Edit distance problem
•Download as PPTX, PDF•
0 likes•320 views
This document discusses edit distance and its dynamic programming algorithm. Edit distance is a way to quantify how dissimilar two strings are by counting the minimum number of operations (insertions, deletions, substitutions) needed to transform one string into the other. The document presents the dynamic programming formulation and algorithm to solve edit distance in quadratic time and linear space.
Report
Share
Report
Share
Recommended
Apt 502 distance tech handouts study guides and visuals
Overview of Distance Learning to include a definition, objectives and examples of handouts, study guides and the need for visuals.
Strongly connected components
This document discusses strong components and how they relate to depth-first search (DFS) algorithms. Strong components are maximal subgraphs of a graph where every node is reachable from every other node. DFS can be used to find strong components by running it on the transpose of the original graph and collecting nodes into trees, with each tree representing a strong component.
Graph theory
This document discusses key concepts in graph theory including the degree of vertices, observations about graphs such as being connected or disconnected, paths and cycles within graphs, and different ways of representing graphs such as adjacency lists and matrices. It also covers finding the shortest path between vertices in a graph.
Lect13 organization
This document discusses different types of computer organization and instruction formats. It covers single accumulator, general register, and stack organizations. It also discusses one, two, three, and zero address instruction formats. Finally, it describes the characteristics of RISC instruction sets, providing an example of a RISC instruction for the operation X=(A+B)*(C+D).
Complexity theory 3
This document discusses algorithms and reductions between computational problems. It covers reductions between problems like 3-colorability and clique cover, and how these reductions show relationships between problems. It also discusses NP-completeness, Cook's theorem, and how Boolean satisfiability was the first problem shown to be NP-complete. Finally, it mentions ways to cope with NP-complete problems, including approximations and heuristics.
Chain matrix multiplication
The document discusses algorithms for chain matrix multiplication. It focuses on different techniques for multiplying matrices in chains, including standard matrix multiplication and dynamic programming approaches for chain matrix multiplication. The document covers this topic in depth with many repetitions of the terms "chain matrix multiplication" and "matrix multiplication".
Activity selection 2
This document discusses greedy algorithms for activity selection problems. It covers greedy activity selection, proving the correctness of greedy activity selection algorithms, and showing that greedy selection provides an optimal solution for activity selection problems. The document focuses on explaining greedy algorithms for activity selection and establishing that greedy selection finds the best set of non-conflicting activities.
Dijekstra
This document discusses shortest path algorithms for graphs, including Dijkstra's algorithm. It focuses on finding the shortest paths between nodes in a graph, even when edge weights are negative. Dijkstra's algorithm is presented as a method for computing shortest paths with negative edge weights.
Recommended
Apt 502 distance tech handouts study guides and visuals
Overview of Distance Learning to include a definition, objectives and examples of handouts, study guides and the need for visuals.
Strongly connected components
This document discusses strong components and how they relate to depth-first search (DFS) algorithms. Strong components are maximal subgraphs of a graph where every node is reachable from every other node. DFS can be used to find strong components by running it on the transpose of the original graph and collecting nodes into trees, with each tree representing a strong component.
Graph theory
This document discusses key concepts in graph theory including the degree of vertices, observations about graphs such as being connected or disconnected, paths and cycles within graphs, and different ways of representing graphs such as adjacency lists and matrices. It also covers finding the shortest path between vertices in a graph.
Lect13 organization
This document discusses different types of computer organization and instruction formats. It covers single accumulator, general register, and stack organizations. It also discusses one, two, three, and zero address instruction formats. Finally, it describes the characteristics of RISC instruction sets, providing an example of a RISC instruction for the operation X=(A+B)*(C+D).
Complexity theory 3
This document discusses algorithms and reductions between computational problems. It covers reductions between problems like 3-colorability and clique cover, and how these reductions show relationships between problems. It also discusses NP-completeness, Cook's theorem, and how Boolean satisfiability was the first problem shown to be NP-complete. Finally, it mentions ways to cope with NP-complete problems, including approximations and heuristics.
Chain matrix multiplication
The document discusses algorithms for chain matrix multiplication. It focuses on different techniques for multiplying matrices in chains, including standard matrix multiplication and dynamic programming approaches for chain matrix multiplication. The document covers this topic in depth with many repetitions of the terms "chain matrix multiplication" and "matrix multiplication".
Activity selection 2
This document discusses greedy algorithms for activity selection problems. It covers greedy activity selection, proving the correctness of greedy activity selection algorithms, and showing that greedy selection provides an optimal solution for activity selection problems. The document focuses on explaining greedy algorithms for activity selection and establishing that greedy selection finds the best set of non-conflicting activities.
Dijekstra
This document discusses shortest path algorithms for graphs, including Dijkstra's algorithm. It focuses on finding the shortest paths between nodes in a graph, even when edge weights are negative. Dijkstra's algorithm is presented as a method for computing shortest paths with negative edge weights.
Lect14 organization
This document discusses addressing modes in computer organization. It defines addressing modes as rules for interpreting or modifying instruction addresses before referencing operands. Some computers specify the addressing mode directly in instructions, while others use a single code to indicate both operation and addressing mode. The advantages of addressing modes are to provide programming versatility through pointers, counters, and indexing, and to reduce the number of bits needed for instruction addresses. The document then describes nine common addressing modes including implied, immediate, register, register indirect, direct, indirect, relative, indexed, and base register addressing.
Minimum spanning trees
This document discusses algorithms related to strong components, depth-first search, minimum spanning trees, and generic approaches. It covers these topics at a high level without providing details on specific algorithms or implementations.
Topological sort
This document discusses algorithms for analyzing direct acyclic graphs and precedence constraint graphs. It covers topological sorting of graphs to determine an ordering of vertices where all directed edges point from earlier to later vertices in the ordering. The document also examines using topological sorting to find strongly connected components in a graph.
Lect10 organization
The document discusses interrupt driven data transfer and program interrupts. It describes how an external device can interrupt the computer when it is ready to transfer data, allowing the computer to momentarily pause its current program. This interrupt driven approach is more efficient than programmed data transfer which wastes computer time checking flags. The document also outlines the microoperations for fetch and decode cycles and interrupt cycles in interrupt driven data transfer, noting how the interrupt enable flip flop (IEN) allows the computer to be interrupted when set to 1.
Lecture02
Running time analysis evaluates the efficiency of algorithms by analyzing how the number of steps required to solve a problem grows as the input size grows. It considers the order of growth or time complexity of an algorithm, often expressed using Big O notation, to determine how efficiently the algorithm will scale to larger problem sizes. The most efficient algorithms have the slowest growth rates as input size increases.
Lecture01
This document discusses algorithms and provides an outline for a course on algorithms. It begins by explaining the origin of the word "algorithm" and providing an informal definition. It then discusses why algorithms are important to study and outlines topics that will be covered in the course, including models of computation and criteria for analyzing algorithms. The course aims to introduce fundamental algorithmic concepts.
Lect8 organization
The document discusses the phases of an instruction cycle in a basic computer, including fetching an instruction from memory, decoding the instruction, reading the effective address from memory if indirect, and executing the instruction. It also describes the microoperations for fetching and decoding instructions, including loading the program counter with the first instruction address and incrementing the sequence counter to provide timing signals. The types of instructions are determined and subdivided into four paths.
Lect7 organization
This document discusses computer organization and control. It describes two types of control organization: hardwired control and microprogrammed control. Hardwired control implements logic with gates and circuits, allowing for fast operation but requiring wiring changes for modifications. Microprogrammed control stores control information in a memory that can be updated, allowing easier changes but slower execution. Block diagrams and a timing diagram are provided to illustrate the hardwired control unit.
Floyd warshal 2
The document is about the Floyd-Warshall algorithm, which is repeated over 20 times. The Floyd-Warshall algorithm is an algorithm for finding shortest paths in a weighted graph. It improves on Dijkstra's algorithm by finding shortest paths between all pairs of vertices instead of just from a single source vertex selected in advance.
Bfs and dfs
This document discusses algorithms for finding shortest paths and traversing connected graphs. It covers breadth-first search and depth-first search algorithms, which are used to traverse graphs in different ways. Breadth-first search prioritizes exploring nodes closest to the starting node, while depth-first search explores nodes as far as possible along each branch before backtracking. The document also presents a generic graph traversal algorithm that can be adapted for either search approach.
Mst 2
This document discusses algorithms for finding minimum spanning trees and presents a generic greedy approach. It provides multiple proofs that the greedy algorithm always finds a minimum spanning tree by sequentially connecting components with the cheapest available edge while ensuring no cycles are formed.
Greedy algorithm
This document discusses greedy algorithms and their application to optimization problems such as coin change problems. It provides examples of using a greedy approach to count money by selecting the largest coins first, but notes that this can fail in some cases. Dynamic programming solutions are then introduced as alternatives to the greedy algorithm for making change that are guaranteed to find the optimal solution. The complexity of coin change problems is also examined.
Lect9 organization
This document discusses different types of computer instructions including register reference instructions, memory reference instructions, and input-output instructions. It describes the control functions and microoperations for register reference instructions which are executed when D7I'T3 is true. Memory reference instructions and an example of the BSA instruction are also mentioned. The input and output processes are defined, noting how input and output flags control the transfer of data between registers and input/output devices. Finally, it states that all input-output instructions have D7=1, I=1, and T3=1 and require the Boolean relation D7IT3 to be true.
Complexity theory 2
The document discusses several topics related to algorithms, graph theory, and cellular communication. It focuses on reductions, graph coloring problems related to fish tanks, and how cellular networks work and are implemented. Several concepts are repeated for emphasis.
Lect6 organization
1. The document discusses the basic types of computer instructions that must be included: arithmetic/logical/shift instructions, data transfer instructions, program control instructions, and input/output instructions.
2. It explains the formats of basic computer instructions, including memory reference instructions that use 12 bits to specify the address mode as direct or indirect.
3. Register reference instructions are recognized by the opcode 111 with a 0 in bit 15, and use the remaining bits to specify an operation on the AC register without a memory operand. Similarly, input-output instructions use the opcode 111 with a 1 in bit 15 and the remaining 12 bits to specify the input-output operation without a memory reference.
Lect11 organization
This document describes the internal organization and logic circuits of a computer system using a register transfer language. It includes:
1) A table summarizing the control functions and micro-operations for the entire computer. This describes the internal organization and allows designing the computer's logic circuits.
2) Examples of register transfer statements and control functions/conditional statements that formulate the control unit's Boolean functions.
3) A list of micro-operations specifying the types of control inputs needed for registers and memory.
4) Diagrams showing the control logic for flip-flops and buses, the accumulator logic, and an adder/logic circuit stage.
5) Examples of exercises analyzing register transfers and microoperations in the system
Lect5 organization
The document discusses the basic components of a computer's organization and design. It describes how a program is a set of instructions that specify the processing sequence. An instruction code is divided into an operation code and operand. The operation code defines the operation like ADD or SUB, while the operand is the data it acts on. It also discusses addressing modes like immediate, direct, and indirect addressing. The document lists the basic computer registers and their functions for manipulating and holding data and addresses. It describes the data transfer process between memory, registers, and the bus.
Dfs 3
This document discusses depth-first search (DFS) algorithms and different data structures used to represent DFS including time stamp structure, tree structure, and parenthesis structure. It focuses on DFS time stamp structure, mentioning this structure multiple times as a way to represent information discovered through depth-first search.
Complexity
This document discusses complexity theory and algorithms. It covers topics such as complexity classes, decision problems, polynomial time verification, and the class NP. The document focuses on computational complexity and determining the difficulty of problems based on the resources required to solve them, such as time and storage space. It also considers whether problems in NP can be solved in polynomial time.
Cis cvs risc
This document compares and contrasts the architectures of traditional CISC machines like VAX and Pentium Pro with RISC machines like UltraSPARC and Cray T3E. It discusses their memory, registers, data formats, instruction formats, addressing modes, instruction sets, and input/output. The VAX uses variable length instructions and has many addressing modes, while the Pentium Pro has a large instruction set. UltraSPARC and Cray T3E are RISC machines with fewer instructions that are register-to-register and fixed length.
Lect12 organization
The document discusses the central processing unit (CPU) and its major components: the control unit, arithmetic logic unit (ALU), and register set. It also covers general register organization and bus connections, as well as stack organization using a stack pointer and the push and pop operations. Finally, it describes reverse polish notation and how stacks can be used to evaluate arithmetic expressions in this notation.
More Related Content
Viewers also liked
Lect14 organization
This document discusses addressing modes in computer organization. It defines addressing modes as rules for interpreting or modifying instruction addresses before referencing operands. Some computers specify the addressing mode directly in instructions, while others use a single code to indicate both operation and addressing mode. The advantages of addressing modes are to provide programming versatility through pointers, counters, and indexing, and to reduce the number of bits needed for instruction addresses. The document then describes nine common addressing modes including implied, immediate, register, register indirect, direct, indirect, relative, indexed, and base register addressing.
Minimum spanning trees
This document discusses algorithms related to strong components, depth-first search, minimum spanning trees, and generic approaches. It covers these topics at a high level without providing details on specific algorithms or implementations.
Topological sort
This document discusses algorithms for analyzing direct acyclic graphs and precedence constraint graphs. It covers topological sorting of graphs to determine an ordering of vertices where all directed edges point from earlier to later vertices in the ordering. The document also examines using topological sorting to find strongly connected components in a graph.
Lect10 organization
The document discusses interrupt driven data transfer and program interrupts. It describes how an external device can interrupt the computer when it is ready to transfer data, allowing the computer to momentarily pause its current program. This interrupt driven approach is more efficient than programmed data transfer which wastes computer time checking flags. The document also outlines the microoperations for fetch and decode cycles and interrupt cycles in interrupt driven data transfer, noting how the interrupt enable flip flop (IEN) allows the computer to be interrupted when set to 1.
Lecture02
Running time analysis evaluates the efficiency of algorithms by analyzing how the number of steps required to solve a problem grows as the input size grows. It considers the order of growth or time complexity of an algorithm, often expressed using Big O notation, to determine how efficiently the algorithm will scale to larger problem sizes. The most efficient algorithms have the slowest growth rates as input size increases.
Lecture01
This document discusses algorithms and provides an outline for a course on algorithms. It begins by explaining the origin of the word "algorithm" and providing an informal definition. It then discusses why algorithms are important to study and outlines topics that will be covered in the course, including models of computation and criteria for analyzing algorithms. The course aims to introduce fundamental algorithmic concepts.
Lect8 organization
The document discusses the phases of an instruction cycle in a basic computer, including fetching an instruction from memory, decoding the instruction, reading the effective address from memory if indirect, and executing the instruction. It also describes the microoperations for fetching and decoding instructions, including loading the program counter with the first instruction address and incrementing the sequence counter to provide timing signals. The types of instructions are determined and subdivided into four paths.
Lect7 organization
This document discusses computer organization and control. It describes two types of control organization: hardwired control and microprogrammed control. Hardwired control implements logic with gates and circuits, allowing for fast operation but requiring wiring changes for modifications. Microprogrammed control stores control information in a memory that can be updated, allowing easier changes but slower execution. Block diagrams and a timing diagram are provided to illustrate the hardwired control unit.
Floyd warshal 2
The document is about the Floyd-Warshall algorithm, which is repeated over 20 times. The Floyd-Warshall algorithm is an algorithm for finding shortest paths in a weighted graph. It improves on Dijkstra's algorithm by finding shortest paths between all pairs of vertices instead of just from a single source vertex selected in advance.
Bfs and dfs
This document discusses algorithms for finding shortest paths and traversing connected graphs. It covers breadth-first search and depth-first search algorithms, which are used to traverse graphs in different ways. Breadth-first search prioritizes exploring nodes closest to the starting node, while depth-first search explores nodes as far as possible along each branch before backtracking. The document also presents a generic graph traversal algorithm that can be adapted for either search approach.
Mst 2
This document discusses algorithms for finding minimum spanning trees and presents a generic greedy approach. It provides multiple proofs that the greedy algorithm always finds a minimum spanning tree by sequentially connecting components with the cheapest available edge while ensuring no cycles are formed.
Greedy algorithm
This document discusses greedy algorithms and their application to optimization problems such as coin change problems. It provides examples of using a greedy approach to count money by selecting the largest coins first, but notes that this can fail in some cases. Dynamic programming solutions are then introduced as alternatives to the greedy algorithm for making change that are guaranteed to find the optimal solution. The complexity of coin change problems is also examined.
Lect9 organization
This document discusses different types of computer instructions including register reference instructions, memory reference instructions, and input-output instructions. It describes the control functions and microoperations for register reference instructions which are executed when D7I'T3 is true. Memory reference instructions and an example of the BSA instruction are also mentioned. The input and output processes are defined, noting how input and output flags control the transfer of data between registers and input/output devices. Finally, it states that all input-output instructions have D7=1, I=1, and T3=1 and require the Boolean relation D7IT3 to be true.
Complexity theory 2
The document discusses several topics related to algorithms, graph theory, and cellular communication. It focuses on reductions, graph coloring problems related to fish tanks, and how cellular networks work and are implemented. Several concepts are repeated for emphasis.
Lect6 organization
1. The document discusses the basic types of computer instructions that must be included: arithmetic/logical/shift instructions, data transfer instructions, program control instructions, and input/output instructions.
2. It explains the formats of basic computer instructions, including memory reference instructions that use 12 bits to specify the address mode as direct or indirect.
3. Register reference instructions are recognized by the opcode 111 with a 0 in bit 15, and use the remaining bits to specify an operation on the AC register without a memory operand. Similarly, input-output instructions use the opcode 111 with a 1 in bit 15 and the remaining 12 bits to specify the input-output operation without a memory reference.
Lect11 organization
This document describes the internal organization and logic circuits of a computer system using a register transfer language. It includes:
1) A table summarizing the control functions and micro-operations for the entire computer. This describes the internal organization and allows designing the computer's logic circuits.
2) Examples of register transfer statements and control functions/conditional statements that formulate the control unit's Boolean functions.
3) A list of micro-operations specifying the types of control inputs needed for registers and memory.
4) Diagrams showing the control logic for flip-flops and buses, the accumulator logic, and an adder/logic circuit stage.
5) Examples of exercises analyzing register transfers and microoperations in the system
Lect5 organization
The document discusses the basic components of a computer's organization and design. It describes how a program is a set of instructions that specify the processing sequence. An instruction code is divided into an operation code and operand. The operation code defines the operation like ADD or SUB, while the operand is the data it acts on. It also discusses addressing modes like immediate, direct, and indirect addressing. The document lists the basic computer registers and their functions for manipulating and holding data and addresses. It describes the data transfer process between memory, registers, and the bus.
Dfs 3
This document discusses depth-first search (DFS) algorithms and different data structures used to represent DFS including time stamp structure, tree structure, and parenthesis structure. It focuses on DFS time stamp structure, mentioning this structure multiple times as a way to represent information discovered through depth-first search.
Complexity
This document discusses complexity theory and algorithms. It covers topics such as complexity classes, decision problems, polynomial time verification, and the class NP. The document focuses on computational complexity and determining the difficulty of problems based on the resources required to solve them, such as time and storage space. It also considers whether problems in NP can be solved in polynomial time.
Viewers also liked (20)
More from Maher Alshammari
Cis cvs risc
This document compares and contrasts the architectures of traditional CISC machines like VAX and Pentium Pro with RISC machines like UltraSPARC and Cray T3E. It discusses their memory, registers, data formats, instruction formats, addressing modes, instruction sets, and input/output. The VAX uses variable length instructions and has many addressing modes, while the Pentium Pro has a large instruction set. UltraSPARC and Cray T3E are RISC machines with fewer instructions that are register-to-register and fixed length.
Lect12 organization
The document discusses the central processing unit (CPU) and its major components: the control unit, arithmetic logic unit (ALU), and register set. It also covers general register organization and bus connections, as well as stack organization using a stack pointer and the push and pop operations. Finally, it describes reverse polish notation and how stacks can be used to evaluate arithmetic expressions in this notation.
Lect15 organization
The document discusses different aspects of computer organization including program control, program control instructions, status bit conditions, program interrupts, types of interrupts, CISC and RISC computers. It provides details on how the program counter controls instruction execution flow and how program control instructions can alter this flow. It also describes status bit registers, different types of interrupts including external, internal and software interrupts. Finally, it outlines the key characteristics of CISC and RISC computer architectures.
Lect1 organization 2
This document provides an introduction to computer organization and digital components. It discusses computer organization, architecture, logic gates, combinational and sequential circuits like flip flops. It also summarizes common digital components such as decoders, encoders, multiplexers, demultiplexers, registers, counters, memory units including RAM and ROM. The document is presented over multiple pages and provides definitions and brief descriptions of the key topics and components in computer organization.
Lect4 organization
Shift microoperations are used to serially transfer data and are used with arithmetic, logical, and other data processing units. There are three types of shifts: 1) logical shifts transfer zeros into the shifted bits, 2) circular shifts circulate bits around the two ends of the register, and 3) arithmetic shifts preserve the sign bit during a right shift and insert zeros during a left shift, changing the sign if overflow occurs. The document discusses drawing logic circuits to perform six shift microoperations on a 4-bit register and includes bonus points for detecting overflow.
Lect2 organization 2
The document discusses various microoperations that are performed by the central processing unit of a computer. It describes register transfer language, which uses a symbolic language to define the internal organization of a computer through sequences of microoperations. The main types of microoperations covered are register transfer operations, arithmetic operations, logic operations, and shift operations. Arithmetic microoperations like addition and subtraction are implemented using binary adders and subtractors. Bus and memory transfer microoperations involve transferring data via a shared bus between components using three-state buffers.
Lect3 organization 2
This document discusses logic microoperations which specify binary operations for strings of bits stored in registers. It provides examples of selective set, selective complement, selective clear, mask, and insert operations. These logic microoperations are useful for manipulating individual bits or portions of words stored in registers. The document concludes with two assignment questions involving designing a circuit to perform logic operations on a two bit word and using logic microoperations to change the value stored in a register.
Matrix chain multiplication 2
This document repeatedly discusses chain matrix multiplication, with the term appearing over 25 times. It seems to focus exclusively on the topic of chain matrix multiplication without providing any other details.
Merge sort
This document discusses the merge sort algorithm, which uses a divide and conquer strategy to sort a list of items. It breaks the list into individual items, recursively sorts each sublist, and then merges the sublists back together in a sorted order. The algorithm has a worst-case running time of O(n log n) for a list of length n, making it an efficient sorting algorithm.
Bellman ford and floyd warshal
This document discusses algorithms for finding shortest paths in graphs, including the Bellman-Ford algorithm and Floyd-Warshall algorithm. It covers the correctness of the Bellman-Ford algorithm through multiple iterations and describes how the Floyd-Warshall algorithm can find all-pairs shortest paths in a graph.
Greedy algorithm huffman encoding
The document discusses the greedy algorithm known as Huffman encoding. Huffman encoding is a lossless data compression algorithm that represents characters using binary codes with variable lengths. It assigns shorter codes to more common characters and longer codes to less common characters to minimize the expected code length. The algorithm builds a binary tree from the character frequencies where each leaf node represents a character and the path from the root to the leaf is the code assigned to that character.
More from Maher Alshammari (12)
Recently uploaded
➒➌➎➏➑➐➋➑➐➐ Dpboss Satta Matka Matka Guessing Kalyan Chart Indian Matka Satta ...
➒➌➎➏➑➐➋➑➐➐ Dpboss Satta Matka Matka Guessing Kalyan Chart Indian Matka Satta ...➒➌➎➏➑➐➋➑➐➐Dpboss Matka Guessing Satta Matka Kalyan Chart Indian Matka
➒➌➎➏➑➐➋➑➐➐ Dpboss Satta Matta Matka Kalyan Chart Indian Matka Dpboss Matka Kalyan panel Chart Matka Guessing Satta Matka Dino Ranch Storyboard / Kids TV Advertising
Storyboard produced for the TV commercial of a toy from the children's show “Dino Ranch”
2024 MATFORCE Youth Poster Contest Winners
This document announces the winners of the 2024 Youth Poster Contest organized by MATFORCE. It lists the grand prize and age category winners for grades K-6, 7-12, and individual age groups from 5 years old to 18 years old.
Ealing London Independent Photography meeting - June 2024
Photographs from trip to American Deep South
哪里购买美国乔治城大学毕业证硕士学位证书原版一模一样
原版一模一样【微信：741003700 】【美国乔治城大学毕业证硕士学位证书】【微信：741003700 】学位证，留信认证（真实可查，永久存档）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，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
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
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
Fed by curiosity and beauty - Remembering Myrsine Zorba
Speech at the conference in the memory of Myrsine Zorba.
Cherries 32 collection of colorful paintings
The cherry: beauty, softness, its heart-shaped plastic has inspired artists since Antiquity. Cherries and strawberries were considered the fruits of paradise and thus represented the souls of men.
A Brief Introduction About Hadj Ounis
Hadj Ounis's most notable work is his sculpture titled "Metamorphosis." This piece showcases Ounis's mastery of form and texture, as he seamlessly combines metal and wood to create a dynamic and visually striking composition. The juxtaposition of the two materials creates a sense of tension and harmony, inviting viewers to contemplate the relationship between nature and industry.
All the images mentioned in 'See What You're Missing'
We've gathered together all of the images mentioned in Will Gompertz's 'See What You're Missing'
Heart Touching Romantic Love Shayari In English with Images
Explore our beautiful collection of Romantic Love Shayari in English to express your love. These heartfelt shayaris are perfect for sharing with your loved one. Get the best words to show your love and care.
Colour Theory for Painting - Fine Artist.pdf
This document is all about Colour Theory for Fine Artist / Painter.
My storyboard for a sword fight scene with lightsabers
My storyboard for a sword fight scene with lightsabers
一比一原版美国亚利桑那大学毕业证（ua毕业证书）如何办理
一模一样【微信：A575476】【美国亚利桑那大学毕业证（ua毕业证书）成绩单Offer】【微信：A575476】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，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）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，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信：A575476】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信：A575476】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
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
→ 【关于价格问题（保证一手价格）
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
Recently uploaded (20)
➒➌➎➏➑➐➋➑➐➐ Dpboss Satta Matka Matka Guessing Kalyan Chart Indian Matka Satta ...
➒➌➎➏➑➐➋➑➐➐ Dpboss Satta Matka Matka Guessing Kalyan Chart Indian Matka Satta ...
Ealing London Independent Photography meeting - June 2024
Ealing London Independent Photography meeting - June 2024
Fed by curiosity and beauty - Remembering Myrsine Zorba
Fed by curiosity and beauty - Remembering Myrsine Zorba
All the images mentioned in 'See What You're Missing'
All the images mentioned in 'See What You're Missing'
Heart Touching Romantic Love Shayari In English with Images
Heart Touching Romantic Love Shayari In English with Images
storyboard: Victor and Verlin discussing about top hat
storyboard: Victor and Verlin discussing about top hat
My storyboard for a sword fight scene with lightsabers
My storyboard for a sword fight scene with lightsabers
Edit distance problem
- 1. Algorithms
- 3. Design & Analysis of Algorithms
- 6. Edit Distance: DP Algorithm
- 7. Edit Distance: DP Algorithm
- 10. Edit Distance
- 11. Edit Distance
- 12. Edit Distance
- 13. Edit Distance
- 14. Edit Distance
- 15. Edit Distance
- 16. Edit Distance
- 17. Edit Distance
- 18. Edit Distance
- 19. Edit Distance
- 20. Edit Distance
- 21. Edit Distance
- 22. Edit Distance
- 23. Edit Distance
- 24. Edit Distance
- 25. Edit Distance
- 26. Edit Distance