Dynamic programming is a technique used to solve complex problems by breaking them down into smaller overlapping subproblems. By storing the results of the subproblems in a cache, we can avoid redundant calculations and improve the overall performance.

Here is an example of how dynamic programming can be implemented in C#:

“`csharp

public class DynamicProgramming

{

// Cache to store the results of subproblems

private int[] cache;

public DynamicProgramming()

{

// Initialize the cache with -1 to indicate that the values have not been calculated yet

cache = new int[100];

for (int i = 0; i < cache.Length; i++)
{
cache[i] = -1;
}
}
// Recursive function to calculate the Fibonacci number
public int Fibonacci(int n)
{
// Base cases
if (n == 0) return 0;
if (n == 1) return 1;
// Check if the value has already been calculated
if (cache[n] != -1) return cache[n];
// Calculate the value and store it in the cache
int result = Fibonacci(n - 1) + Fibonacci(n - 2);
cache[n] = result;
return result;
}
}
class Program
{
static void Main(string[] args)
{
DynamicProgramming dp = new DynamicProgramming();
// Calculate the Fibonacci number for n=10
int result = dp.Fibonacci(10);
Console.WriteLine(result);
}
}
```
In this example, we have a `DynamicProgramming` class that contains a cache array to store the results of subproblems. The cache is initialized with -1 to indicate that the values have not been calculated yet.
The `Fibonacci` function is a recursive function that calculates the Fibonacci number for the given input `n`. Before calculating the value, it checks if the value has already been calculated and stored in the cache. If so, it returns the cached value. Otherwise, it calculates the value recursively, stores it in the cache, and returns the result.
In the `Main` method, we create an instance of the `DynamicProgramming` class and call the `Fibonacci` function to calculate the Fibonacci number for `n=10`. The result is then printed to the console.
By using dynamic programming and caching the results, we can significantly improve the performance of the Fibonacci calculation, especially for large values of `n`.