1- Incremental approach

1.1- Input-Centric Strategy

• What new input can we add to the solution at this iteration?
• How can we incorporate this input into the current solution in a way that is consistent with the overall approach?
• What impact will this input have on the overall solution?

1.2- Output-Centric Strategy

• What output can we add to the solution at this iteration?
• How can we incorporate this output into the current solution in a way that is consistent with the overall approach?
• What impact will this output have on the overall solution?

1.3- Iterative Improvement Strategy

• How can we improve the current approximation of the solution?
• What changes can we make to the current solution that will bring us closer to the final solution?
• How can we evaluate the quality of the improved solution and determine whether it is good enough to move on to the next iteration?

2- Decrease and Conquer Approach

2.1- Evaluating the Problem at a Smaller Scale

• How can we reduce the scale of the problem?
• What are the key features of the problem that we need to preserve in order to maintain its essential characteristics?
• Can we find a solution to the reduced problem that is likely to be compatible with a solution to the larger problem?

2.2- Expanding the Solution to a Larger Scale

• How can we expand the solution to the reduced problem to a larger scale?
• What are the limitations of the solution at the larger scale?
• How can we overcome these limitations and find a solution to the larger problem?

2.3- Comparison and Refinement

• How does the solution to the larger problem compare to the solution to the smaller problem?
• Are there any inconsistencies or conflicts between the two solutions?
• How can we refine the solution to the larger problem to make it consistent with the solution to the smaller problem?

3- Divide and Conquer Approach

3.1- Dividing the Problem into Smaller Problems

• How can we divide the problem into smaller problems?
• What are the key characteristics of the smaller problems that need to be preserved in order to maintain the essential characteristics of the larger problem?
• How can we ensure that the smaller problems are independent and can be solved individually?

3.2- Solving the Smaller Problems

• How can we solve each of the smaller problems individually?
• What are the key features of the solutions to the smaller problems that need to be preserved in order to maintain the essential characteristics of the larger solution?
• How can we evaluate the quality of the solutions to the smaller problems and determine whether they are good enough to be combined?

3.3- Combining the Solutions to the Smaller Problems

• How can we combine the solutions to the smaller problems to form a solution to the larger problem?
• What are the key challenges in combining the solutions in a way that is consistent with the overall approach?
• How can we evaluate the quality of the combined solution and determine whether it is good enough to be considered a solution to the larger problem?

4- Transform and Conquer Approach

4.1- Input Format

• What is the current input format of the problem?
• How can the input format be changed to make the problem easier to solve?
• Are there any potential drawbacks to changing the input format?

4.2- Output Format

• What is the current output format of the problem?
• How can the output format be changed to make the problem easier to solve?
• Are there any potential drawbacks to changing the output format?

4.3- Constraints

• What are the current constraints of the problem?
• How can the constraints be changed to make the problem easier to solve?
• Are there any potential drawbacks to changing the constraints of the problem?

5- Greedy Approach

5.1- Heuristic Evaluation

• What is the heuristic that is being used to evaluate different options?
• How does the heuristic work, and how is it used to choose the most promising option?
• Are there any potential drawbacks to using this heuristic, and are there any situations in which it might not be effective?

5.2- Expanding the Solution

• How does the greedy approach expand the solution step by step?
• What are the potential benefits of this approach, and why might it be effective in some situations?
• Are there any potential drawbacks to using the greedy approach, and are there any situations in which it might not be the best choice?