What are the two defining characteristics of a dynamic programming problem?

Conditions

• The problem can be solved using an algorithmic approach.
• The problem can be divided into subproblems.

Reasoning, step by step

1. Identify the two conditions required for a problem to be classified as a dynamic programming problem.
2. Define optimal substructure: the optimal solution to the main problem can be constructed from the optimal solutions of its subproblems.
3. Define overlapping subproblems: the same subproblems are encountered repeatedly during the recursive breakdown.
4. Visualize these conditions using a Venn diagram where the intersection of 'Optimal Substructures' and 'Overlapping Subproblems' is labeled 'Dynamic Programming Problem'.

Example

The video uses a Venn diagram to show that a Dynamic Programming Problem is the intersection of Optimal Substructures and Overlapping Subproblems.

Common misconceptions

• Assuming that a problem only needs one of the two conditions to be a dynamic programming problem.
• Confusing overlapping subproblems with simply having subproblems.

Watch the explanation

Explore next

• How does the factorial example illustrate the core mechanism of dynamic programming?
• What does optimal substructure mean in dynamic programming?
• What are overlapping subproblems in dynamic programming?