and two-dimensional arrays

... into the array before any information can be retrieved from it • These initial values can be assigned to the elements of the array as constants, or they can be read into the array from a file Simple Program Design, Fourth Edition Chapter 7 ...

... into the array before any information can be retrieved from it • These initial values can be assigned to the elements of the array as constants, or they can be read into the array from a file Simple Program Design, Fourth Edition Chapter 7 ...

Solution

... big-Oh notation) or cite one of the rules given in the book or in the lecture slides. (a) Show that if f(n) is O(g(n)) and d(n) is O(h(n)), then f(n)+d(n) is O(g(n)+ h(n)). Solution Recall the de_nition of big-Oh notation: we need constants c > 0 and n0 _ 1 such that f(n) + d(n) _ c(g(n) + h(n)) for ...

... big-Oh notation) or cite one of the rules given in the book or in the lecture slides. (a) Show that if f(n) is O(g(n)) and d(n) is O(h(n)), then f(n)+d(n) is O(g(n)+ h(n)). Solution Recall the de_nition of big-Oh notation: we need constants c > 0 and n0 _ 1 such that f(n) + d(n) _ c(g(n) + h(n)) for ...

Chapter 10

... searching is always at the bottom of the list, it will take many comparisons to find the searchItem. Also, if the searchItem for which we are searching is not in the list, then we will compare the searchItem with every element in the list. A sequential search is therefore not efficient for large lis ...

... searching is always at the bottom of the list, it will take many comparisons to find the searchItem. Also, if the searchItem for which we are searching is not in the list, then we will compare the searchItem with every element in the list. A sequential search is therefore not efficient for large lis ...

High Dimensional Similarity Joins: Algorithms and Performance

... Multidimensional divide and conquer creates 2d partitions of the space and thus needs 2d output buers during the partitioning phase. In summary, we expect that such an approach might be suitable for low dimensionalities and data sets with similar statistical characteristics, but it is not promisin ...

... Multidimensional divide and conquer creates 2d partitions of the space and thus needs 2d output buers during the partitioning phase. In summary, we expect that such an approach might be suitable for low dimensionalities and data sets with similar statistical characteristics, but it is not promisin ...

Range-Efficient Counting of Distinct Elements in a Massive Data

... space linear in the input size. Thus, we focus on designing randomized approximation schemes for range-eﬃcient computation of F0 . Definition 1. For parameters 0 < < 1 and 0 < δ < 1, an (, δ)-estimator for a number Y is a random variable X such that Pr[|X − Y | > Y ] < δ. 1.1. Our results. We co ...

... space linear in the input size. Thus, we focus on designing randomized approximation schemes for range-eﬃcient computation of F0 . Definition 1. For parameters 0 < < 1 and 0 < δ < 1, an (, δ)-estimator for a number Y is a random variable X such that Pr[|X − Y | > Y ] < δ. 1.1. Our results. We co ...

document

... 2) If the size of the array is omitted, an array just big enough to hold the initialization is created. Therefore, if the user writes: E.g : int Array[] = {1,2,5,10,-3}; An array similar to the one mentioned above is created with the declared elements. This is very useful in that the size of the arr ...

... 2) If the size of the array is omitted, an array just big enough to hold the initialization is created. Therefore, if the user writes: E.g : int Array[] = {1,2,5,10,-3}; An array similar to the one mentioned above is created with the declared elements. This is very useful in that the size of the arr ...

W. Dean. Algorithms and the mathematical foundations of computer

... of the concept natural number. In order to defend this view, it is usually understood to be incumbent on the neo-logicist not only to defend this claim, but also to respond to traditional challenges such as the so-called Bad Company objection and the Julius Caesar problem, which might appear to stan ...

... of the concept natural number. In order to defend this view, it is usually understood to be incumbent on the neo-logicist not only to defend this claim, but also to respond to traditional challenges such as the so-called Bad Company objection and the Julius Caesar problem, which might appear to stan ...

Constant-Time Local Computation Algorithms

... constant time (e.g., coloring). They conclude that there are non-trivial LCL algorithms with constant-time distributed algorithms (an example is weak coloring on graphs of odd degree, where weak coloring means that every vertex has at least one neighbor colored differently from it). Cole and Vishkin ...

... constant time (e.g., coloring). They conclude that there are non-trivial LCL algorithms with constant-time distributed algorithms (an example is weak coloring on graphs of odd degree, where weak coloring means that every vertex has at least one neighbor colored differently from it). Cole and Vishkin ...

apworkshoparrays

... answer to these questions is simple -- it is the art of programming a computer. It is the art of designing efficient and elegant methods of getting a computer to solve problems, theoretical or practical, small or large, simple or complex. It is the art of translating this design into an effective an ...

... answer to these questions is simple -- it is the art of programming a computer. It is the art of designing efficient and elegant methods of getting a computer to solve problems, theoretical or practical, small or large, simple or complex. It is the art of translating this design into an effective an ...

Paper ~ Which Algorithm Should I Choose At Any Point of the

... difficult feature-algorithm mapping can be learnt satisfactorily. Even if the above two requirements have been met, given an unknown problem, a preliminary uniform sampling has to be done to extract the features; the sampling may be biased due to the alias errors generated by under-sampling [17]. ...

... difficult feature-algorithm mapping can be learnt satisfactorily. Even if the above two requirements have been met, given an unknown problem, a preliminary uniform sampling has to be done to extract the features; the sampling may be biased due to the alias errors generated by under-sampling [17]. ...

6.896 Project Presentations

... • Identify all load and store operations in user code, and replace them with calls to functions from the runtime system. • Implement the runtime system. An initial implementation is to divide memory into blocks and to use a hash table to store a lock and backup values for each block. • Experiment wi ...

... • Identify all load and store operations in user code, and replace them with calls to functions from the runtime system. • Implement the runtime system. An initial implementation is to divide memory into blocks and to use a hash table to store a lock and backup values for each block. • Experiment wi ...

Counting Inversions, Offline Orthogonal Range Counting, and Related Problems Timothy M. Chan

... of improved algorithms and data structures. sense to look at the preprocessing time more carefully. Unfortunately, it is not known how to construct a Offline orthogonal range counting. A slightly data structure with optimal query performance in linear trickier version (Section 2.2) of our initial√ a ...

... of improved algorithms and data structures. sense to look at the preprocessing time more carefully. Unfortunately, it is not known how to construct a Offline orthogonal range counting. A slightly data structure with optimal query performance in linear trickier version (Section 2.2) of our initial√ a ...

The Unbearable Lightness of Consensus

... From fail-stop to fail-silent We assume a majority of correct processes In the 1-N algorithm, the writer writes in a majority using a timestamp determined locally and the reader selects a value from a majority and then imposes this value on a majority In the N-N algorithm, the writers determi ...

... From fail-stop to fail-silent We assume a majority of correct processes In the 1-N algorithm, the writer writes in a majority using a timestamp determined locally and the reader selects a value from a majority and then imposes this value on a majority In the N-N algorithm, the writers determi ...

Wavelength management in WDM rings to maximize the

... of the maxRPC and maxPC problems are their profit versions where connections (or paths) are associated with non-negative profits and the objective is to color with at most w colors a set of connections (or paths) with the maximum total profit. A simple iterative algorithm has approximation ratio 1.5 ...

... of the maxRPC and maxPC problems are their profit versions where connections (or paths) are associated with non-negative profits and the objective is to color with at most w colors a set of connections (or paths) with the maximum total profit. A simple iterative algorithm has approximation ratio 1.5 ...

Analysis of Algorithms

... 1. O() is used for upper bounds “grows slower than”! 2. Ω() used for lower bounds “grows faster than”! 3. Θ() used for denoting matching upper and lower bounds. “grows as fast as”! These are bounds on running time, not for the problem! The thumbrules for getting the running time are! 1. Throw away a ...

... 1. O() is used for upper bounds “grows slower than”! 2. Ω() used for lower bounds “grows faster than”! 3. Θ() used for denoting matching upper and lower bounds. “grows as fast as”! These are bounds on running time, not for the problem! The thumbrules for getting the running time are! 1. Throw away a ...

ppt

... – A square matrix M such that the matrix power Mk=M for k a positive integer is called a periodic matrix. – If k is the least such integer, then the matrix is said to have period k. – If k = 1, then M2 = M and M is called idempotent. ...

... – A square matrix M such that the matrix power Mk=M for k a positive integer is called a periodic matrix. – If k is the least such integer, then the matrix is said to have period k. – If k = 1, then M2 = M and M is called idempotent. ...

Document

... • Step 1: If the problem size is small, solve this problem directly; otherwise, split the original problem into 2 sub-problems with equal sizes. • Step 2: Recursively solve these 2 sub-problems by applying this algorithm. • Step 3: Merge the solutions of the 2 sub-problems into a solution of the ori ...

... • Step 1: If the problem size is small, solve this problem directly; otherwise, split the original problem into 2 sub-problems with equal sizes. • Step 2: Recursively solve these 2 sub-problems by applying this algorithm. • Step 3: Merge the solutions of the 2 sub-problems into a solution of the ori ...

Speeding Up HMM Decoding and Training by Exploiting Sequence

... guarantees no degradation in efficiency even when k > log n and is experimentally more than five times faster than VA. 4. The same speedup factors apply to the Viterbi training algorithm. 5. For the Baum-Welch training algorithm, we show how to preprocess a repeated substring of size ` once in O(`k ...

... guarantees no degradation in efficiency even when k > log n and is experimentally more than five times faster than VA. 4. The same speedup factors apply to the Viterbi training algorithm. 5. For the Baum-Welch training algorithm, we show how to preprocess a repeated substring of size ` once in O(`k ...

Data Structures Lecture 15 Name:__________________

... 2) Consider the coin-change problem: Given a set of coin types and an amount of change to be returned, determine the fewest number of coins for this amount of change. a) What "greedy" algorithm would you use to solve this problem with US coin types of {1, 5, 10, 25, 50} and a change amount of 29-cen ...

... 2) Consider the coin-change problem: Given a set of coin types and an amount of change to be returned, determine the fewest number of coins for this amount of change. a) What "greedy" algorithm would you use to solve this problem with US coin types of {1, 5, 10, 25, 50} and a change amount of 29-cen ...

Efficient Algorithms and Problem Complexity

... Remarks Regarding nextFit The performance ratio is indeed 2, i.e., for some instances, nextFit uses (almost) twice as many bins as is optimal. [Can you find one?] It is an online algorithm: items are processed as they arrive. It is a 1-bounded-space algorithm: at most one bin is open at a time. Thes ...

... Remarks Regarding nextFit The performance ratio is indeed 2, i.e., for some instances, nextFit uses (almost) twice as many bins as is optimal. [Can you find one?] It is an online algorithm: items are processed as they arrive. It is a 1-bounded-space algorithm: at most one bin is open at a time. Thes ...

The Scala Experience Safe Programming Can be Fun!

... • Worst case analysis • Size of the inspected array: n n/2 n/4 ….. 1 • Each step is very fast (a small constant number of operations) • There are log2(n) such steps • So it takes ~ log2(n) steps per search • Much faster then ~ n ...

... • Worst case analysis • Size of the inspected array: n n/2 n/4 ….. 1 • Each step is very fast (a small constant number of operations) • There are log2(n) such steps • So it takes ~ log2(n) steps per search • Much faster then ~ n ...

Randomized local-spin mutual exclusion

... MX lock. Then spin trying to capture node lock. • In addition to randomized and deterministic promotion, an exiting process promotes also the process that holds the MX lock, if any. ...

... MX lock. Then spin trying to capture node lock. • In addition to randomized and deterministic promotion, an exiting process promotes also the process that holds the MX lock, if any. ...

UNIT-I - WordPress.com

... omega notation represent the lower bound of an algorithm’s running time, i.e. we can give smallest amount of time taken by the algorithm to complete. Let f(n) and g(n) be the two non-negative functions. We say that f(n) is said to be O(g(n)) if and only if there exists a positive constant ‘c’ and ...

... omega notation represent the lower bound of an algorithm’s running time, i.e. we can give smallest amount of time taken by the algorithm to complete. Let f(n) and g(n) be the two non-negative functions. We say that f(n) is said to be O(g(n)) if and only if there exists a positive constant ‘c’ and ...

Python XML Element Trees

... Unfortunately, sorting the address book is not completely successful because the operation does not correctly manage the indentation used in the example. This is a general problem with sorting the contents of an XML element that is of mixed complex type. In this case, it can be fixed by applying the ...

... Unfortunately, sorting the address book is not completely successful because the operation does not correctly manage the indentation used in the example. This is a general problem with sorting the contents of an XML element that is of mixed complex type. In this case, it can be fixed by applying the ...

# Sorting algorithm

A sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the use of other algorithms (such as search and merge algorithms) which require input data to be in sorted lists; it is also often useful for canonicalizing data and for producing human-readable output. More formally, the output must satisfy two conditions: The output is in nondecreasing order (each element is no smaller than the previous element according to the desired total order); The output is a permutation (reordering) of the input.Further, the data is often taken to be in an array, which allows random access, rather than a list, which only allows sequential access, though often algorithms can be applied with suitable modification to either type of data.Since the dawn of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. For example, bubble sort was analyzed as early as 1956. A fundamental limit of comparison sorting algorithms is that they require linearithmic time – O(n log n) – in the worst case, though better performance is possible on real-world data (such as almost-sorted data), and algorithms not based on comparison, such as counting sort, can have better performance. Although many consider sorting a solved problem – asymptotically optimal algorithms have been known since the mid-20th century – useful new algorithms are still being invented, with the now widely used Timsort dating to 2002, and the library sort being first published in 2006.Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures such as heaps and binary trees, randomized algorithms, best, worst and average case analysis, time-space tradeoffs, and upper and lower bounds.