Theory - NUS School of Computing
... Step 2: If the symbol being read is 1, then write a 0, move the head right, and Repeat Step 2. If the symbol being read is B, then move right, and go to Step 3. Step 3: If the symbol begin read is 1, then write a 2, move the head right, and repeat Step 3. If the symbol being read is B, then go to St ...
... Step 2: If the symbol being read is 1, then write a 0, move the head right, and Repeat Step 2. If the symbol being read is B, then move right, and go to Step 3. Step 3: If the symbol begin read is 1, then write a 2, move the head right, and repeat Step 3. If the symbol being read is B, then go to St ...
File
... multipliers are ignored. So a O(4n) algorithm is equivalent to O(n), which is how it should be written. • If f(n) and g(n) are functions defined on positive integer number n, then f(n) = O(g(n)) • That is, f of n is big oh of g of n if and only if there exists positive constants c and n, such that f ...
... multipliers are ignored. So a O(4n) algorithm is equivalent to O(n), which is how it should be written. • If f(n) and g(n) are functions defined on positive integer number n, then f(n) = O(g(n)) • That is, f of n is big oh of g of n if and only if there exists positive constants c and n, such that f ...
thm11 - parallel algo intro
... For example, W1(n) = O(n) and W2(n) = O(n log n) • Consider two parallel algorithms A1and A2 for the same problem. A1: W1(n) work in T1(n) time. A2: W2(n) work in T2(n) time. If W1(n) and W2(n) are asymptotically the same then A1 is more efficient than A2 if T1(n) = o(T2(n)). For example, W1(n) = W2 ...
... For example, W1(n) = O(n) and W2(n) = O(n log n) • Consider two parallel algorithms A1and A2 for the same problem. A1: W1(n) work in T1(n) time. A2: W2(n) work in T2(n) time. If W1(n) and W2(n) are asymptotically the same then A1 is more efficient than A2 if T1(n) = o(T2(n)). For example, W1(n) = W2 ...
Lecture
... known as the base case. • Every recursive algorithm must have a base case. • The rest of the algorithm is known as the general case. The general case contains the logic needed to reduce the size of the ...
... known as the base case. • Every recursive algorithm must have a base case. • The rest of the algorithm is known as the general case. The general case contains the logic needed to reduce the size of the ...
Rishi B. Jethwa and Mayank Agarwal
... links all the points together. The constraint on TSP is that the first and the last point the tour should be same and the edges cannot be repeated. Vertices can be repeated. No polynomial solution exists for this type of problems which has alas combinatory solutions. So we are interested in mainly g ...
... links all the points together. The constraint on TSP is that the first and the last point the tour should be same and the edges cannot be repeated. Vertices can be repeated. No polynomial solution exists for this type of problems which has alas combinatory solutions. So we are interested in mainly g ...
Joint Regression and Linear Combination of Time
... where S1 and S2 are row selection matrices and D a diagonal matrix which contains the shift monomial on the diagonal. S1 will select the first mB linear independent rows of K. The canonical kernel K is unfortunately unknown but a numerical basis Z for the kernel can be computed from either the SVD o ...
... where S1 and S2 are row selection matrices and D a diagonal matrix which contains the shift monomial on the diagonal. S1 will select the first mB linear independent rows of K. The canonical kernel K is unfortunately unknown but a numerical basis Z for the kernel can be computed from either the SVD o ...
Algorithms examples Correctness and testing
... • Run your tests by redirecting the standard input and (eventually) the standard output to capture the results. If the input test file is input.txt and the results file is output.txt you can run your program from the ...
... • Run your tests by redirecting the standard input and (eventually) the standard output to capture the results. If the input test file is input.txt and the results file is output.txt you can run your program from the ...
Algorithms, Complexity and Quantum Fourier Transform
... power to computation. It is very likely that the primalitytesting is not an exception and any randomised algorithm can be derandomised. Even though it is yet to be demonstrated, there are many indications that P equals BP P . Last but not least we have quantum algorithms, or families of quantum netw ...
... power to computation. It is very likely that the primalitytesting is not an exception and any randomised algorithm can be derandomised. Even though it is yet to be demonstrated, there are many indications that P equals BP P . Last but not least we have quantum algorithms, or families of quantum netw ...
Notes for Lecture 11
... if the length of P is n-1 then by adding edge (u, v) we obtain a Hamilton circuit in G. Step 3: if no Hamilton circuit is found for every (u, v) then ...
... if the length of P is n-1 then by adding edge (u, v) we obtain a Hamilton circuit in G. Step 3: if no Hamilton circuit is found for every (u, v) then ...
lecture1212
... if the length of P is n-1 then by adding edge (u, v) we obtain a Hamilton circuit in G. Step 3: if no Hamilton circuit is found for every (u, v) then ...
... if the length of P is n-1 then by adding edge (u, v) we obtain a Hamilton circuit in G. Step 3: if no Hamilton circuit is found for every (u, v) then ...
Algorithms Lecture 5 Name:___________________________
... might be more efficient. Assume that I had a simple Θ(n2) sorting algorithm with n = 100, then there is roughly 1002 / 2 or 5,000 amount of work. Suppose I split the problem down into two smaller problems of size 50. If I run the n2 algorithm on both smaller problems of size 50, then what would be ...
... might be more efficient. Assume that I had a simple Θ(n2) sorting algorithm with n = 100, then there is roughly 1002 / 2 or 5,000 amount of work. Suppose I split the problem down into two smaller problems of size 50. If I run the n2 algorithm on both smaller problems of size 50, then what would be ...
Integer Multiplication Algorithm Learning Objectives
... For most of the time we will be considering a computational model where individual elements in the matrices are viewed as “small” and can be added or multiplied in constant time. Today however, we talk about an algorithm for multiplying very large numbers.Say, we want to multiply two n-bit numbers: ...
... For most of the time we will be considering a computational model where individual elements in the matrices are viewed as “small” and can be added or multiplied in constant time. Today however, we talk about an algorithm for multiplying very large numbers.Say, we want to multiply two n-bit numbers: ...
String-Matching Problem
... Rabin-Karp Algorithm Correctness: T is a string of
characters over an alphabet of size d, P
is string of characters over an alphabet of
size d and |P| <= |T|, d is the size of the
alphabet and q is a prime number
...
... Rabin-Karp Algorithm Correctness
Approaching P=NP: Can Soap Bubbles Solve The Steiner Tree
... Soap is rumored to solve the Steiner Tree Problem (STP). Steiner Tree Problem: Description: Given a weighted graph G, G(V,E,w), where V is the set of vertices, E is the set of edges, and w is the set of weights, and S, a subset of V, find the subset of G that contains S and has the minimum weight. ...
... Soap is rumored to solve the Steiner Tree Problem (STP). Steiner Tree Problem: Description: Given a weighted graph G, G(V,E,w), where V is the set of vertices, E is the set of edges, and w is the set of weights, and S, a subset of V, find the subset of G that contains S and has the minimum weight. ...
Particle Bee Algorithm (PBA), Particle Swarm
... prefabrication units such as steel beams, ready mixed concrete, prefabricated elements and large panel formwork such as machinery and equipment, and a wide variety of other building materials within a construction site. However, it is a difficult combinatorial optimization problem to determine the l ...
... prefabrication units such as steel beams, ready mixed concrete, prefabricated elements and large panel formwork such as machinery and equipment, and a wide variety of other building materials within a construction site. However, it is a difficult combinatorial optimization problem to determine the l ...
Tutorial 1 C++ Programming
... • What is the time complexity of f(n), if g(n) is: To answer this, we must draw the recursive execution tree… a) g(n) = O(1) O(n), a sum of geometric series of 1+2+4+…+2log2 n = 1+2+4+…+n = c*n b) g(n) = O(n) O(n log n), a sum of (n+n+n+…+n) log2 n times, so, n log n c) g(n) = O(n2) O(n2), a sum of ...
... • What is the time complexity of f(n), if g(n) is: To answer this, we must draw the recursive execution tree… a) g(n) = O(1) O(n), a sum of geometric series of 1+2+4+…+2log2 n = 1+2+4+…+n = c*n b) g(n) = O(n) O(n log n), a sum of (n+n+n+…+n) log2 n times, so, n log n c) g(n) = O(n2) O(n2), a sum of ...
Embedded Algorithm in Hardware: A Scalable Compact Genetic
... Distribution Algorithm and Block-based Neural Network as an Evolvable Hardware", IEEE Congress on Evolutionary Computation, Hong Kong, June 1-6, 2008, pp.3365-3372. Jewajinda, Y. and Chongstitvatana, P., "A Cooperative Approach to Compact Genetic Algorithm for Evolvable Hardware", IEEE World Congres ...
... Distribution Algorithm and Block-based Neural Network as an Evolvable Hardware", IEEE Congress on Evolutionary Computation, Hong Kong, June 1-6, 2008, pp.3365-3372. Jewajinda, Y. and Chongstitvatana, P., "A Cooperative Approach to Compact Genetic Algorithm for Evolvable Hardware", IEEE World Congres ...
Slides
... • P is the class of problems that can be solved in polynomial Tme – These problems are considered tractable – Problems that are not in P are considered intractable ...
... • P is the class of problems that can be solved in polynomial Tme – These problems are considered tractable – Problems that are not in P are considered intractable ...
Bioinformatics Questions
... CMPT 881 (2007): Introduction to Computational Biology Assignment #1, Due October 22 in class Instructions: The questions below are of varying difficulty. Your mark will be based on your overall performance on the assignment. Answering only the easy and straightforward questions may get you a lowe ...
... CMPT 881 (2007): Introduction to Computational Biology Assignment #1, Due October 22 in class Instructions: The questions below are of varying difficulty. Your mark will be based on your overall performance on the assignment. Answering only the easy and straightforward questions may get you a lowe ...