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Lecture 8 dynamic programming

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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]
Divide-and-conquer - Example
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
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]
Example
 
 
Step 2: Recursive Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Step 2: Recursive Solution ,[object Object],[object Object]
Example
Example
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 3: Optimal Solution Value
Step 3: Optimal Solution Value
Step 3: Optimal Solution Value
Step 3: Optimal Solution Value
Step 3: Optimal Solution Value
Step 3: Optimal Solution Value
Step 3: Optimal Solution Value
Step 4: Optimal Solution ,[object Object]

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Lecture 8 dynamic programming