Algorithms Lecture #21 Dr.Sohail Aslam.

Slides:

Advertisements

Similar presentations

Section 13-4: Matrix Multiplication

Advertisements

Algorithm Design Methodologies Divide & Conquer Dynamic Programming Backtracking.

Test practice Multiplication. Multiplication 9x2.

Dynamic Programming An algorithm design paradigm like divide-and-conquer “Programming”: A tabular method (not writing computer code) Divide-and-Conquer.

Multiplying by 10, 100 or 1000 x 100 = x 100 = x 100 = x 100 = x 100 = x 100 = C.

Matrix Multiplication To Multiply matrix A by matrix B: Multiply corresponding entries and then add the resulting products (1)(-1)+ (2)(3) Multiply each.

Catalan Numbers.

8-1 Percent and Estimation Pages Indicator(s)  N8 Develop and analyze algorithms for computing with percents and demonstrate fluency in use.

8.2 Operations With Matrices

EXAMPLE 4 Multiplying Numbers in Scientific Notation Find the product ( ) ( ). = ( ) ( ) = =

EXAMPLE 1 Add and subtract matrices

1 Today’s Material Dynamic Programming – Chapter 15 –Introduction to Dynamic Programming –0-1 Knapsack Problem –Longest Common Subsequence –Chain Matrix.

2.4 Multiplying and Dividing Real Numbers Objectives: Multiply and divide positive and negative numbers. Define properties of zero. Standards Addressed:

Matrix Multiplication The Introduction. Look at the matrix sizes.

3.6 Multiplying Matrices Homework 3-17odd and odd.

Notes Over 4.2 Finding the Product of Two Matrices Find the product. If it is not defined, state the reason. To multiply matrices, the number of columns.

4-3 Matrix Multiplication Objective: To multiply a matrix by a scalar multiple.

Reducing a Set Covering Matrix. S I T E S Cost Areas

13.3 Product of a Scalar and a Matrix.  In matrix algebra, a real number is often called a.  To multiply a matrix by a scalar, you multiply each entry.

12-1 Organizing Data Using Matrices

Least Common Multiple.

Multiplying 2 Digit Factors

Lecture 5 Dynamic Programming

Umm Al-Qura University

Matrix Multiplication

Partial Products Algorithm for Multiplication

Lecture 5 Dynamic Programming

Multiplying Matrices.

Algorithm Lecture #09 Dr.Sohail Aslam.

Lecture 5 Multiplication and Division

Equivalent Fractions and Multipliers

Dynamic Programming Steps.

EXAMPLE 5 Use matrix multiplication to reflect a polygon

[ ] [ ] [ ] [ ] EXAMPLE 3 Scalar multiplication Simplify the product:

Solving Linear Systems Using Inverse Matrices

Designing Algorithms for Multiplication of Fractions

Terms used in Multiplication

Multiplication More complicated than addition

Multiplying fractions by fractions

Algorithms Lecture # 30 Dr. Sohail Aslam.

Algorithms Lecture #37 Dr. Sohail Aslam.

Linear Algebra Lecture 18.

Algorithms Lecture #07 Dr.Sohail Aslam.

Designing Algorithms for Multiplication of Fractions

Multiplying Matrices.

Algorithms Lecture # 29 Dr. Sohail Aslam.

Algorithms Lecture #19 Dr.Sohail Aslam.

x/÷ Numbers Year 3-4 – Multiply and divide a multiple of 10

Dynamic Programming Steps.

Algorithms Lecture # 27 Dr. Sohail Aslam.

Algorithms Lecture #43 Dr.Sohail Aslam.

Algorithms Lecture # 01 Dr. Sohail Aslam.

What is the dimension of the matrix below?

Algorithms Lecture # 02 Dr. Sohail Aslam.

Matrix Multiplication

Multiplying Matrices.

Algorithms Lecture #15 Dr.Sohail Aslam.

Multiplying Up.

Multiplying Matrices.

Matrix Multiplication Sec. 4.2

Multiplying and Dividing Decimals

2008 Multiple Choice.

Algorithms Lecture #42 Dr. Sohail Aslam.

Multiplying Matrices.

Algorithms Lecture # 26 Dr. Sohail Aslam.

Algorithms Lecture # 25 Dr. Sohail Aslam.

Presentation transcript:

Algorithms Lecture #21 Dr.Sohail Aslam

Design & Analysis of Algorithms

Chain Matrix Multiplication

Chain Matrix Multiply Algorithm

Chain Matrix Multiply Algorithm

Chain Matrix Multiply Algorithm

Chain Matrix Multiply Algorithm

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem

0/1 Knapsack Problem: DP Approach

0/1 Knapsack Problem: DP Approach

0/1 Knapsack Problem: DP Approach

0/1 Knapsack Problem

O/1 Knapsack

Design and Analysis of Algorithms