Download presentation
Presentation is loading. Please wait.
1
Robbing a House with Greedy Algorithms
Casey O’Brien
2
Knapsack Problem
4
Your Knapsack Max Weight: 10 pounds
5
Item
6
Item Value 13 5 3 6 9
7
Item Value Weight 13 8 5 3 0.6 6 1.5 9
8
Goal: Maximize total value
Constraint: Total weight cannot exceed 10 pounds
9
Item Value Weight 13 8 5 3 0.6 6 1.5 9
10
Item Value Weight Value/Weight 13 8 1.6 5 1 3 0.6 6 1.5 4 9
11
Play The Robber!
12
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
13
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
14
Item Value Weight Value/Weight Knapsack 12 8 1.6 5 1 3 0.6 6 1.5 4 9
15
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
16
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
17
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
18
Final Knapsack: Final Value: $14
19
Play The Robber!
20
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
21
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
22
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
23
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
24
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
25
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
26
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
27
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
28
Final Knapsack: Final Value: $19
29
Final Knapsack: Final Value: $16
30
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
31
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
32
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
33
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
34
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
35
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
36
Final Knapsack: Final Value: $14
37
Final Knapsack: Final Value: $20
38
Final Knapsack: Final Value: $17
39
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
40
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
41
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
42
Final Knapsack: Final Value: $15
43
Final Knapsack: Final Value: $18
44
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
45
Greedy Algorithms
46
Greedy by Largest Value
47
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
48
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
49
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
50
Final Knapsack: Final Value: $19
51
Greedy by Smallest Weight
52
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
53
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
54
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
55
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
56
Final Knapsack: Final Value: $18
57
Greedy by Largest Ratio
58
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
59
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
60
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
61
Item Value Weight Value/Weight Knapsack 13 8 1.6 5 1 3 0.6 6 1.5 4 9
62
Final Knapsack: Final Value: $18
63
Greedy Algorithms do not guarantee optimal solution
Problem: Greedy Algorithms do not guarantee optimal solution
64
Exhaustive Enumeration
65
Exhaustive Enumeration
Try All Possibilities
66
How Many Possibilities?
75
Final Knapsack: Final Value: $20
76
Problem: Takes Too Long!
77
40 Items
78
~1 Trillion Possibilities
40 Items ~1 Trillion Possibilities
79
~1 Trillion Possibilities
40 Items ~1 Trillion Possibilities ~35,000 Years to Compute
80
What Can We Do?
81
Settle For Less Than Optimal
82
Recall Greedy Algorithms:
By Value: $19 By Weight: $18 By Ratio: $18 Optimal: $20
83
Moral of the Story: We can use Greedy Algorithms to approximate solutions to the knapsack problem quickly.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.