Closest pair problems (Divide and Conquer)
•
1 like•354 views
The document describes the divide and conquer algorithm for solving the closest pair problem. It divides the set of points into two equal subsets, recursively finds the closest pairs within each subset, and then examines point pairs between the two subsets that fall within a strip of width 2d, where d is the minimum of the closest pairs in each subset. It scans points within this strip to update the closest pair distance. The runtime of this algorithm is O(n log n) when applying the Master Theorem.
Report
Share
Report
Share
Recommended
CLOSEST PAIR (Final)
This document describes the closest pair problem and an efficient divide and conquer algorithm to solve it in O(n log n) time. The problem is to find the shortest distance between any two points in a set of n points. A naive O(n2) brute force approach compares all pairs of points. The divide and conquer approach partitions the points into halves, solves the subproblems recursively, and merges the results by checking at most 6 points within a rectangle region to find the closest pair between subsets.
Quick sort
Quicksort is a sorting algorithm that works by partitioning an array around a pivot value, and then recursively sorting the sub-partitions. It chooses a pivot element and partitions the array based on whether elements are less than or greater than the pivot. Elements are swapped so that those less than the pivot are moved left and those greater are moved right. The process recursively partitions the sub-arrays until the entire array is sorted.
Merge sort algorithm power point presentation
This is a merge sort algorithm presentation. Those are want to learn merge sort by a simple example , he/she can watch to understand easily
Greedy Algorihm
This document outlines greedy algorithms, their characteristics, and examples of their use. Greedy algorithms make locally optimal choices at each step in the hopes of finding a global optimum. They are simple to implement and fast, but may not always reach the true optimal solution. Examples discussed include coin changing, traveling salesman, minimum spanning trees using Kruskal's and Prim's algorithms, and Huffman coding.
B tree
B+ trees are balanced search trees where all data records are stored in the leaf nodes and internal nodes store only keys. Records are accessed faster through linked leaf nodes. Nodes must be at least half full, and internal nodes have between n/2 and n child nodes. Search, insertion, and deletion operations may cause nodes to split or combine to maintain balance. B+ trees are commonly used to index large files to enable efficient retrieval of records.
Stressen's matrix multiplication
Strassen's algorithm improves on the basic matrix multiplication algorithm which runs in O(N3) time. It achieves this by dividing the matrices into sub-matrices and performing 7 multiplications and 18 additions on the sub-matrices, rather than the 8 multiplications of the basic algorithm. This results in a runtime of O(N2.81) using divide and conquer, providing an asymptotic improvement over the basic O(N3) algorithm.
Divide and Conquer - Part 1
Divide and Conquer Algorithms - D&C forms a distinct algorithm design technique in computer science, wherein a problem is solved by repeatedly invoking the algorithm on smaller occurrences of the same problem. Binary search, merge sort, Euclid's algorithm can all be formulated as examples of divide and conquer algorithms. Strassen's algorithm and Nearest Neighbor algorithm are two other examples.
And or graph
The document discusses AND/OR graphs, which are a type of graph or tree used to represent solutions to problems that can be decomposed into smaller subproblems. AND/OR graphs have nodes that represent goals or states, with successors labeled as either AND or OR branches. AND branches signify subgoals that must all be achieved to satisfy the parent goal, while OR branches indicate alternative subgoals that could achieve the parent goal. The graph helps model how decomposed subproblems relate and their solutions combine to solve the overall problem.
Recommended
CLOSEST PAIR (Final)
This document describes the closest pair problem and an efficient divide and conquer algorithm to solve it in O(n log n) time. The problem is to find the shortest distance between any two points in a set of n points. A naive O(n2) brute force approach compares all pairs of points. The divide and conquer approach partitions the points into halves, solves the subproblems recursively, and merges the results by checking at most 6 points within a rectangle region to find the closest pair between subsets.
Quick sort
Quicksort is a sorting algorithm that works by partitioning an array around a pivot value, and then recursively sorting the sub-partitions. It chooses a pivot element and partitions the array based on whether elements are less than or greater than the pivot. Elements are swapped so that those less than the pivot are moved left and those greater are moved right. The process recursively partitions the sub-arrays until the entire array is sorted.
Merge sort algorithm power point presentation
This is a merge sort algorithm presentation. Those are want to learn merge sort by a simple example , he/she can watch to understand easily
Greedy Algorihm
This document outlines greedy algorithms, their characteristics, and examples of their use. Greedy algorithms make locally optimal choices at each step in the hopes of finding a global optimum. They are simple to implement and fast, but may not always reach the true optimal solution. Examples discussed include coin changing, traveling salesman, minimum spanning trees using Kruskal's and Prim's algorithms, and Huffman coding.
B tree
B+ trees are balanced search trees where all data records are stored in the leaf nodes and internal nodes store only keys. Records are accessed faster through linked leaf nodes. Nodes must be at least half full, and internal nodes have between n/2 and n child nodes. Search, insertion, and deletion operations may cause nodes to split or combine to maintain balance. B+ trees are commonly used to index large files to enable efficient retrieval of records.
Stressen's matrix multiplication
Strassen's algorithm improves on the basic matrix multiplication algorithm which runs in O(N3) time. It achieves this by dividing the matrices into sub-matrices and performing 7 multiplications and 18 additions on the sub-matrices, rather than the 8 multiplications of the basic algorithm. This results in a runtime of O(N2.81) using divide and conquer, providing an asymptotic improvement over the basic O(N3) algorithm.
Divide and Conquer - Part 1
Divide and Conquer Algorithms - D&C forms a distinct algorithm design technique in computer science, wherein a problem is solved by repeatedly invoking the algorithm on smaller occurrences of the same problem. Binary search, merge sort, Euclid's algorithm can all be formulated as examples of divide and conquer algorithms. Strassen's algorithm and Nearest Neighbor algorithm are two other examples.
And or graph
The document discusses AND/OR graphs, which are a type of graph or tree used to represent solutions to problems that can be decomposed into smaller subproblems. AND/OR graphs have nodes that represent goals or states, with successors labeled as either AND or OR branches. AND branches signify subgoals that must all be achieved to satisfy the parent goal, while OR branches indicate alternative subgoals that could achieve the parent goal. The graph helps model how decomposed subproblems relate and their solutions combine to solve the overall problem.
Greedy Algorithm - Knapsack Problem
The document discusses the knapsack problem and greedy algorithms. It defines the knapsack problem as an optimization problem where given constraints and an objective function, the goal is to find the feasible solution that maximizes or minimizes the objective. It describes the knapsack problem has having two versions: 0-1 where items are indivisible, and fractional where items can be divided. The fractional knapsack problem can be solved using a greedy approach by sorting items by value to weight ratio and filling the knapsack accordingly until full.
Operator Precedence Grammar
This document discusses operator precedence parsing and describes the third and fourth steps:
- Parsing the input string based on a precedence relation table by shifting and reducing tokens.
- Constructing a parse tree from the parse table by focusing on reduce actions and building the tree from the bottom up.
Two examples are provided to demonstrate how operator precedence parsing can determine if an input string is valid based on a given grammar. Parse tables and trees are constructed to show the parsing process.
Breadth First Search & Depth First Search
The slides attached here describes how Breadth first search and Depth First Search technique is used in Traversing a graph/tree with Algorithm and simple code snippet.
Quicksort Presentation
Quick Sort is a recursive divide and conquer sorting algorithm that works by partitioning a list around a pivot value and recursively sorting the sublists. It has average case performance of O(n log n) time. The algorithm involves picking a pivot element, partitioning the list based on element values relative to the pivot, and recursively sorting the sublists until the entire list is sorted. An example using Hoare's partition scheme is provided to demonstrate the partitioning and swapping steps.
Input-Buffering
Algorithm for Buffer Pairs, Algorithm for Sentinels,
Working of Buffer Pairs and Sentinels with example
SINGLE-SOURCE SHORTEST PATHS
The document discusses different single-source shortest path algorithms. It begins by defining shortest path and different variants of shortest path problems. It then describes Dijkstra's algorithm and Bellman-Ford algorithm for solving the single-source shortest paths problem, even in graphs with negative edge weights. Dijkstra's algorithm uses relaxation and a priority queue to efficiently solve the problem in graphs with non-negative edge weights. Bellman-Ford can handle graphs with negative edge weights but requires multiple relaxation passes to converge. Pseudocode and examples are provided to illustrate the algorithms.
Merge sort algorithm
This power point presentation will give you the knowledge of merge sort algorithm how it works with a given problem solving example. It also describe about the time complexity of merge sort algorithm, and the program in c .
Asymptotic Notation
The document discusses algorithm analysis and asymptotic notation. It defines algorithm analysis as comparing algorithms based on running time and other factors as problem size increases. Asymptotic notation such as Big-O, Big-Omega, and Big-Theta are introduced to classify algorithms based on how their running times grow relative to input size. Common time complexities like constant, logarithmic, linear, quadratic, and exponential are also covered. The properties and uses of asymptotic notation for equations and inequalities are explained.
Merge Sort
Merge sort is a divide and conquer algorithm that divides an array into halves, recursively sorts the halves, and then merges the sorted halves back together. The key steps are:
1. Divide the array into equal halves until reaching base cases of arrays with one element.
2. Recursively sort the left and right halves by repeating the divide step.
3. Merge the sorted halves back into a single sorted array by comparing elements pairwise and copying the smaller element into the output array.
Merge sort has several advantages including running in O(n log n) time in all cases, accessing data sequentially with low random access needs, and being suitable for external sorting of large data sets that do not fit in memory
contiguous memory allocation.pptx
This presentation describes about the various memory allocation methods like first fit, best fit and worst fit in memory management and also about fragmentation problem and solution for the problem.
Lecture 1 introduction to parallel and distributed computing
This gives you an introduction to parallel and distributed computing. More details: https://sites.google.com/view/vajira-thambawita/leaning-materials
Dynamic Programming
Dynamic Programming :
Dynamic programming is a technique for solving problems by breaking them down into smaller subproblems, solving each subproblem once, and storing the solution to each subproblem so that it can be reused in the future. Some characteristics of dynamic programming include:
Optimal substructure: Dynamic programming problems typically have an optimal substructure, meaning that the optimal solution to the problem can be obtained by solving the subproblems optimally and combining their solutions.
Overlapping subproblems: Dynamic programming problems often involve overlapping subproblems, meaning that the same subproblems are solved multiple times. To avoid solving the same subproblem multiple times, dynamic programming algorithms store the solutions to the subproblems in a table or array, so that they can be reused later.
Bottom-up approach: Dynamic programming algorithms usually solve problems using a bottom-up approach, meaning that they start by solving the smallest subproblems and work their way up to the larger ones.
Efficiency: Dynamic programming algorithms can be very efficient, especially when the subproblems overlap significantly. By storing the solutions to the subproblems and reusing them, dynamic programming algorithms can avoid redundant computations and achieve good time and space complexity.
Applicability: Dynamic programming is applicable to a wide range of problems, including optimization problems, decision problems, and problems that involve sequential decisions. It is often used to solve problems in computer science, operations research, and economics.
Algorithm Design Techniques
Iterative techniques, Divide and Conquer, Dynamic Programming, Greedy Algorithms.
Greedy Algorithms
Greedy algorithms, kruskal's algorithm, merging sorted lists, knapsack problem, union find data structure with path compression
Graph coloring using backtracking
This document summarizes graph coloring using backtracking. It defines graph coloring as minimizing the number of colors used to color a graph. The chromatic number is the fewest colors needed. Graph coloring is NP-complete. The document outlines a backtracking algorithm that tries assigning colors to vertices, checks if the assignment is valid (no adjacent vertices have the same color), and backtracks if not. It provides pseudocode for the algorithm and lists applications like scheduling, Sudoku, and map coloring.
Database , 12 Reliability
The document outlines concepts related to distributed database reliability. It begins with definitions of key terms like reliability, availability, failure, and fault tolerance measures. It then discusses different types of faults and failures that can occur in distributed systems. The document focuses on techniques for ensuring transaction atomicity and durability in the face of failures, including logging, write-ahead logging, and various execution strategies. It also covers checkpointing and recovery protocols at both the local and distributed level, particularly two-phase commit.
Doubly Linked List || Operations || Algorithms
Doubly linked list and operations on it. Insertion, Deletion, Traversing at all locations- First, Last, Middle.
Basic definitions and structured example.
Algorithms for all the operations.
Greedy algorithm
Greedy algorithms make locally optimal choices at each step to try to find a global optimum. They choose the best option available at each state. For the travelling salesman problem, the greedy approach is to always choose the nearest unvisited city from the current city to build the route. While greedy algorithms are simple to implement, they do not always find the true optimal solution, especially for large complex problems, as they only consider the best choice at each step rather than the overall route.
Floyd Warshall Algorithm
This document presents an overview of the Floyd-Warshall algorithm. It begins with an introduction to the algorithm, explaining that it finds shortest paths in a weighted graph with positive or negative edge weights. It then discusses the history and naming of the algorithm, attributed to researchers in the 1950s and 1960s. The document proceeds to provide an example of how the algorithm works, showing the distance and sequence tables that are updated over multiple iterations to find shortest paths between all pairs of vertices. It concludes with discussing the time and space complexity, applications, and references.
DAA-Floyd Warshall Algorithm.pptx
The Floyd-Warshall algorithm finds the shortest paths between all pairs of vertices in a weighted graph. It works by computing the shortest path between every pair of vertices through dynamic programming. The algorithm proceeds in steps, where in each step it considers all vertices as potential intermediate vertices to find even shorter paths between vertex pairs. This is done by comparing the newly computed shortest paths to the values stored in the previous matrix.
Daa notes 1
This slides contains assymptotic notations, recurrence relation like subtitution method, iteration method, master method and recursion tree method and sorting algorithms like merge sort, quick sort, heap sort, counting sort, radix sort and bucket sort.
LU-17 Closest pair and convex hull using divide and conquer.pptx
The Closest Pair Problem can be solved using a divide and conquer algorithm. The algorithm works as follows:
1. Sort the points by x-coordinate and then y-coordinate.
2. Divide the points into two subsets by a median splitting line.
3. Recursively find the closest pairs in the subsets. Combine the results, checking for closer pairs that cross the splitting line.
The algorithm runs in O(n log n) time, making it efficient for solving the Closest Pair Problem.
ClosestPair_Kleinberg_and_Tardos.pptx_enjoy
The document describes an algorithm for finding the closest pair of points among a set of n points in a plane. The algorithm uses a divide and conquer approach, recursively dividing the points into halves and finding the closest pairs within each half. It then finds the closest pair where one point is in each half. This is done by only considering points within a threshold distance of the dividing line. The points within this threshold are sorted, and distances only need to be checked between neighboring points, resulting in an overall runtime of O(n log n).
More Related Content
What's hot
Greedy Algorithm - Knapsack Problem
The document discusses the knapsack problem and greedy algorithms. It defines the knapsack problem as an optimization problem where given constraints and an objective function, the goal is to find the feasible solution that maximizes or minimizes the objective. It describes the knapsack problem has having two versions: 0-1 where items are indivisible, and fractional where items can be divided. The fractional knapsack problem can be solved using a greedy approach by sorting items by value to weight ratio and filling the knapsack accordingly until full.
Operator Precedence Grammar
This document discusses operator precedence parsing and describes the third and fourth steps:
- Parsing the input string based on a precedence relation table by shifting and reducing tokens.
- Constructing a parse tree from the parse table by focusing on reduce actions and building the tree from the bottom up.
Two examples are provided to demonstrate how operator precedence parsing can determine if an input string is valid based on a given grammar. Parse tables and trees are constructed to show the parsing process.
Breadth First Search & Depth First Search
The slides attached here describes how Breadth first search and Depth First Search technique is used in Traversing a graph/tree with Algorithm and simple code snippet.
Quicksort Presentation
Quick Sort is a recursive divide and conquer sorting algorithm that works by partitioning a list around a pivot value and recursively sorting the sublists. It has average case performance of O(n log n) time. The algorithm involves picking a pivot element, partitioning the list based on element values relative to the pivot, and recursively sorting the sublists until the entire list is sorted. An example using Hoare's partition scheme is provided to demonstrate the partitioning and swapping steps.
Input-Buffering
Algorithm for Buffer Pairs, Algorithm for Sentinels,
Working of Buffer Pairs and Sentinels with example
SINGLE-SOURCE SHORTEST PATHS
The document discusses different single-source shortest path algorithms. It begins by defining shortest path and different variants of shortest path problems. It then describes Dijkstra's algorithm and Bellman-Ford algorithm for solving the single-source shortest paths problem, even in graphs with negative edge weights. Dijkstra's algorithm uses relaxation and a priority queue to efficiently solve the problem in graphs with non-negative edge weights. Bellman-Ford can handle graphs with negative edge weights but requires multiple relaxation passes to converge. Pseudocode and examples are provided to illustrate the algorithms.
Merge sort algorithm
This power point presentation will give you the knowledge of merge sort algorithm how it works with a given problem solving example. It also describe about the time complexity of merge sort algorithm, and the program in c .
Asymptotic Notation
The document discusses algorithm analysis and asymptotic notation. It defines algorithm analysis as comparing algorithms based on running time and other factors as problem size increases. Asymptotic notation such as Big-O, Big-Omega, and Big-Theta are introduced to classify algorithms based on how their running times grow relative to input size. Common time complexities like constant, logarithmic, linear, quadratic, and exponential are also covered. The properties and uses of asymptotic notation for equations and inequalities are explained.
Merge Sort
Merge sort is a divide and conquer algorithm that divides an array into halves, recursively sorts the halves, and then merges the sorted halves back together. The key steps are:
1. Divide the array into equal halves until reaching base cases of arrays with one element.
2. Recursively sort the left and right halves by repeating the divide step.
3. Merge the sorted halves back into a single sorted array by comparing elements pairwise and copying the smaller element into the output array.
Merge sort has several advantages including running in O(n log n) time in all cases, accessing data sequentially with low random access needs, and being suitable for external sorting of large data sets that do not fit in memory
contiguous memory allocation.pptx
This presentation describes about the various memory allocation methods like first fit, best fit and worst fit in memory management and also about fragmentation problem and solution for the problem.
Lecture 1 introduction to parallel and distributed computing
This gives you an introduction to parallel and distributed computing. More details: https://sites.google.com/view/vajira-thambawita/leaning-materials
Dynamic Programming
Dynamic Programming :
Dynamic programming is a technique for solving problems by breaking them down into smaller subproblems, solving each subproblem once, and storing the solution to each subproblem so that it can be reused in the future. Some characteristics of dynamic programming include:
Optimal substructure: Dynamic programming problems typically have an optimal substructure, meaning that the optimal solution to the problem can be obtained by solving the subproblems optimally and combining their solutions.
Overlapping subproblems: Dynamic programming problems often involve overlapping subproblems, meaning that the same subproblems are solved multiple times. To avoid solving the same subproblem multiple times, dynamic programming algorithms store the solutions to the subproblems in a table or array, so that they can be reused later.
Bottom-up approach: Dynamic programming algorithms usually solve problems using a bottom-up approach, meaning that they start by solving the smallest subproblems and work their way up to the larger ones.
Efficiency: Dynamic programming algorithms can be very efficient, especially when the subproblems overlap significantly. By storing the solutions to the subproblems and reusing them, dynamic programming algorithms can avoid redundant computations and achieve good time and space complexity.
Applicability: Dynamic programming is applicable to a wide range of problems, including optimization problems, decision problems, and problems that involve sequential decisions. It is often used to solve problems in computer science, operations research, and economics.
Algorithm Design Techniques
Iterative techniques, Divide and Conquer, Dynamic Programming, Greedy Algorithms.
Greedy Algorithms
Greedy algorithms, kruskal's algorithm, merging sorted lists, knapsack problem, union find data structure with path compression
Graph coloring using backtracking
This document summarizes graph coloring using backtracking. It defines graph coloring as minimizing the number of colors used to color a graph. The chromatic number is the fewest colors needed. Graph coloring is NP-complete. The document outlines a backtracking algorithm that tries assigning colors to vertices, checks if the assignment is valid (no adjacent vertices have the same color), and backtracks if not. It provides pseudocode for the algorithm and lists applications like scheduling, Sudoku, and map coloring.
Database , 12 Reliability
The document outlines concepts related to distributed database reliability. It begins with definitions of key terms like reliability, availability, failure, and fault tolerance measures. It then discusses different types of faults and failures that can occur in distributed systems. The document focuses on techniques for ensuring transaction atomicity and durability in the face of failures, including logging, write-ahead logging, and various execution strategies. It also covers checkpointing and recovery protocols at both the local and distributed level, particularly two-phase commit.
Doubly Linked List || Operations || Algorithms
Doubly linked list and operations on it. Insertion, Deletion, Traversing at all locations- First, Last, Middle.
Basic definitions and structured example.
Algorithms for all the operations.
Greedy algorithm
Greedy algorithms make locally optimal choices at each step to try to find a global optimum. They choose the best option available at each state. For the travelling salesman problem, the greedy approach is to always choose the nearest unvisited city from the current city to build the route. While greedy algorithms are simple to implement, they do not always find the true optimal solution, especially for large complex problems, as they only consider the best choice at each step rather than the overall route.
Floyd Warshall Algorithm
This document presents an overview of the Floyd-Warshall algorithm. It begins with an introduction to the algorithm, explaining that it finds shortest paths in a weighted graph with positive or negative edge weights. It then discusses the history and naming of the algorithm, attributed to researchers in the 1950s and 1960s. The document proceeds to provide an example of how the algorithm works, showing the distance and sequence tables that are updated over multiple iterations to find shortest paths between all pairs of vertices. It concludes with discussing the time and space complexity, applications, and references.
DAA-Floyd Warshall Algorithm.pptx
The Floyd-Warshall algorithm finds the shortest paths between all pairs of vertices in a weighted graph. It works by computing the shortest path between every pair of vertices through dynamic programming. The algorithm proceeds in steps, where in each step it considers all vertices as potential intermediate vertices to find even shorter paths between vertex pairs. This is done by comparing the newly computed shortest paths to the values stored in the previous matrix.
Daa notes 1
This slides contains assymptotic notations, recurrence relation like subtitution method, iteration method, master method and recursion tree method and sorting algorithms like merge sort, quick sort, heap sort, counting sort, radix sort and bucket sort.
What's hot (20)
Lecture 1 introduction to parallel and distributed computing
Lecture 1 introduction to parallel and distributed computing
Similar to Closest pair problems (Divide and Conquer)
LU-17 Closest pair and convex hull using divide and conquer.pptx
The Closest Pair Problem can be solved using a divide and conquer algorithm. The algorithm works as follows:
1. Sort the points by x-coordinate and then y-coordinate.
2. Divide the points into two subsets by a median splitting line.
3. Recursively find the closest pairs in the subsets. Combine the results, checking for closer pairs that cross the splitting line.
The algorithm runs in O(n log n) time, making it efficient for solving the Closest Pair Problem.
ClosestPair_Kleinberg_and_Tardos.pptx_enjoy
The document describes an algorithm for finding the closest pair of points among a set of n points in a plane. The algorithm uses a divide and conquer approach, recursively dividing the points into halves and finding the closest pairs within each half. It then finds the closest pair where one point is in each half. This is done by only considering points within a threshold distance of the dividing line. The points within this threshold are sorted, and distances only need to be checked between neighboring points, resulting in an overall runtime of O(n log n).
Data Science Cheatsheet.pdf
This document provides a summary of key machine learning concepts and techniques:
- It outlines common probability distributions including binomial, normal, and Poisson distributions.
- It describes concepts like bias-variance tradeoff, cross-validation, and model evaluation metrics for regression and classification.
- It summarizes supervised learning algorithms like linear regression, logistic regression, decision trees, random forests, and support vector machines.
- It also covers unsupervised learning techniques including k-means clustering, hierarchical clustering, and evaluating cluster quality.
Closest point on line segment to point
This document discusses two methods for finding closest points between line segments and points or between two lines:
1) To find the closest point on a line segment to a given point, project the point onto the extended line containing the segment and clamp the projection point to the segment endpoints.
2) To find the closest points between two lines, set up a system of equations requiring the vector between candidate points to be perpendicular to both lines, yielding a 2x2 linear system whose solution gives the closest points.
3) Closest points on non-parallel lines in 3D are unique, while in 2D lines always intersect unless parallel.
ClosestPairClosestPairClosestPairClosestPair
ClosestPairClosestPairClosestPairClosestPairClosestPairClosestPairClosestPairClosestPairClosestPairClosestPairClosestPair
matrixMultiplication
This document summarizes an investigation of using a dual tree algorithm and space partitioning trees to approximate matrix multiplication more efficiently than the naive O(MDN) approach under certain conditions. It presents an algorithm that organizes the row vectors of the left matrix and column vectors of the right matrix into ball trees, then performs a dual tree comparison to estimate the product matrix entries. For this to provide better complexity than naive multiplication, the vectors must fall into clusters proportional to D^τ for some τ > 0. However, uniformly distributed vectors would result in exponentially small expected cluster sizes, limiting the practical applicability of this approach. Future work is needed to address this issue.
Image_Processing-ch2surface r_part_2.ppt
This document discusses various digital image processing techniques including zooming, shrinking, pixel relationships, and distance measures. It describes two main techniques for zooming images: nearest neighbor interpolation and bilinear interpolation. Nearest neighbor assigns pixel values by finding the closest pixel in the original image, while bilinear interpolation uses weighted averages. The document also defines concepts like adjacency, connectivity, regions, boundaries, foreground, background, and different distance measures between pixels like Euclidean, city block, and chessboard distances. Examples are provided to illustrate nearest neighbor zooming and calculating distances between pixels.
Seminar Report (Final)
The document describes a seminar report on using a divide and conquer algorithm to find the closest pair of points from a set of points in two dimensions. It discusses implementing both a brute force algorithm that compares all pairs, taking O(n^2) time, and a divide and conquer algorithm that recursively divides the point set into halves and finds the closest pairs in each subset and near the dividing line, taking O(nlogn) time. It provides pseudocode for both algorithms and discusses the history and improvements made to the closest pair problem over time, reducing the number of distance computations needed.
factoring
The security of the RSA algorithm depends on the difficulty of factoring large numbers. The best known factoring algorithms are trial division, Dixon's algorithm, the quadratic sieve, and the number field sieve. The quadratic sieve and number field sieve are parallelizable algorithms that improve on Dixon's algorithm by using a "sieving" technique to more efficiently find relations between factors. While factoring performance improves incrementally over time, a large key size (over 300 bits) is still considered secure against the best known factoring methods.
Vectors2
The document discusses various topics related to vectors and planes:
1. It explains the vector product in three forms - mathematical calculation, 3D picture, and in terms of sine. It provides an example to calculate the vector product of two vectors.
2. It discusses the different forms of the equation of a plane - parametric, scalar product, and Cartesian forms. It provides examples to write the equation of a plane in these different forms.
3. It explains how to find the foot of the perpendicular from a point to a plane. It provides examples to find the foot and shortest distance.
4. It discusses how to find acute angles between lines, planes, and a line and plane. Examples
Correlation analysis in Biostatistics .pptx
Correlation analysis measures the strength and direction of association between two variables. There are different types of correlation including simple, multiple, and partial correlation. Scatter diagrams and correlation coefficients like Pearson's r and Spearman's rho are common methods to study correlation. Pearson's r assumes a linear relationship between variables while Spearman's rho can be used when variables are ranked. A correlation coefficient close to 1 or -1 indicates a strong correlation while a value near 0 suggests no correlation.
Daa chapter11
The document discusses approximation algorithms for NP-complete problems. It introduces the concept of approximation ratios, which measure how close an approximate solution from a polynomial-time algorithm is to the optimal solution. The document then provides examples of approximation algorithms with a ratio of 2 for the vertex cover and traveling salesman problems. It also discusses using backtracking to find all possible solutions to the subset sum problem.
12_Graph.pptx
A graph is a collection of nodes connected by edges. It can be represented using an adjacency matrix or adjacency lists. The adjacency matrix stores whether each possible edge exists in an n×n matrix, while adjacency lists only store the existing edges to save space for sparse graphs. Dijkstra's algorithm finds the shortest path from a source node to all other nodes in a graph by maintaining a set of processed nodes and updating the distance to unprocessed nodes through neighboring processed nodes.
Brute force
The document discusses brute force algorithms. It provides examples of problems that can be solved using brute force, including sorting algorithms like selection sort and bubble sort. It then summarizes two geometric problems - the closest pair problem and the convex hull problem - and provides pseudocode for brute force algorithms to solve each problem. The time complexity of these brute force algorithms is O(n^3).
Lecture 6
This document discusses singular value decomposition (SVD) and its applications. SVD decomposes a matrix into three component matrices that reveal useful properties about the matrix's structure and rank. SVD can be used to find the best-fitting line to a set of points by minimizing the sum of squared distances between points and the line. The solution involves computing the SVD of a transformed matrix and taking the right singular vector corresponding to the second largest singular value.
7.5 lines and_planes_in_space
Here are the steps to find the line of intersection of the two planes:
1) Write the equations of the planes in standard form:
Plane 1: x + 2y - z = 4
Plane 2: 2x - y + z = 1
2) Set the equations equal to each other and solve as a system of equations:
x + 2y - z = 4
2x - y + z = 1
3) Eliminate one variable:
Subtract the second equation from the first:
(x + 2y - z) - (2x - y + z) = 4 - 1
-x + y = 3
4) Substitute back into one of the
Derivatives and slope 2.1 update day1
The document discusses how to identify tangent lines and find derivatives using limits. It defines the slope of a tangent line as the rate of change of a graph at a given point. To calculate slope, it uses the limit of the difference quotient as the change in x (Δx) approaches 0. This defines the derivative as the slope of the tangent line. It provides an example of finding the derivative of f(x)=x^2 at the point (2,4) using this limit process.
Derivatives and slope 2.1 update day1
The document discusses how to identify tangent lines and find derivatives using limits. It defines the slope of a tangent line as the rate of change of a graph at a given point. To calculate slope, it uses the limit of the difference quotient as the change in x (Δx) approaches 0. This defines the derivative as the slope of the tangent line. It provides an example of finding the derivative of f(x)=x^2 at the point (2,4) using this limit process.
Divide and Conquer - Part II - Quickselect and Closest Pair of Points
This document discusses divide and conquer algorithms. It covers the closest pair of points problem, which can be solved in O(n log n) time using a divide and conquer approach. It also discusses selection algorithms like quickselect that can find the median or kth element of an unsorted array in linear time O(n) on average. The document provides pseudocode for these algorithms and analyzes their time complexity using recurrence relations. It also provides an overview of topics like mergesort, quicksort, and solving recurrence relations that were covered in previous lectures.
Measures of variation and dispersion report
This document discusses various statistical measures of dispersion and variation in data, including range, interquartile range, mean deviation, and standard deviation. It provides formulas and examples for calculating each measure. The range is defined as the difference between the highest and lowest values. The interquartile range is the difference between the first and third quartiles. Mean deviation measures the average distance from the mean. Standard deviation uses the differences from the mean to calculate the average deviation and is the most common measure of variation.
Similar to Closest pair problems (Divide and Conquer) (20)
LU-17 Closest pair and convex hull using divide and conquer.pptx
LU-17 Closest pair and convex hull using divide and conquer.pptx
Divide and Conquer - Part II - Quickselect and Closest Pair of Points
Divide and Conquer - Part II - Quickselect and Closest Pair of Points
More from Gem WeBlog
Analysis of optimization algorithms
This document discusses four key concepts related to optimization algorithms:
1) Algorithms are iterative processes that aim to generate improved solutions over time.
2) Algorithms can be modeled as self-organizing systems with exploration and exploitation.
3) Exploration and exploitation are two conflicting components that require balancing.
4) Genetic algorithms use three main evolutionary operators: crossover, mutation, and selection.
Particle swarm intelligence
The particle swarm optimization (PSO) algorithm was developed in 1995 as a metaheuristic algorithm based on swarm intelligence. It uses a population of candidate solutions called particles that search through the problem space to find the best solution. Each particle adjusts its trajectory based on its own experience and the experience of neighboring particles. The algorithm keeps track of each particle's best solution (personal best) and the best solution in the swarm (global best) to determine the particle's new velocity and position in the search space iteration by iteration until an optimal solution is found.
Nature inspired metaheuristics
The document discusses different types of nature-inspired metaheuristics used for optimization problems. It describes deterministic methods like hill-climbing that always produce the same output for a given input, and stochastic methods like genetic algorithms that can produce different outputs for the same input due to randomness. Gradient-based methods use gradients to find optimal parameters, while gradient-free methods do not. Metaheuristics employ intensification to exploit good solutions locally and diversification to explore globally. Population-based metaheuristics maintain a set of candidate solutions, while trajectory-based methods rely on a single agent. Examples of various metaheuristics are provided.
Darwin's theory of evolution
Genetic algorithms are a family of population-based metaheuristic optimization algorithms inspired by biological evolution, including natural selection and genetics. They maintain and improve a population of candidate solutions by evaluating their fitness and applying operations like selection, crossover and mutation to generate new solutions. Originally developed by John Holland and colleagues in 1960 based on Charles Darwin's theory of evolution, genetic algorithms have become one of the most popular evolutionary algorithms.
no free-lunch theorem
The no-free-lunch (NFL) theorem states that there is no single algorithm that works best for solving all types of problems. While some algorithms may perform better on certain problem types due to their complexity and characteristics, no algorithm will outperform all others across all possible problems. The NFL theorem demonstrates that the performance of any two algorithms will be equal when averaged across all possible problem types, meaning that there is no universally best algorithm and the best choice depends on the specific problem being addressed.
Video and animation
Video and animation involve capturing and displaying sequences of images to depict motion. Video uses real-world images while animation uses drawn or computer-generated images. MPEG standards like MPEG-1, 2, and 4 are used to compress digital video for storage and transmission by removing spatial and temporal redundancies between frames. MPEG compression involves three frame types - I, P, and B frames. I-frames are independent while P and B frames use motion prediction from previous and following frames. Grouping frames into GOPs allows efficient compression. The MPEG encoding and decoding process reconstructs frames using motion vectors and compensating for prediction errors.
Mpeg video compression
MPEG video compression works by reducing both spatial and temporal redundancy. It uses three types of frames - I frames which are intra-coded, P frames which use forward prediction from I or P frames, and B frames which use both forward and backward prediction. I frames provide anchors for the encoding and allow fast forwarding, while P and B frames allow for motion estimation between frames to reduce redundancy over time. MPEG compression groups frames into GOPs and uses motion vectors to predict how objects move between frames, reducing the need to encode redundant pixel data in each frame.
Digital audio
This document discusses digital audio, including its representation and processing. It begins by outlining the uses and applications of digital audio, such as creating moods and enhancing multimedia games. It then covers topics like analog vs. digital audio, producing digital audio through digitization and microphones, representation through sampling and quantization, perceptual encoding, common file formats like MP3 and WAV, and audio streaming using RealAudio. The key aspects of digital audio processing like compression, decompression, and codecs are also summarized.
Designing multimedia
This document discusses the process of designing multimedia projects. It outlines the key phases: conceptualization, analysis, design, development, implementation, and evaluation.
The analysis phase involves studying user needs, content requirements, technical specifications, and constraints. In the design phase, project specifications are created along with storyboards, flowcharts and navigation structures.
The development phase uses authoring tools to create prototypes based on the design. Content like graphics, audio and video are integrated. Formative evaluation tests for bugs during this stage. The implementation phase involves legal/ethical reviews and accessibility testing. Summative evaluation assesses the full project before release.
Testing and Rolling Out Enterprise Applications
The document discusses various aspects of testing and rolling out enterprise applications. It describes different types of testing like functional testing, non-functional testing, white box testing, black box testing and gray box testing. It also discusses different testing levels from unit testing to acceptance testing and production testing. The document then covers testing approaches, environments, performance testing and security testing in detail. Finally, it provides an overview of user acceptance testing and strategies for rolling out enterprise applications.
Constructing Enterprise Applications
The document discusses the process of constructing enterprise applications. It involves translating the design into code components through various activities like achieving construction readiness, constructing solution layers, code review, testing, and creating deployable packages. Construction readiness includes defining a construction plan, package structure, configuration management plan, and development environment. Solution layers include infrastructure, presentation, business, data access, and integration components. Code review and static/dynamic analysis help ensure quality. The overall process aims to fulfill requirements through proper architecture, techniques, and tools.
Architecting and Designing Enterprise Applications
The document discusses the architecture, views, and viewpoints of enterprise applications. It describes how architecture serves as a blueprint and is organized into views and viewpoints representing stakeholder perspectives. The architecture description consists of aspects depicted by models using languages like UML. Enterprise architecture helps conceptualize and analyze business scenarios considering applications, users, and data. Popular frameworks like TOGAF define architecture domains including business, applications, data, and technology. The blueprint of an application includes logical, technical, data, and infrastructure architectures. Logical architecture defines layers like business, data access, and presentation. Technical architecture identifies frameworks, patterns, and integration. Infrastructure services provide common functions.
Incepting Enterprise Applications
This document discusses the key activities involved in incepting an enterprise application, including enterprise analysis, business modeling, requirements elicitation and analysis, requirements validation, and planning and estimation. Enterprise analysis involves identifying business opportunities and stakeholders. Business modeling helps understand business processes and includes creating AS-IS and TO-BE models. Requirements elicitation captures functional and non-functional requirements through use cases and prototypes. Requirements validation ensures requirements meet business needs. Planning and estimation prepares project plans and estimates costs and effort based on techniques like use case points and function points.
Introduction to BEA
This document discusses enterprise applications, including what defines an enterprise application, how they can be categorized, and the challenges they face. Enterprise applications are applications that satisfy an organization's business and functional requirements while also considering efficiency, scalability, security, and other non-functional needs. They can be categorized based on their visibility to end users, the industry domain, type of processing, and whether they are custom-built or readymade. Developing successful enterprise applications requires business case readiness, a clear strategy for execution, and excellence in implementation. It also discusses the key skills needed and how to measure the success of enterprise applications.
Pointers and Structures
Structures in Functions discusses pointers to structures, accessing structure members, passing structures as function arguments by value and by reference, returning structures from functions, arrays of structures, and self-referential structures. Key points include passing a pointer to a structure as a function argument to avoid copying large structures, defining an array of structures to store multiple records, and using a pointer as a member of a structure to create self-referential linked structures like linked lists.
Dynamic memory allocation
The document discusses dynamic memory allocation in C using functions like malloc(), calloc(), free(), and realloc(). It provides:
1) malloc() allocates memory at runtime and returns a pointer to the allocated block. It does not initialize the memory.
2) calloc() also allocates memory at runtime but initializes all bits to zero.
3) free() frees up previously allocated memory so it can be used again.
4) realloc() resizes previously allocated memory blocks, allowing memory usage to grow or shrink as needed.
Function pointer
Pointers can point to functions and be used to call those functions. A function pointer must be initialized with the address of a function before being called. Function pointers allow functions to be passed as parameters and can be used to select between functions at runtime based on some condition.
10. NULL pointer
A null pointer points to nothing or nowhere and is initialized to NULL or 0. Pointers must be initialized to NULL to indicate no memory is allocated yet. Functions returning pointers may need to indicate errors by returning a null pointer. Passing NULL to a function avoids passing an invalid memory address. Dereferencing a null pointer will cause a program to abort, so pointers should be checked against NULL before accessing their value.
13. Pointer and 2D array
A two dimensional array can be accessed using two subscripts, with the first representing the row number and the second representing the column number. Elements are stored in memory row by row. A 2D array can be viewed as a collection of 1D arrays, with each row representing an array of the second dimension size. The base address of the 2D array points to the first element at index [0][0], and any element can be accessed using the generalized form of base_pointer[i][j].
12.string and pointer
String and pointer
https://youtube.com/playlist?list=PLZce0V9wfp454q4iqLYh8AAdLQS36TLWC ---
My Channel for “Pointers in C”
More from Gem WeBlog (20)
Architecting and Designing Enterprise Applications
Architecting and Designing Enterprise Applications
Recently uploaded
Impartiality as per ISO /IEC 17025:2017 Standard
This document provides basic guidelines for imparitallity requirement of ISO 17025. It defines in detial how it is met and wiudhwdih jdhsjdhwudjwkdbjwkdddddddddddkkkkkkkkkkkkkkkkkkkkkkkwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwioiiiiiiiiiiiii uwwwwwwwwwwwwwwwwhe wiqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq gbbbbbbbbbbbbb owdjjjjjjjjjjjjjjjjjjjj widhi owqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq uwdhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhwqiiiiiiiiiiiiiiiiiiiiiiiiiiiiw0pooooojjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj whhhhhhhhhhh wheeeeeeee wihieiiiiii wihe
e qqqqqqqqqqeuwiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiqw dddddddddd cccccccccccccccv s w c r
cdf cb bicbsad ishd d qwkbdwiur e wetwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww w
dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffw
uuuuhhhhhhhhhhhhhhhhhhhhhhhhe qiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc ccccccccccccccccccccccccccccccccccc bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbu uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuum
m
m mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm m i
g i dijsd sjdnsjd ndjajsdnnsa adjdnawddddddddddddd uw
一比一原版(uofo毕业证书)美国俄勒冈大学毕业证如何办理
原版一模一样【微信：741003700 】【(uofo毕业证书)美国俄勒冈大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(uofo毕业证书)美国俄勒冈大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(uofo毕业证书)美国俄勒冈大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(uofo毕业证书)美国俄勒冈大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(uofo毕业证书)美国俄勒冈大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
Object Oriented Analysis and Design - OOAD
This ppt gives detailed description of Object Oriented Analysis and design.
Mechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering PROJECT REPORT ON SUMMER VOCATIONAL TRAINING
AT MBB AIRPORT
Beckhoff Programmable Logic Control Overview Presentation
This presentation is to describe the overview of PLC Beckhoff for beginners
一比一原版(osu毕业证书)美国俄勒冈州立大学毕业证如何办理
原版一模一样【微信：741003700 】【(osu毕业证书)美国俄勒冈州立大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(osu毕业证书)美国俄勒冈州立大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(osu毕业证书)美国俄勒冈州立大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(osu毕业证书)美国俄勒冈州立大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(osu毕业证书)美国俄勒冈州立大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
OOPS_Lab_Manual - programs using C++ programming language
This manual contains programs on object oriented programming concepts using C++ language.
Levelised Cost of Hydrogen (LCOH) Calculator Manual
The aim of this manual is to explain the
methodology behind the Levelized Cost of
Hydrogen (LCOH) calculator. Moreover, this
manual also demonstrates how the calculator
can be used for estimating the expenses associated with hydrogen production in Europe
using low-temperature electrolysis considering different sources of electricity
DESIGN AND MANUFACTURE OF CEILING BOARD USING SAWDUST AND WASTE CARTON MATERI...
The need for ecofriendly materials as building materials in this century cannot be overemphasized
Height and depth gauge linear metrology.pdf
Height gauges may also be used to measure the height of an object by using the underside of the scriber as the datum. The datum may be permanently fixed or the height gauge may have provision to adjust the scale, this is done by sliding the scale vertically along the body of the height gauge by turning a fine feed screw at the top of the gauge; then with the scriber set to the same level as the base, the scale can be matched to it. This adjustment allows different scribers or probes to be used, as well as adjusting for any errors in a damaged or resharpened probe.
A high-Speed Communication System is based on the Design of a Bi-NoC Router, ...
The Network on Chip (NoC) has emerged as an effective
solution for intercommunication infrastructure within System on
Chip (SoC) designs, overcoming the limitations of traditional
methods that face significant bottlenecks. However, the complexity
of NoC design presents numerous challenges related to
performance metrics such as scalability, latency, power
consumption, and signal integrity. This project addresses the
issues within the router's memory unit and proposes an enhanced
memory structure. To achieve efficient data transfer, FIFO buffers
are implemented in distributed RAM and virtual channels for
FPGA-based NoC. The project introduces advanced FIFO-based
memory units within the NoC router, assessing their performance
in a Bi-directional NoC (Bi-NoC) configuration. The primary
objective is to reduce the router's workload while enhancing the
FIFO internal structure. To further improve data transfer speed,
a Bi-NoC with a self-configurable intercommunication channel is
suggested. Simulation and synthesis results demonstrate
guaranteed throughput, predictable latency, and equitable
network access, showing significant improvement over previous
designs
FULL STACK PROGRAMMING - Both Front End and Back End
This ppt gives details about Full Stack Programming and its basics.
SCALING OF MOS CIRCUITS m .pptx
this ppt explains about scaling parameters of the mosfet it is basically vlsi subject
Recently uploaded (20)
EV BMS WITH CHARGE MONITOR AND FIRE DETECTION.pptx
EV BMS WITH CHARGE MONITOR AND FIRE DETECTION.pptx
Mechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdf
Beckhoff Programmable Logic Control Overview Presentation
Beckhoff Programmable Logic Control Overview Presentation
OOPS_Lab_Manual - programs using C++ programming language
OOPS_Lab_Manual - programs using C++ programming language
SENTIMENT ANALYSIS ON PPT AND Project template_.pptx
SENTIMENT ANALYSIS ON PPT AND Project template_.pptx
Levelised Cost of Hydrogen (LCOH) Calculator Manual
Levelised Cost of Hydrogen (LCOH) Calculator Manual
DESIGN AND MANUFACTURE OF CEILING BOARD USING SAWDUST AND WASTE CARTON MATERI...
DESIGN AND MANUFACTURE OF CEILING BOARD USING SAWDUST AND WASTE CARTON MATERI...
A high-Speed Communication System is based on the Design of a Bi-NoC Router, ...
A high-Speed Communication System is based on the Design of a Bi-NoC Router, ...
FULL STACK PROGRAMMING - Both Front End and Back End
FULL STACK PROGRAMMING - Both Front End and Back End
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
1FIDIC-CONSTRUCTION-CONTRACT-2ND-ED-2017-RED-BOOK.pdf
Closest pair problems (Divide and Conquer)
- 2. The Closest-Pair Problem Let P be a set of n > 1 points in the Cartesian plane. If 2 ≤ n ≤ 3, Problem can be solved by the brute-force algorithm If n > 3, If n > 3, Divide the points into two subsets Pl and Pr of n/2 and n/2 points, respectively, by drawing a vertical line through the median m of their x coordinates n/2 points lie to the left of or on the line itself, and n/2 points lie to the right of or on the line. Recursively do for subsets Pl and Pr
- 3. The Closest-Pair Problem Let dl and dr be the smallest distances between pairs of points in Pl and Pr, respectively, Let d = min{ dl, dr } Note: d is not necessarily the smallest distance between all the point pairs because points of a closer pair can lie on the the point pairs because points of a closer pair can lie on the opposite sides of the separating line Step combining the solutions to the smaller subproblems, we need to examine such points Limit our attention to the points inside the symmetric vertical strip of width 2d around the separating line, since the distance between any other pair of points is at least d
- 4. The Closest-Pair Problem Let S be the list of points inside the strip of width 2d around the separating line, obtained from Q and hence ordered in nondecreasing order of their y coordinate. Scan this list, updating the information about dmin, if a closer pair of points is encountered min pair of points is encountered Initially, dmin = d, and subsequently dmin ≤ d Let p(x, y) be a point on this list. For a point p’(x’,y’) to have a chance to be closer to p than dmin, the point must follow p on list S and the difference between their y coordinates must be less than dmin (why?). Geometrically, this means that p must belong to the rectangle
- 6. Analysis Applying the Master Theorem, a = 2 b = 2 Analysis b = 2 d = 1