java实现排列组合

• 排列公式

• 组合公式

1. 计算n! = n * (n-1) * ...*2 *1

/**
     * 计算n的阶乘
     *
     * @param n
     * @return 返回 n!
     */
    private static long factorial(int n) {
        long sum = 1;
        while (n > 0) {
            sum = sum * n--;
        }
        return sum;
    }

2.计算排列A(n,m)个数

/**
     * 计算排列A(n, m)
     *
     * @param m
     * @param n
     * @return 返回A(n, m)的排列个数
     */
    private static long arrangement(int m, int n) {
        return m <= n ? factorial(n) / factorial(n - m) : 0;
    }

3.计算组合C(n,m)个数

/**
     * 计算组合C(n, m)
     *
     * @param m
     * @param n
     * @return 返回C(n, m)的组合个数
     */
    private static long combination(int m, int n) {
        return m < n ? factorial(n) / (factorial(n - m) * factorial(m)) : 0;
    }

4.展示排列情况

public static void arrangementSelect(String[] dataList, int n) {
        System.out.println(String.format("A(%d, %d) = %d ", dataList.length, n, arrangement(n, dataList.length)));
        arrangementSelectRes(dataList, new String[n], 0);
    }

    private static void arrangementSelectRes(String[] dataList, String[] resultList, int resultIndex) {
        int resultLen = resultList.length;
        if (resultIndex >= resultLen) { // 全部选择完时，输出排列结果
            System.out.println(Arrays.asList(resultList));
            return;
        }
        // 递归选择下一个
        for (int i = 0; i < dataList.length; i++) {
            // 判断待选项是否存在于排列结果中
            boolean exists = false;
            for (int j = 0; j < resultIndex; j++) {
                if (dataList[i].equals(resultList[j])) {
                    exists = true;
                    break;
                }
            }
            if (!exists) { // 排列结果不存在该项，才可选择
                resultList[resultIndex] = dataList[i];
                arrangementSelectRes(dataList, resultList, resultIndex + 1);
            }
        }
    }

5.展示组合情况

public static void combinationSelect(String[] dataList, int n) {
        System.out.println(String.format("C(%d, %d) = %d", dataList.length, n, combination(n, dataList.length)));
        combinationSelect(dataList, 0, new String[n], 0);
    }
    private static void combinationSelect(String[] dataList, int dataIndex, String[] resultList, int resultIndex) {
        int resultLen = resultList.length;
        int resultCount = resultIndex + 1;
        if (resultCount > resultLen) { // 全部选择完时，输出组合结果
            System.out.println(Arrays.asList(resultList));
            return;
        }
        // 递归选择下一个
        for (int i = dataIndex; i < dataList.length + resultCount - resultLen; i++) {
            resultList[resultIndex] = dataList[i];
            combinationSelect(dataList, i + 1, resultList, resultIndex + 1);
        }
    }

6.测试

public static void main(String[] args) {
        // 计算n的阶乘
        System.out.println(arrangement(3, 6));
        System.out.println(combination(3, 6));
        String[] a = {"a", "b", "c", "d", "e", "f"};
        arrangementSelect(a, 3);
        combinationSelect(a,3);
    }

7.输出结果如图：