Lecture 11: Algorithms - United International College
... the value of a term if the term exceeds the maximum of the terms previously examined. • Finiteness: it terminates after all the integers in the sequence have been examined. • Effectiveness: the algorithm can be carried out in a finite amount of time since each step is either a comparison or an assig ...
... the value of a term if the term exceeds the maximum of the terms previously examined. • Finiteness: it terminates after all the integers in the sequence have been examined. • Effectiveness: the algorithm can be carried out in a finite amount of time since each step is either a comparison or an assig ...
Lecture Notes: Variance, Law of Large Numbers, Central Limit
... Example. Let Sn be the number of heads on n tosses of a fair coin. Let’s estimate the probability that the number of heads for n = 100 is between 40 and 60. Since E(S100 ) = 50, we are asking for the complement of the probability that the number of heads is at least 61 or at most 39; in other words, ...
... Example. Let Sn be the number of heads on n tosses of a fair coin. Let’s estimate the probability that the number of heads for n = 100 is between 40 and 60. Since E(S100 ) = 50, we are asking for the complement of the probability that the number of heads is at least 61 or at most 39; in other words, ...
A Randomized Approximate Nearest Neighbors
... Given a collection of n points x1 , x2 , . . . , xn in Rd and an integer k << n, the task of finding the k nearest neighbors for each xi is known as the “Nearest Neighbors Problem”; it is ubiquitous in a number of areas of Computer Science: Machine Learning, Data Mining, Artificial Intelligence, etc ...
... Given a collection of n points x1 , x2 , . . . , xn in Rd and an integer k << n, the task of finding the k nearest neighbors for each xi is known as the “Nearest Neighbors Problem”; it is ubiquitous in a number of areas of Computer Science: Machine Learning, Data Mining, Artificial Intelligence, etc ...
Lecture 4 Divide and Conquer Maximum/minimum Median finding
... number (the median corresponds to k = dn/2e). Given an array A[1, 2, . . . , n], one algorithm for selecting the kth smallest element is simply to sort A then return A[dn/2e]. This takes Θ(n log n) time using, say, MergeSort. How could we hope to do better? Well, suppose we had a black box that gave ...
... number (the median corresponds to k = dn/2e). Given an array A[1, 2, . . . , n], one algorithm for selecting the kth smallest element is simply to sort A then return A[dn/2e]. This takes Θ(n log n) time using, say, MergeSort. How could we hope to do better? Well, suppose we had a black box that gave ...
Lecture No. 10(A) : Method of Conditional Probabilities 1 - CSE-IITM
... r-clique, hence for all such n, r, R(r, r) > n. The above analysis also guarantees that for ...
... r-clique, hence for all such n, r, R(r, r) > n. The above analysis also guarantees that for ...
Applications of Number Theory in Computer Science Curriculum
... The correct value is 0.53 To provide an intuitive explanation of why the probability is so low, one may point out that 1 arrives not so frequently, since the probability that 1 is sent is only 0.2, and it makes a small sample To get good, results one needs to take a large sample This can be explaine ...
... The correct value is 0.53 To provide an intuitive explanation of why the probability is so low, one may point out that 1 arrives not so frequently, since the probability that 1 is sent is only 0.2, and it makes a small sample To get good, results one needs to take a large sample This can be explaine ...
Powerpoint slides
... Gaussian distribution (of any radius) • This implies a 2n time algorithm for SVP • Recent work by my coauthors: also CVP in 2n ! A close inspection of our algorithm shows that 2n/2 should be the right answer • So far we are only able to achieve that above ...
... Gaussian distribution (of any radius) • This implies a 2n time algorithm for SVP • Recent work by my coauthors: also CVP in 2n ! A close inspection of our algorithm shows that 2n/2 should be the right answer • So far we are only able to achieve that above ...
Where are the hard problems
... • p1 the probability of a constraint •between variables Vi and Vj • p2 probability Vi=x and Vj=y are in conflict ...
... • p1 the probability of a constraint •between variables Vi and Vj • p2 probability Vi=x and Vj=y are in conflict ...
1 What is the Subset Sum Problem? 2 An Exact Algorithm for the
... In iteration i, we compute the sums of all subsets of {x1 , x2 , ..., xi }, using as a starting point the sums of all subsets of {x1 , x2 , ..., xi−1 }. Once we find the sum of a subset S’ is greater than t, we ignore that sum, as there is no reason to maintain it. No superset of S’ can possibly be ...
... In iteration i, we compute the sums of all subsets of {x1 , x2 , ..., xi }, using as a starting point the sums of all subsets of {x1 , x2 , ..., xi−1 }. Once we find the sum of a subset S’ is greater than t, we ignore that sum, as there is no reason to maintain it. No superset of S’ can possibly be ...
Fisher–Yates shuffle
The Fisher–Yates shuffle (named after Ronald Fisher and Frank Yates), also known as the Knuth shuffle (after Donald Knuth), is an algorithm for generating a random permutation of a finite set—in plain terms, for randomly shuffling the set. A variant of the Fisher–Yates shuffle, known as Sattolo's algorithm, may be used to generate random cyclic permutations of length n instead. The Fisher–Yates shuffle is unbiased, so that every permutation is equally likely. The modern version of the algorithm is also rather efficient, requiring only time proportional to the number of items being shuffled and no additional storage space.Fisher–Yates shuffling is similar to randomly picking numbered tickets (combinatorics: distinguishable objects) out of a hat without replacement until there are none left.