Lecture 8 dynamic programming

Algorithms Analysis lecture 8 Minimum and Maximum Alg + Dynamic Programming

Min and Max ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Finding Minimum or Maximum ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Simultaneous Min, Max ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis of Simultaneous Min, Max ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],set both min and max to the first element compare the first two elements , assign the smallest one to min and the largest one to max

Example: Simultaneous Min, Max ,[object Object],[object Object],[object Object],[object Object],[object Object],We performed: 3(n-1)/2 = 6 comparisons 3 comparisons 3 comparisons

Example: Simultaneous Min, Max ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],We performed: 3n/2 - 2 = 7 comparisons 1 comparison 3 comparisons 3 comparisons

Advanced Design and Analysis Techniques ,[object Object]

Dynamic Programming ,[object Object],[object Object],[object Object],[object Object],[object Object]

Divide-and-conquer ,[object Object],[object Object],[object Object],[object Object]

Dynamic programming ,[object Object],[object Object],[object Object],[object Object],[object Object]

Difference between DP and Divide-and-Conquer ,[object Object],[object Object]

Elements of Dynamic Programming (DP) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Steps to Designing a Dynamic Programming Algorithm ,[object Object],[object Object],[object Object],[object Object]

Fibonacci Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object]

Fibonacci Numbers ,[object Object],[object Object],[object Object],[object Object]

Fibonacci Numbers ,[object Object],[object Object],[object Object]

Ex1:Assembly-line scheduling ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Ex1:Assembly-line scheduling ,[object Object]

Problem Definition ,[object Object],[object Object],[object Object],[object Object],[object Object],start end

Step 1: Optimal Solution Structure ,[object Object],[object Object],[object Object],[object Object],[object Object]

Step 1: Optimal Solution Structure ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Step 1: Optimal Solution Structure ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Step 2: Recursive Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Step 2: Recursive Solution ,[object Object],[object Object]

Step 2: Recursive Solution ,[object Object],[object Object],[object Object],[object Object],[object Object]

Step 2: Recursive Solution ,[object Object],[object Object],[object Object]

Step 3: Optimal Solution Value

Step 4: Optimal Solution ,[object Object]

Lecture 8 dynamic programming

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Lecture 8 dynamic programming