当对象只有最终字段时，如何编写递归方法来生成算术序列？

Posted 2021-03-30

所以我正在完成我的第一个CS类，所以我的经验肯定是在低端，但是对于一个赋值，我必须创建一个方法来生成并返回算术序列中索引n的数量，并带有起始值init和常见差异差异

这根本不容易使用递归，但需要递归。我也仅限于可以使用的字段，方法和方法签名。

我也了解如何使用下面的代码制作此方法。

public class ArithmeticNumberGenerator implements NumberGenerator {
    private int init; // first term in the sequence
    private final int diff; // common difference

    /**
     * Constructs an arithmetic number generator with given
     * start value init and common difference diff
     * @param init start value
     * @param diff common difference
     * @throws IllegalArgumentException if any of the input arguments
     * is illegal
     */
    public ArithmeticNumberGenerator(int init, int diff) throws 
IllegalArgumentException {
        if (init < 0 || diff < 0)
            throw new IllegalArgumentException("Cannot use negative numbers.");
        else {
            this.init = init;
            this.diff = diff;
        }
    }

    @Override
    public int generateNumber(int n) {
        // Time Complexity: O(?)
        // This method generates the number of index n
        // in an arithmetic sequence recursively

        if (n == 0)
            return init;
        else {
            init = init + diff;
            return generateNumber(n - 1);
        }
    }
}

但是，对于赋值，“init”字段应该是final，并且在这种情况下我无法弄清楚如何实现此方法。任何帮助将不胜感激。

答案

如果我正确理解了问题，你必须使用递归，并且上面的所有方法签名都是固定的，并且init必须是最终的。以下遵守这些规则。

public static class ArithmeticNumberGenerator implements NumberGenerator {

    private final int init; // first term in the sequence
    private final int diff; // common difference
    /**
     * Constructs an arithmetic number generator with given start value init
     * and common difference diff
     * 
     * @param init
     *            start value
     * @param diff
     *            common difference
     * @throws IllegalArgumentException
     *             if any of the input arguments is illegal
     */
    public ArithmeticNumberGenerator(int init, int diff) throws IllegalArgumentException {
        if (init < 0 || diff < 0)
            throw new IllegalArgumentException("Cannot use negative numbers.");
        else {
            this.init = init;
            this.diff = diff;
        }
    }

    @Override
    public int generateNumber(int n) {
        // Time Complexity: O(?)
        // This method generates the number of index n
        // in an arithmetic sequence recursively

        if (n == 0)
            return init;
        else {
            ArithmeticNumberGenerator g = new ArithmeticNumberGenerator(init+diff, diff);
            return g.generateNumber(n - 1);
        }
    }
}