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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. Network Design
· Greedy Network Design: Design efficient networks with minimum cost.
· Greedy Communication Scheduling: Schedule communication to maximize efficiency.
16. 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.
17. Computational Scheduling
· Greedy Task Scheduling: Schedule tasks to minimize completion time.
· Greedy Job Allocation: Allocate jobs to minimize total processing time.
18. Multi-Objective Optimization
· Greedy Multi-Objective Scheduling: Schedule tasks to optimize multiple objectives.
· Greedy Multi-Objective Resource Allocation: Allocate resources to optimize multiple metrics.
19. 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.
20. 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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