Memoization

Memoization is a technique used in dynamic programming to improve the efficiency of recursive algorithms. It involves storing the results of expensive function calls and reusing them when the same inputs occur again.

In the context of dynamic programming, memoization can be thought of as a way to avoid redundant computation of subproblems. Instead of recomputing the solution for each subproblem, we can store the results in a data structure, such as an array or a hashmap, and use these results for future computations.

Memoization can greatly reduce the time complexity of a recursive algorithm by eliminating redundant calculations. It allows us to solve problems that would otherwise be infeasible to solve within a reasonable amount of time.

Let's take a look at an example of using memoization in the implementation of the Fibonacci sequence:

1class Main {
2  public static void main(String[] args) {
3    // Replace with your Java logic here
4    int n = 10;
5    int result = fibonacci(n);
6    System.out.println("The Fibonacci number at position " + n + " is: " + result);
7  }
8
9  private static int fibonacci(int n) {
10    int[] memo = new int[n + 1];
11    return memoizedFibonacci(n, memo);
12  }
13
14  private static int memoizedFibonacci(int n, int[] memo) {
15    if (n <= 1) {
16      return n;
17    }
18
19    if (memo[n] != 0) {
20      return memo[n];
21    }
22
23    int fib = memoizedFibonacci(n - 1, memo) + memoizedFibonacci(n - 2, memo);
24    memo[n] = fib;
25    return fib;
26  }
27}

In this example, we use memoization to optimize the calculation of the Fibonacci number at a given position. By storing the intermediate results in the memo array, we eliminate redundant calculations and improve the time complexity of the algorithm.

Memoization is a powerful technique that can be applied to various algorithms to achieve significant performance improvements. It is particularly useful in situations where the same subproblems are encountered multiple times, as it allows us to avoid recalculating the results.

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class Main {

  public static void main(String[] args) {

    // Replace with your Java logic here

    int n = 10;

    int result = fibonacci(n);

    System.out.println("The Fibonacci number at position " + n + " is: " + result);

  }

​

  private static int fibonacci(int n) {

    int[] memo = new int[n + 1];

    return memoizedFibonacci(n, memo);

  }

​

  private static int memoizedFibonacci(int n, int[] memo) {

    if (n <= 1) {

      return n;

    }

​

    if (memo[n] != 0) {

      return memo[n];

    }

​

    int fib = memoizedFibonacci(n - 1, memo) + memoizedFibonacci(n - 2, memo);

    memo[n] = fib;

    return fib;

  }

}