Common Problems and Examples

Dynamic programming is a powerful technique that can be used to solve a wide range of problems. In this section, we will explore some common problems and examples that can be solved using dynamic programming techniques.

Problem 1: Fibonacci Sequence

The Fibonacci sequence is a classic example that can be solved using dynamic programming. The sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones.

To solve this problem using dynamic programming, we can use memoization to store the solutions for each Fibonacci number and avoid redundant calculations. Here's an example implementation:

1const fibonacci = (n, memo = {}) => {
2  if (n <= 1) {
3    return n;
4  }
5
6  if (n in memo) {
7    return memo[n];
8  }
9
10  memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo);
11  return memo[n];
12}
13
14console.log(fibonacci(5)); // Output: 5
15console.log(fibonacci(10)); // Output: 55
16console.log(fibonacci(20)); // Output: 6765

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console.log('Hello World');