How to implement a dynamic programming algorithm in Java

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There are several steps to implementing a dynamic programming algorithm in Java:

  1. Identify the problem and determine if it is suitable for a dynamic programming solution.
  2. Define the subproblems and identify the optimal substructure property of the problem.
  3. Create a table or an array to store the solutions to the subproblems.
  4. Write a recursive function that takes the current subproblem as input and returns the solution to that subproblem.
  5. Use memoization to store the solutions to the subproblems in the table or array and check if a solution has already been computed before computing it again.
  6. Return the final solution from the table or array.

Here is an example of a dynamic programming algorithm for solving the Fibonacci sequence problem in Java:

public int fibonacci(int n) {
    int[] memo = new int[n + 1];
    return fibonacci(n, memo);
}

private int fibonacci(int n, int[] memo) {
    if (n <= 0) {
        return 0;
    } else if (n == 1) {
        return 1;
    } else if (memo[n] > 0) {
        return memo[n];
    }
    memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo);
    return memo[n];
}

The above code uses memoization to store the solutions to the subproblems in an array, memo, and checks if a solution has already been computed before computing it again.

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