Greedy aproach towards problem solution
- 1. GREEDY APROACH TOWARDS PROBLEM SOLUTION RASHID ANSARI 170847980002 MTECH (ACDS)
- 2. GREEDY ALGORITHM Definition-: A greedy algorithm is an algorithm that follows the problem solving approach of making the locally optimal choice at each stage with the hope of finding a global optimum.
- 3. GREEDY ALGORITHM Simply…… A greedy algorithm always makes the choice that looks best at the moment Everyday examples: Playing cards Invest on stocks Choose a university The hope: a locally optimal choice will lead to a globally optimal solution
- 4. MIN No. Of Coins Problem Given a value V, we want to make change for V Rs. We have infinite supply of each of the denominations in Indian currency. {1,2,5,10,20,50,100,200,500,2000}coins/notes Example- Input: value = 70 We need a 50 Rs note and a 20 Rs note. Output:2
- 5. PROPERTIES OF OPTIMAL GREEDY ALGORITHM Two ingredients that are exhibited by most problems that lend themselves to a greedy strategy Greedy-choice property Optimal substructure
- 6. Greedy-Choice Property : A global optimum can be arrived at by selecting a local optimum. Optimal Substructure : An optimal solution to the problem contains an optimal solution to subproblems
- 7. Applications Activity Selection Problem Minimum spanning tree Knapsack Problem Optimal Merging Traveling Salesman Problem Huffman Coding
- 8. Kruskal’s Alogorithm For Minimum Spanning Tree
- 15. This is minimum spanning tree
- 16. ACTIVITY SELECTION PROBLEM Problem -: given n activities with their start and finish times. Select the maximum number of activites that can be performed by a single person, assuming that a person can only work on a single activity at a time
- 17. ACTIVITY SELECTION PROBLEM Solution Greedy Approcah Sort the activities according to their finishing time Select the first activity from the sorted array and print it. DO the following for remaining activities in the sorted array. If the start time of this activity is greater than or equal to the finish time of previously selected activity then select this activity and print it.
- 18. ACTIVITY SELECTION PROBLEM ACTIVITY A1 A2 A3 A4 A5 A6 START 0 3 1 5 5 8 FINISH 6 4 2 9 7 9 ACTIVITY A3 A2 A1 A5 A6 A4 START 1 3 0 5 8 5 FINISH 2 4 6 7 9 9 SORTED Step 1:
- 19. ACTIVITY SELECTION PROBLEM Step 2 A3 Step 3 A3->A2 A3->A2->A5 A3->A2->A5->A6 TOTAL = 4 ACTIVITES ACTIVITY A3 A2 A1 A5 A6 A4 START 1 3 0 5 8 5 FINISH 2 4 6 7 9 9
- 21. DRAWBACK Very often they don’t provide a globally optimum solution Hard to verify: Showing a greedy algorithm is correct often requires a nuanced argument.
- 22. THANKYOU!