Activity Selection & Fractional Knapsack

Greedy Algorithm Principles

Greedy algorithms make locally optimal choices at each step, hoping to find global optimum.

Production Code Example:

import java.util.*;
public class FractionalKnapsack {
    static class Item { int weight, value; Item(int w, int v) { weight = w; value = v; } }
    public double getMaxValue(Item[] items, int capacity) {
        Arrays.sort(items, (a, b) -> Double.compare((double)b.value / b.weight, (double)a.value / a.weight));
        double totalVal = 0.0;
        for (Item item : items) {
            if (capacity >= item.weight) {
                capacity -= item.weight; totalVal += item.value;
            } else {
                totalVal += item.value * ((double)capacity / item.weight); break;
            }
        }
        return totalVal;
    }
}

Key Complexity & Algorithmic Takeaways:

When implementing Activity Selection & Fractional Knapsack in coding interviews and production applications, keep these core guidelines in mind:

• Time Complexity Analysis: Always evaluate best-case, average-case, and worst-case time complexities ($O(1)$, $O(\log n)$, $O(n)$, $O(n \log n)$, $O(n^2)$).
• Space Complexity & Memory Bounds: Account for auxiliary memory usage, call stack frame recursion overhead, and heap allocations.
• Edge Cases & Validation: Test empty inputs, null pointers, single-element collections, duplicate values, and integer overflow bounds.
• Optimal vs Naive Solutions: Start with a clear brute-force solution, then optimize using techniques like Hashing, Two Pointers, Windowing, or Dynamic Programming.

Summary Takeaway:

Mastering Activity Selection & Fractional Knapsack provides the foundational problem-solving skills needed to pass technical coding interviews at top tech companies and write ultra-performant software systems.