Dynamic Programming.MD

Dynamic Programming

Basic Concept

• Recursive solution: repeated calls for same inputs --> optimize using Dynamic Programming by storing the results of subproblems.

• Fibonacci Example

  • Recursive Solution

  int fib(int n) {
    if (n <= 1)
      return 1;
     return fib(n-1) + fib(n-2);
  }

  • Dynamic Programming Solution

  int fib(int n) {
    int f[n + 1];
    f[0] = 1;
    f[1] = 1;
    
    for (int i = 0; i <= n; i++) {
      f[i] = f[i-1] + f[i-2];
    }
    
    return f[n];
  }