java - 动态规划的记忆化

Question

我正在尝试学习动态规划的记忆化，我正在观看麻省理工学院在 youtube 上的视频，试图跟进它。我不知道如何将第 N 个值与数组进行比较。

int[] memo;
public int fib(int n) {
    int f = 0;

    if n is in memo then return memo[n] <----not sure how to code this line.

    if (n<=2) {
        f = 1;
    } else {
        f = fib(n-1) + fib(n-2);
    }

    memo[n] = f;
    return f;
}

Answer 1

用 ArrayList 做:

ArrayList<Integer> memo = new ArrayList<Integer>();

public int fib(int n) {
    if (memo.size() == 0)
       memo.add(0); // element 0 is never accessed
    return fib2(n);
}

private int fib2(int n) {
    int f = 0;

    if (n < memo.size())
       return memo.get(n);

    if (n<=2) {
        f = 1;
    } else {
       f = fib2(n-2) + fib2(n-1);
    }

    memo.add(f); // elements inserted in order
    return f;
}

用数组做:

int[] memo;

public int fib(int n) {
    memo = new int[n+1]; // all initialized to 0
    return fib2(n);
}

private int fib2(int n) {
    int f = 0;

    if (memo[n] != 0)
       return memo[n];

    if (n <= 2) {
        f = 1;
    } else {
        f = fib2(n-2) + fib2(n-1);
    }

    memo[n] = f;
    return f;
}