Document

... Friends & Strong Induction Recursive Algorithm: •Assume you have an algorithm that works. •Use it to write an algorithm that works. ...

... Friends & Strong Induction Recursive Algorithm: •Assume you have an algorithm that works. •Use it to write an algorithm that works. ...

Phase Diagram for the Constrained Integer Partitioning Problem.

... Phase transitions in random combinatorial problems have been the subject of much recent attention. The random optimum partitioning problem is an exceedingly rare case of an NP-hard problem for which the existence of a sharp phase transition has been rigorously established, as have many detailed prop ...

... Phase transitions in random combinatorial problems have been the subject of much recent attention. The random optimum partitioning problem is an exceedingly rare case of an NP-hard problem for which the existence of a sharp phase transition has been rigorously established, as have many detailed prop ...

On intersecting a set of parallel line segments with a convex polygon

... Figure 9: The endpoints of e′ are to the left of the corresponding endpoints of e If we allow two segments to be on the same vertical line, then there will be at most 2 partition points on the left segment and two partition points on the right segment that satisfy the condition in Fact 4. A pair of ...

... Figure 9: The endpoints of e′ are to the left of the corresponding endpoints of e If we allow two segments to be on the same vertical line, then there will be at most 2 partition points on the left segment and two partition points on the right segment that satisfy the condition in Fact 4. A pair of ...

Streaming algorithms for embedding and computing edit distance in

... designing an embedding protocol, there is a major technical challenge when we do not have access to both of the strings at the same time and we should remove the mismatched characters. We do not know which one are those. Deleting symbols at random is unlikely to provide a good result. Moreover, we w ...

... designing an embedding protocol, there is a major technical challenge when we do not have access to both of the strings at the same time and we should remove the mismatched characters. We do not know which one are those. Deleting symbols at random is unlikely to provide a good result. Moreover, we w ...

... designing an embedding protocol, there is a major technical challenge when we do not have access to both of the strings at the same time and we should remove the mismatched characters. We do not know which one are those. Deleting symbols at random is unlikely to provide a good result. Moreover, we w ...

Chapter 22

... Returns a negative value if element1 is less than element2, a positive value if element1 is greater than element2, and zero if they are equal. public boolean equals(Object element) Returns true if the specified object is also a comparator and imposes the same ordering as this comparator. GeometricOb ...

... Returns a negative value if element1 is less than element2, a positive value if element1 is greater than element2, and zero if they are equal. public boolean equals(Object element) Returns true if the specified object is also a comparator and imposes the same ordering as this comparator. GeometricOb ...

3. Keyword Cover Search Module

... Recently, the spatial keyword search has received considerable attention from research community. Some existing works focus on retrieving individual objects by specifying a query consisting of a query location and a set of query keywords (or known as document in some context). Each retrieved object ...

... Recently, the spatial keyword search has received considerable attention from research community. Some existing works focus on retrieving individual objects by specifying a query consisting of a query location and a set of query keywords (or known as document in some context). Each retrieved object ...

Recursion

... • Recursive function - invokes itself directly or indirectly – direct recursion - function is invoked by a statement in its own body – indirect recursion - one function initiates a sequence of function invocations that eventually invokes the original ...

... • Recursive function - invokes itself directly or indirectly – direct recursion - function is invoked by a statement in its own body – indirect recursion - one function initiates a sequence of function invocations that eventually invokes the original ...

Order of Growth - inst.eecs.berkeley.edu

... interpreter. The program spends most of its time in the read-eval-print-loop (often called a REPL), which continuously reads a line of input, translates this into an expression object (we call this “parsing the input”), evaluates that expression object, and prints the result. Nearly all interpreters ...

... interpreter. The program spends most of its time in the read-eval-print-loop (often called a REPL), which continuously reads a line of input, translates this into an expression object (we call this “parsing the input”), evaluates that expression object, and prints the result. Nearly all interpreters ...

Lecture Notes for Algorithm Analysis and Design

... (ii) Most textbooks have far too much material for one semester and often intimidate an average student. Even when I pick and choose topics, the ones not covered have a distracting effect on the reader. (iii) Not prescribing a textbook in a course (that I have done in the past) creates insecurity am ...

... (ii) Most textbooks have far too much material for one semester and often intimidate an average student. Even when I pick and choose topics, the ones not covered have a distracting effect on the reader. (iii) Not prescribing a textbook in a course (that I have done in the past) creates insecurity am ...

Recursion (Ch. 10)

... Algorithm analysis There are usually several approaches (i.e., algorithms) to solve a problem. Which one is the right one? the best? Typically, the one that is fastest (for all or at least most real world inputs) How can we tell which algorithm is the fastest? • theoretical analysis • experimental a ...

... Algorithm analysis There are usually several approaches (i.e., algorithms) to solve a problem. Which one is the right one? the best? Typically, the one that is fastest (for all or at least most real world inputs) How can we tell which algorithm is the fastest? • theoretical analysis • experimental a ...

Chapter 19 Java Data Structures

... trick is to create a new larger array to replace the current array if the current array cannot hold new elements in the list. Initially, an array, say data of Object[] type, is created with a default size. When inserting a new element into the array, first ensure there is enough room in the array. I ...

... trick is to create a new larger array to replace the current array if the current array cannot hold new elements in the list. Initially, an array, say data of Object[] type, is created with a default size. When inserting a new element into the array, first ensure there is enough room in the array. I ...

... Algorithm analysis There are usually several approaches (i.e., algorithms) to solve a problem. Which one is the right one? the best? Typically, the one that is fastest (for all or at least most real world inputs) How can we tell which algorithm is the fastest? • theoretical analysis • experimental a ...

Computing intersections in a set of line segments: the Bentley

... Proof: Consider any position of the sweep line. We will show that each intersection among the dead segments has appeared as minimum element in the X-structure. If this claim is true, then the third if-then statement in the algorithm in Figure 1 implies that all intersections among the dead segments ...

... Proof: Consider any position of the sweep line. We will show that each intersection among the dead segments has appeared as minimum element in the X-structure. If this claim is true, then the third if-then statement in the algorithm in Figure 1 implies that all intersections among the dead segments ...

PDF - 4up

... is a collection of data stored sequentially. It supports insertion and deletion anywhere in the list. A stack can be perceived as a special type of the list where insertions and deletions take place only at the one end, referred to as the top of a stack. A queue represents a waiting list, where inse ...

... is a collection of data stored sequentially. It supports insertion and deletion anywhere in the list. A stack can be perceived as a special type of the list where insertions and deletions take place only at the one end, referred to as the top of a stack. A queue represents a waiting list, where inse ...

Variations of Diffie

... a machine M that can get a non-negligible advantage ε between D4 and R4 given any six-tuple (g1, g2, g3, u1, u2, u3), which comes from either R6 or D6 M’ runs M on the quadruple (g1g2, g3, u1u2, u3) and simply forwards the answer If the input comes from D4(D6 respectively), it outputs 1 and ...

... a machine M that can get a non-negligible advantage ε between D4 and R4 given any six-tuple (g1, g2, g3, u1, u2, u3), which comes from either R6 or D6 M’ runs M on the quadruple (g1g2, g3, u1u2, u3) and simply forwards the answer If the input comes from D4(D6 respectively), it outputs 1 and ...

Range-Efficient Counting of Distinct Elements in a Massive Data

... 1.3. Related work. Estimating F0 of a data stream is a very well studied problem, because of its importance in various database and networking applications. It is well known that computing F0 exactly requires space linear in the number of distinct values, in the worst case. Flajolet and Martin [FM85 ...

... 1.3. Related work. Estimating F0 of a data stream is a very well studied problem, because of its importance in various database and networking applications. It is well known that computing F0 exactly requires space linear in the number of distinct values, in the worst case. Flajolet and Martin [FM85 ...

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 ...

STP A Decision Procedure for Bit

... Protocol Replay: Try to reproduce a dialog between an initiator and a network host Auto Generation of modules for honeypots so that they can correctly respond to connection attempts by worms ...

... Protocol Replay: Try to reproduce a dialog between an initiator and a network host Auto Generation of modules for honeypots so that they can correctly respond to connection attempts by worms ...

recursively

... How many students total are directly behind you in your "column" of the classroom? – You have poor vision, so you can see only the people right next to you. So you can't just look back and count. – But you are allowed to ask questions of the person next to you. ...

... How many students total are directly behind you in your "column" of the classroom? – You have poor vision, so you can see only the people right next to you. So you can't just look back and count. – But you are allowed to ask questions of the person next to you. ...

TCSS 343: Large Integer Multiplication Suppose we want to multiply

... Since we can multiply two 1-bit integers in constant time, T(1) = 1. (If we wanted to be more accurate, we would say T(1) = d, for some constant d.) In the recursive case, in order to multiply two n-bit integers, we need to solve three instances of the problem of multiplying two (n/2)-bit integers a ...

... Since we can multiply two 1-bit integers in constant time, T(1) = 1. (If we wanted to be more accurate, we would say T(1) = d, for some constant d.) In the recursive case, in order to multiply two n-bit integers, we need to solve three instances of the problem of multiplying two (n/2)-bit integers a ...

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

... In a nutshell, we propose to choose, at any point of the search, the algorithm which has the best predicted performance to run (for one generation). A typical scenario of running our algorithm is that after some trials in which each algorithm runs in parallel and interacts indirectly, an algorithm w ...

... In a nutshell, we propose to choose, at any point of the search, the algorithm which has the best predicted performance to run (for one generation). A typical scenario of running our algorithm is that after some trials in which each algorithm runs in parallel and interacts indirectly, an algorithm w ...

# Quicksort

Quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order. Developed by Tony Hoare in 1959, with his work published in 1961, it is still a commonly used algorithm for sorting. When implemented well, it can be about two or three times faster than its main competitors, merge sort and heapsort.Quicksort is a comparison sort, meaning that it can sort items of any type for which a ""less-than"" relation (formally, a total order) is defined. In efficient implementations it is not a stable sort, meaning that the relative order of equal sort items is not preserved. Quicksort can operate in-place on an array, requiring small additional amounts of memory to perform the sorting.Mathematical analysis of quicksort shows that, on average, the algorithm takes O(n log n) comparisons to sort n items. In the worst case, it makes O(n2) comparisons, though this behavior is rare.