0/1Knapsack
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The document discusses the 0/1 knapsack problem and different approaches to find the optimal solution. It describes the problem as filling a knapsack from objects with given weights and benefits to maximize the total benefit within a weight limit. It then summarizes dynamic programming and greedy approaches to solve the problem, and shows the optimal solution is to choose items with weights 3, 4, and 5 to get a total benefit of 9 within the weight limit of 7.
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This presentation discusses different types of beams and beam supports and reactions. It defines a beam as a structural element that can withstand loads by resisting bending. There are several types of beams including simply supported beams, fixed beams, cantilever beams, overhanging beams, and continuous beams. The types of supports include simply supported, fixed, and hinged. The reaction in a beam depends on the type of beam, loads applied, and support type. Reactions always occur at support ends and can be in the form of forces or couples.
Beam , support and reaction
This document discusses different types of beams and beam supports and reactions. It defines a beam as a structural element that can withstand loads by resisting bending. It describes simply supported beams, fixed beams, cantilever beams, overhanging beams, continuous beams, and trussed beams. It also discusses types of loads and notes that the reaction in a beam depends on the type of beam, loads, and supports, with reactions always generated at support ends for forces or couples.
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### How TDM Works
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4. **Multiplexer and Demultiplexer**: At the transmitting end, a multiplexer combines multiple input signals into a single composite signal by assigning each signal to a specific time slot. At the receiving end, a demultiplexer separates the composite signal back into individual signals based on their respective time slots.
### Types of TDM
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### Applications of TDM
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### Advantages of TDM
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0/1Knapsack
- 1. 0/1 Knapsack Problem and Optimal merge pattern
- 2. The Problem: We have a knapsack to be filled with enlisted objects of given weight and benefit ,total weight=7 find the optimal merge pattern to do so . WEIGHT: 1 3 4 5 BENEFIT: 1 4 5 7
- 3. Approaches to solve the problem ● The Greedy approach:Make the locally optimal choice at each stage with the hope of finding a global optimum. ● The brute-force approach:It is a trial and error method used to find global optimum.(i.e Compute all possible combinations and search for optimal) ● The Dynamic Programming approach:Formula is to break a large problem down into small sub steps so that, at any given stage, optimal solutions are known to sub-problems. ● The 4th approach: Discussed at the end of presentation.
- 4. Benefit Weight 0 1 2 3 4 5 6 7 1 1 4 3 5 4 7 5
- 5. If total weight is zero , no matter what i have the max benefit would still be zero. Benefit Weight 0 1 2 3 4 5 6 7 1 1 0 4 3 0 5 4 0 7 5 0
- 6. Even though the total weight is high all i have is 1 item so max is 1 Benefit Weight 0 1 2 3 4 5 6 7 1 1 0 1 1 1 1 1 1 1 4 3 0 5 4 0 7 5 0
- 7. Max(4+1 or 1),hence 5 max(4+0 or 1), hence 4 Benefit Weight 0 1 2 3 4 5 6 7 1 1 0 1 1 1 1 1 1 1 4 3 0 1 1 4 5 5 5 5 5 4 0 1 1 4 7 5 0
- 8. Max(5+4 or 5), hence 9 max(7+1 or 6),hence 8 Max(7+1 or 9),hence 9 Benefit Weight 0 1 2 3 4 5 6 7 1 1 0 1 1 1 1 1 1 1 4 3 0 1 1 4 5 5 5 5 5 4 0 1 1 4 5 6 6 9 7 5 0 1 1 4 5 7 8 9
- 9. The 4th approach :solves problem through machine learning(i.e)study of pattern recognition and computational learning theory. Benefit Weight 0 1 2 3 4 5 6 7 1 1 0 1 1 1 1 1 1 1 4 3 0 1 1 4 5 5 5 5 5 4 0 1 1 4 5 6 6 9 7 5 0 1 1 4 5 7 8 9
- 10. Thank you !