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Greedy Algorithms Concepts
Review strategy choices and proofs.
1. What is the primary characteristic of a greedy algorithm?
Makes locally optimal choices at each step
Solves problems by breaking them into subproblems and combining solutions
Uses backtracking to explore all possible paths
Relies on dynamic programming for optimal substructure
2. Which of the following problems is typically solved using a greedy algorithm?
Traveling Salesman Problem
Activity Selection Problem
Longest Common Subsequence
0-1 Knapsack Problem
3. What two key properties must a problem satisfy for a greedy algorithm to guarantee an optimal solution?
Optimal substructure and overlapping subproblems
Greedy choice property and overlapping subproblems
Optimal substructure and greedy choice property
Backtracking capability and exponential time complexity
4. Which of the following are examples of greedy algorithms?
Kruskal's Algorithm
Prim's Algorithm
Floyd-Warshall Algorithm
Huffman Coding
5. Which properties describe problems suitable for greedy algorithms?
Greedy choice property
Optimal substructure
Overlapping subproblems
No need for backtracking
6. The 'greedy choice property' states that a globally optimal solution can be reached by making locally optimal (greedy) choices at each step.
True
False
7. The 0-1 Knapsack problem can be optimally solved using a greedy algorithm.
True
False
8. What term describes the property that a globally optimal solution contains optimal solutions to its subproblems?
9. Name the greedy algorithm that finds a minimum spanning tree by adding edges in increasing order of weight, avoiding cycles using a union-find data structure.
10. What greedy algorithm constructs variable-length prefix codes with minimum total length, commonly used in data compression?
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