Worked Examples: Greedy Algorithms

These examples are designed to step through the logical process of applying the algorithmic concepts.

Example 1: Activity Selection

❓ Problem: Why earliest finish?

💡 Solution: Leaves maximal time for future resources.

Example 2: Counter-Example

❓ Problem: Shortest duration first?

💡 Solution: Fails. [1-5], [4-7], [6-10]. Shortest [4-7] blocks both.

Example 3: Fractional Knapsack

❓ Problem: Strategy?

💡 Solution: Take item with max Value/Weight ratio.

Example 4: Huffman Optimality

❓ Problem: Prefix property solution.

💡 Solution: No code is prefix of another. Unambiguous.

Example 5: Huffman Cost

❓ Problem: Cost of tree?

💡 Solution: $\sum f_i \cdot depth_i$.

Example 6: Complexity

❓ Problem: Activity Select with Sort.

💡 Solution: $O(n \log n)$.