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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

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Algorithms

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  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

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