and Education • <Research> • Mobile Computing • Sensor & Actuator Networks • Social Network • Web Science & Engineering 2/17

  3. Lecture Guide • Goal • Introduce some important parts of the undergraduate-level “algorithms” course offered by KoreaTech • You learn the core algorithm design strategies and specific algorithms • You can practice Java programming for the specific algorithms • Lecture Contents & Schedule • 1st day (3 hours): Introduction of Algorithm, Algorithm Efficiency • 2nd day (3 hours): Algorithm Complexity • 3rd day (3 hours): Algorithm Design Strategy 1 – Divide & Conquer • 4th day (3 hours): Algorithm Design Strategy 2 – Dynamic Programming • 5th day (3 hours): Algorithm Design Strategy 3 – Greedy Approach • 6thday (3 hours): Algorithm Design Strategy 4 – Backtracking • Lecture Homepage • http://link.koreatech.ac.kr/courses/2013_1/AP-KOICA/AP-KOICA20131.html

  4. Whatis Algorithms? • A computer program is composed of individual modules, understandable by a computer, that solve specific tasks (such as sorting). • These specific tasks are called problems. • A problem may contain variables that are not assigned specific values in the statement of the problem. • These variables are called parameters to the problem. • Each specific assignment of values to the parameters is called an instance of the problem.

  5. Whatis Algorithms? • To produce a computer program that can solve all instances of a problem, we must specify a general step-by-step procedure for producing the solution to each instance. • This step-by-step procedure is called an algorithm. • We say that the algorithm solves the problem. • A problem can be solved by many different algorithms. • Features of algorithm • Correct • Finite length • Terminate for all inputs.

  6. Importance of Efficient Algorithms • Sequential Search vs. Binary Search • Sequential Search • It begins at the first position in the array and looks at each value in turn until the item is found. index seqsearch(intn,type[] S, type x){ index location; location = 1; while (location <= n && S[location] != x) location++; if (location > n) location = 0; return location; }

  7. Importance of Efficient Algorithms • Sequential Search vs. Binary Search • Binary Search (with sorted array) • It first compares x with the middle item of the array. • If they are equal, the algorithm is done. • If x is smaller than the middle item, • then x must be in the first half of the array • and the algorithm repeats the searching procedure on the first half of the array. • If x is larger than the middle item, • then the search is repeated on the second half of the array. • This procedure is repeated until x is found or it is determined that x is not in the array.

  8. Importance of Efficient Algorithms • Sequential Search vs. Binary Search • Binary Search (with sorted array) index binsearch(intn, keytype[] S, keytypex) { index location, low, high, mid; low = 1; high = n; location = 0; while (low <= high && location == 0) { mid = (low + high) / 2; if (x == S[mid]) location = mid; else if (x < S[mid]) high = mid – 1; else low = mid + 1; } return location; }

  9. Importance of Efficient Algorithms • Sequential Search vs. Binary Search • What is the number of times the algorithm does the basic (or critical) operation for an instance of size n? • Sequential Search • Minimum (Best): 1 • Maximum (Worst): n • Binary Search • Minimum (Best): 1 • Maximum (Worst): log2n+1 • Array size – 16(=24)  # of the operation executions – 5 • Array size – 32(=25)  # of the operation executions – 6 • Array size – 64(=26)  # of the operation executions – 7 • … • Array size – 2k # of the operation executions – k+1 • Array size – n  # of the operation executions – log2n+1

  10. Importance of Efficient Algorithms • Sequential Search vs. Binary Search

  11. Importance of Efficient Algorithms • Fibonacci Sequence • 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, …

  12. Importance of Efficient Algorithms • Fibonacci Sequence: Recursive vs. Iterative • Recursive Algorithm • Recursive algorithms have… • Stopping condition • Recursive call of the function itself long fib(int n) { if (n <= 1) return n; else return (fib(n-1) + fib(n-2)); }

  13. Importance of Efficient Algorithms • Fibonacci Sequence: Recursive vs. Iterative • Recursive Algorithm • Demerits • So many “duplicate calculation” of the same values

  14. Importance of Efficient Algorithms • Fibonacci Sequence: Recursive vs. Iterative • Recursive Algorithm • The number of function calls • For an even number n n=2  above 2 n=4  above 22=4 n=6  above 23=8 … n=50  above 225=33554432

  15. Importance of Efficient Algorithms • Fibonacci Sequence: Recursive vs. Iterative • Iterative Algorithm long fib2 (int n) { index i; long[] f = new long[n+1]; f[0] = 0; if (n > 0) { f[1] = 1; for (i = 2; i <= n; i++) f[i] = f[i-1] + f[i-2]; } return f[n]; }

  16. Importance of Efficient Algorithms • Fibonacci Sequence: Recursive vs. Iterative • Iterative Algorithm • The number of f[i] calculations : n + 1 • Assume that it takes 1 nano second for each of “calculation” and “function call”

  17. [Programming Practice 1] • Sequential Search vs. Binary Search • Visit • http://link.koreatech.ac.kr/courses/2013_1/AP-KOICA/AP-KOICA20131.html • Download “SearchMain.java” and run it • Analyze the source codes • Complete the source codes while insert right codes within the two functions • public static intsequentialSearch() • public static intbinarySearch() • Compare the execution times of the two functions

More Related