How does the factorial example illustrate the core mechanism of dynamic programming?

Conditions

• The problem can be broken down into smaller subproblems.
• The solution to the original problem can be constructed from the solutions to the subproblems.

Reasoning, step by step

1. Start with the problem of finding 4 factorial.
2. Apply the recursive formula: $4! = 4 \times 3!$.
3. Break down further: $3! = 3 \times 2!$, $2! = 2 \times 1!$.
4. Reach the base case: $1! = 1$.
5. Build the solution back up: $2! = 2 \times 1 = 2$, $3! = 3 \times 2 = 6$, $4! = 4 \times 6 = 24$.

Example

The video shows the step-by-step breakdown of $4!$ and the subsequent build-up of the final answer: $1 \rightarrow 2 \rightarrow 6 \rightarrow 24$.

Common misconceptions

• Assuming that dynamic programming only involves breaking down problems without building them back up.
• Thinking that the base case is not necessary in recursive breakdowns.

Watch the explanation

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• What is the formal definition of dynamic programming?
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