Subset Sum Problem
The Subset Sum Problem is a classical decision problem in computer science and computational complexity theory. Given a set of integers and a target sum, the problem is to determine whether there exists a subset of the given set whose sum is equal to the target ___ ______ _______ _____ ________ _______ ________ __________ ____.
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Differentiate between Cubic-time and Factorial-time algorithms. Give example of one algorithm each for these two running times.
Write the Dijkstra’s shortest path algorithm. Also, find the time complexity of this shortest path algorithm. Find the shortest paths from the vertex ‘A’ using Dijkstra’s shortest path algorithm for the graph given in Figure 1. Show all the steps of computation.
Explain the algorithm to find the optimal Binary Search Tree. Demonstrate this algorithm to find the Optimal Binary Search Tree for the following probability data (where pi represents the probability that the search will be for the key node ki, whereas qi represents that the search is for dummy node di. Make suitable assumptions, if any)
| i | 0 | 1 | 2 | 3 | 4 |
| pi | 0.10 | 0.15 | 0.20 | 0.10 | |
| qi | 0.05 | 0.10 | 0.10 | 0.10 | 0.10 |
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Consider the following Graph:
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