Greedy Algorithm Problems in Data Structures and Algorithms (DSA)

Greedy Algorithm Problems in Data Structures and Algorithms (DSA).

1. Basic Greedy Problems

• Fractional Knapsack Problem: Maximize the value in a knapsack with fractional items.
• Activity Selection Problem: Select the maximum number of activities that don’t overlap.
• Job Sequencing Problem: Schedule jobs to maximize profit with deadlines.
• Huffman Coding: Construct an optimal prefix code for a set of characters.
• Minimum Number of Coins: Find the minimum number of coins for a given amount.
• Maximum Subarray Sum (Kadane's Algorithm): Find the maximum sum of a contiguous subarray.
• Change-Making Problem: Compute the minimum number of coins for change.
• Greedy Coloring of Graphs: Color a graph using the minimum number of colours.
• Minimum Spanning Tree (Kruskal’s Algorithm): Find the minimum spanning tree of a graph.
• Minimum Spanning Tree (Prim’s Algorithm): Another method to find the minimum spanning tree.

2. Interval and Scheduling Problems

• Interval Scheduling Maximization: Find the maximum number of non-overlapping intervals.
• Job Scheduling with Deadlines: Schedule jobs to maximize profit with deadlines.
• Weighted Interval Scheduling: Maximize profit with intervals having weights and deadlines.
• Minimum Number of Platforms: Find the minimum number of platforms required for a train schedule.
• Event Scheduling: Schedule events to maximize the number of non-overlapping events.
• Conference Room Scheduling: Find the minimum number of rooms required for a conference.

3. Graph Problems

• Dijkstra’s Shortest Path Algorithm: Find the shortest path from a source to all nodes.
• Prim’s Algorithm for MST: Find the minimum spanning tree using a priority queue.
• Kruskal’s Algorithm for MST: Find the minimum spanning tree using edge sorting and union-find.
• Shortest Path with a Fixed Number of Edges: Find the shortest path with exactly k edges.
• Traveling Salesman Problem (TSP) Approximation: Find a near-optimal solution for TSP.
• Maximum Flow in a Network: Find the maximum flow using algorithms like Ford-Fulkerson.
• Minimum Cut in a Network: Find the minimum cut in a flow network.
• Shortest Path in Weighted Graphs (Greedy Approach): Find shortest paths with a modified greedy approach.

4. Partitioning and Selection Problems

• Greedy Set Cover: Find a minimum number of sets to cover a universe of elements.
• Kth Largest Element: Find the Kth largest element in an unsorted array.
• Partition Problem: Determine if a set can be partitioned into subsets with equal sum.
• Maximum Sum of Non-Adjacent Elements: Find the maximum sum of non-adjacent elements in an array.
• Weighted Job Scheduling: Schedule jobs with weights to maximize total profit.
• Greedy Knapsack Problem: Solve the knapsack problem with fractional values.

5. String and Text Processing

• Greedy String Matching: Find patterns in strings using a greedy approach.
• Minimum Window Substring: Find the smallest substring containing all characters of another string.
• Optimal Merge Pattern: Minimize the cost of merging multiple files.
• Longest Common Subsequence (Greedy Approximation): Find a long common subsequence with greedy methods.
• Network and Flow Problems
• Maximum Bipartite Matching: Find the maximum matching in a bipartite graph.
• Minimum Vertex Cover: Find the minimum vertex cover in a bipartite graph.
• Maximum Independent Set: Find a maximum independent set in a graph.
• Network Flow (Edmonds-Karp Algorithm): Find maximum flow using a BFS-based approach.

6. Geometry and Spatial Problems

• Convex Hull: Find the convex hull of a set of points.
• Closest Pair of Points: Find the closest pair of points using a greedy approach.
• Line Intersection: Find intersections of lines using greedy algorithms.

7. Miscellaneous Greedy Problems

• Minimum Cost Path with Obstacles: Find the minimum cost path in a grid with obstacles.
• Minimum Cost to Merge Stones: Merge stones with minimum cost to form one pile.
• Water Trapping: Calculate the amount of water trapped between elevations.
• Greedy Box Packing: Pack boxes in a container with minimum wasted space.
• Greedy Travel Path: Find an efficient travel path using greedy heuristics.
• Optimal Resource Allocation: Allocate resources optimally with greedy methods.
• Greedy Scheduling: Schedule tasks to minimize overall completion time.
• Greedy Stock Trading: Maximize profit from stock trading with limited transactions.
• Greedy Tournament Scheduling: Schedule tournaments to maximize efficiency.

8. Approximation Algorithms

• Greedy TSP Approximation: Approximate solution for the Traveling Salesman Problem.
• Greedy Vertex Cover: Approximate the minimum vertex cover in a graph.
• Greedy Knapsack Problem: Approximate solution for the 0/1 knapsack problem.
• Greedy Graph Coloring: Approximate colouring of graphs with minimum colours.
• Greedy Set Packing: Approximate solution for the set packing problem.

9. Scheduling and Allocation

• Job Shop Scheduling: Allocate jobs to machines with minimum makespan.
• Resource Allocation: Allocate resources to maximize utilization.
• Interval Partitioning: Partition intervals into a minimum number of resources.
• Load Balancing: Distribute tasks to minimize the maximum load.

10. Array and Sequence Optimization

• Minimum Difference Partition: Partition an array to minimize the difference between sums.
• Largest Sum of K Contiguous Elements: Find the largest sum of k contiguous elements.
• Minimum Cost to Cut a Rod: Find the minimum cost of cutting a rod into pieces.
• Greedy Array Rearrangement: Rearrange an array to maximize a certain metric.

11. Resource Management

• Greedy Load Balancing: Distribute resources to minimize the maximum load.
• Greedy Job Scheduling with Deadlines: Schedule jobs to maximize profit by deadlines.
• Optimal Resource Allocation for Tasks: Allocate resources to tasks optimally.

12. Graph Approximation

• Greedy Approximation for Steiner Tree: Approximate solution for the Steiner tree problem.
• Greedy Solution for the Set Cover Problem: Approximate set cover with greedy methods.
• Greedy Approach for Facility Location: Approximate facility location problems.

13. Financial and Operational Optimization

• Greedy Investment Strategy: Maximize returns from investments using greedy methods.
• Greedy Pricing Strategy: Set prices to maximize revenue.
• Greedy Supply Chain Management: Optimize supply chain operations with greedy algorithms.

14. Network Design

Greedy Network Design: Design efficient networks with minimum cost.
Greedy Communication Scheduling: Schedule communication to maximize efficiency.

15. Computational Geometry

• Greedy Point Selection: Select points to cover a region with minimal number of points.
• Greedy Polygon Triangulation: Triangulate a polygon using greedy methods.

16. Computational Scheduling

• Greedy Task Scheduling: Schedule tasks to minimize completion time.
• Greedy Job Allocation: Allocate jobs to minimize total processing time.

17. Multi-Objective Optimization

• Greedy Multi-Objective Scheduling: Schedule tasks to optimize multiple objectives.
• Greedy Multi-Objective Resource Allocation: Allocate resources to optimize multiple metrics.

18. Game Theory and Strategic Planning

• Greedy Game Strategy: Develop strategies for games using greedy algorithms.
• Greedy Resource Allocation in Games: Allocate resources optimally in-game scenarios.

19. Advanced Greedy Algorithms

• Greedy Approach for Maximum Independent Set: Approximate solution for the maximum independent set.
• Greedy Algorithm for Vertex Cover in Non-Bipartite Graphs: Approximate vertex cover in general graphs.
• Greedy Algorithm for Shortest Path with Constraints: Find the shortest path under constraints.
• Greedy Algorithm for Network Flow with Multiple Sources: Solve network flow problems with multiple sources.
• Greedy Algorithm for Weighted Graph Coloring: Approximate graph coloring with weights.
• Greedy Algorithm for Cutting Stock Problem: Solve cutting stock problems with greedy methods.
• Greedy Approach for Vehicle Routing Problem: Approximate solution for vehicle routing.
• Greedy Algorithm for Multi-Dimensional Knapsack Problem: Approximate multi-dimensional knapsack solutions.
• Greedy Algorithm for Optimal Path Planning: Find optimal path planning using greedy heuristics.
• Greedy Algorithm for Multiple Knapsack Problem: Solve multiple knapsack problems with greedy methods.
• Greedy Algorithm for Bandwidth Allocation: Optimize bandwidth allocation with greedy approaches.
• Greedy Approach for Scheduling with Resource Constraints: Schedule tasks considering resource constraints.
• Greedy Algorithm for Weighted Job Scheduling: Maximize profit with weighted job scheduling.
• Greedy Algorithm for Large-Scale Network Optimization: Optimize large-scale networks with greedy methods.
• Greedy Algorithm for Task Assignment in Parallel Systems: Assign tasks in parallel systems optimally.
• Greedy Algorithm for Optimal Sequencing: Sequence tasks or events optimally.
• Greedy Approach for Inventory Management: Optimize inventory levels using greedy algorithms.
• Greedy Algorithm for Optimal Time Management: Manage time effectively with greedy approaches.

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