Greedy Algorithms Interview Questions (original) (raw)

Last Updated : 18 Sep, 2025

Greedy is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. Greedy algorithms are used for optimization problems.

Easy Problems

Medium Problems

Hard Problems

Top Theoretical Interview Questions on Greedy Algorithms

1. Explain the difference between Greedy Algorithms and Dynamic Programming. Why can’t we always use Greedy instead of DP?

Greedy Algorithms make decisions based only on the current state, assuming locally optimal choices lead to a globally optimal solution.
Dynamic Programming (DP) solves problems by solving all subproblems and using their solutions to build up the final solution.

**Key Reason Greedy Fails Sometimes:

Greedy works only if the problem exhibits the greedy choice property and optimal substructure.
DP works even if overlapping subproblems exist, because it considers all combinations.

**Example where Greedy fails but DP works: 0/1 Knapsack Problem.

2. In Huffman Encoding, why does the greedy approach of combining the two least frequent symbols yield the optimal prefix code?

Huffman's algorithm repeatedly combines the two symbols with the least frequencies.

**Why Greedy Works: The Greedy Choice Property holds because combining the least frequent symbols minimizes the total weighted path length.
**Optimal Substructure: A smaller optimal tree leads to an optimal overall tree.

**Note: Therefore, Huffman encoding produces the minimal average code length.

3. Describe a real-world scenario where the greedy algorithm does not yield the optimal solution. Why does the greedy approach fail in that case?

**Scenario: Airline seat booking for maximizing revenue with dynamic pricing.
**Greedy Approach: Always allocate the current seat to the customer offering the highest immediate price.

**Why It Fails:

Future high-value customers may be blocked by earlier greedy decisions.
The optimal strategy may involve rejecting early low-paying customers to save space for higher-paying ones.

**Note: Greedy lacks global foresight; optimal solutions require dynamic programming or predictive models.

4. Why does the Fractional Knapsack problem allow greedy algorithms but not the 0/1 Knapsack problem?

In Fractional Knapsack, taking a fraction of an item is allowed, enabling proportional value maximization based on value-to-weight ratio.

Greedy works because partial decisions can be adjusted at each step without restriction. In contrast, in 0/1 Knapsack, items cannot be divided and greedy choices may prevent better combinations later.

**Note: This violates the greedy choice property.

**5. How is the Greedy algorithm applied in the Coin Change problem and why does it fail for certain coin denominations?

**Greedy approach: Always pick the largest denomination coin that does not exceed the remaining amount.

**Why it fails:

Works in canonical coin systems (e.g., US coins).
Fails in non-canonical systems, e.g., coin denominations {1, 3, 4} for amount 6: Greedy picks 4 + 1 + 1 = 3 coins. Optimal is 3 + 3 = 2 coins.

**Note: Greedy Choice Property fails for arbitrary coin sets.

**6. In interval partitioning problems, why does the greedy approach of scheduling activities based on earliest start time fail to produce the minimum number of resources?

**Greedy Strategy: Sort activities by earliest start time and assign them to available resources.

**Why it fails:

Earliest start does not guarantee minimum overlap.
Correct strategy: Sort by earliest finish time and schedule accordingly.

**Note: Greedy approach fails because it ignores how end times affect future conflicts, violating optimal substructure.

**7. Is the Greedy strategy always faster than Dynamic Programming? Justify with time complexity arguments.

Greedy algorithms usually run in O(n log n) or O(n) due to simple sorting and linear traversal.
Dynamic Programming often runs in O(n²) or O(nW), depending on problem size and constraints.

**However, speed does not mean correctness:

Greedy is faster but applicable only where optimal substructure and greedy choice properties hold.
DP is slower but handles overlapping subproblems and complex dependencies.

**Note: Greedy is not always the right choice despite being faster.

8. Explain with an example how Greedy fails in scheduling jobs with deadlines and varying profits where each job takes more than unit time.

Standard greedy approach assumes unit time jobs.

**Example:

Job A: deadline 4, profit 100, time 2.
Job B: deadline 2, profit 50, time 1.

Greedy picks Job A first (highest profit), consuming time 2, but misses Job B’s deadline. Optimal solution schedules Job B first, maximizing total profit.

**Note: Greedy fails when job durations vary and require global planning.

**9. In Minimum Number of Platforms problem (Railway Scheduling), explain why sorting arrival and departure times and processing them sequentially is optimal.

Sort arrival and departure times separately.
Use two pointers to process them.

**Why optimal?

At each step, we know exactly how many platforms are occupied.
This is because the problem exhibits optimal substructure
The minimum platforms up to any point depend only on current arrival and departure events.

**Note: Greedy works perfectly due to the predictable linear structure of the timeline.

10. Can a greedy approach solve the Set Cover problem optimally? Why or why not?

**Set Cover Problem: Find the minimum number of sets covering all elements.
**Greedy Approach: At each step, pick the set covering the largest number of uncovered elements.

**Why it fails to be optimal:

Set Cover is NP-Hard.
Greedy provides a logarithmic approximation factor but not the exact minimum.

**Note: Greedy is useful for approximations but not guaranteed optimal for Set Cover.