从Java中的矩阵返回所有组合[关闭]

Question

我见过这个问题的不同版本，但从来没有一个好的答案。我有一个 MXN 数组，想要返回 M 大小的所有可能组合。让我举个例子，有一个 3X3 数组。结果应该是 27 种组合。我在这里尝试递归方法，但到目前为止没有运气。

Answer 1

如果这个程序可以帮助你，请尝试。我用过这个矩阵

   int[][] matrix = {{1, 2, 3},
                {4, 5, 6},
                {7, 8, 9}};

输出是 27 种组合，如下所示。

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Main {
    private static List<int[]> combine(int[][] matrix) {
        int sizeArray[] = new int[matrix.length];
        int counterArray[] = new int[matrix.length];
        int total = 1;
        for (int i = 0; i < matrix.length; ++i) {
            sizeArray[i] = matrix[i].length;
            total *= matrix[i].length;
        }
        List<int[]> list = new ArrayList<>(total);
        StringBuilder sb;
        for (int count = total; count > 0; --count) {
            sb = new StringBuilder();
            for (int i = 0; i < matrix.length; ++i) {
                sb.append(matrix[i][counterArray[i]]);
            }
            int tmpi[] = new int[sb.toString().length()];
            for (int tmp = 0; tmp < sb.toString().length(); tmp++) {
                tmpi[tmp] = Integer.parseInt("" + sb.toString().toCharArray()[tmp]);
            }
            list.add(tmpi);
            for (int incIndex = matrix.length - 1; incIndex >= 0; --incIndex) {
                if (counterArray[incIndex] + 1 < sizeArray[incIndex]) {
                    ++counterArray[incIndex];
                    break;
                }
                counterArray[incIndex] = 0;
            }
        }
        return list;
    }

    public static void main(String[] args) {
        int[][] matrix = {{1, 2, 3},
                {4, 5, 6},
                {7, 8, 9}};
        int i = 0;
        for (int[] c : (combine(matrix))) {
            System.out.println(Arrays.toString(c));
            i++;
        }
        System.out.println(i);
    }
}

测试

[1, 4, 7]
[1, 4, 8]
[1, 4, 9]
[1, 5, 7]
[1, 5, 8]
[1, 5, 9]
[1, 6, 7]
[1, 6, 8]
[1, 6, 9]
[2, 4, 7]
[2, 4, 8]
[2, 4, 9]
[2, 5, 7]
[2, 5, 8]
[2, 5, 9]
[2, 6, 7]
[2, 6, 8]
[2, 6, 9]
[3, 4, 7]
[3, 4, 8]
[3, 4, 9]
[3, 5, 7]
[3, 5, 8]
[3, 5, 9]
[3, 6, 7]
[3, 6, 8]
[3, 6, 9]
27

Answer 2

递归版本：

import java.util.Arrays;

public class Matrix  {
    private static int counter = 0;

    private static void combin2(int depth, int[][]matrix, int[] output)
    {
        int[] row = matrix[depth];

        if(depth == 0) {
            counter = 0;
            output = new int[matrix.length];
            System.out.println("matrix length: " + matrix.length);
        }

        for(int i=0; i<row.length; i++) {
            output[depth] = row[i];

            if(depth == (matrix.length-1)) {
                //print the combination
                System.out.println(Arrays.toString(output));
                counter++;
            } else {
                //recursively generate the combination
                combin2(depth+1, matrix, output);
            }
        }
    }

    public static void main(String[] args) {
        int[][] matrix = new int[][] {{1, 2, 3, 4}, {5, 6, 7, 8}};
        combin2(0, matrix, null);
        System.out.println("counter = " + counter);
        System.out.println("");

        matrix = new int[][]{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
        combin2(0, matrix, null);
        System.out.println("counter = " + counter);
        System.out.println("");

        matrix = new int[][]{{1, 2, 3}, {4,5,6}, {7,8,9}, {10,11,12}};
        combin2(0, matrix, null);
        System.out.println("counter = " + counter);
        System.out.println("");
    }
}

输出：

matrix length: 2
[1, 5]
[1, 6]
[1, 7]
[1, 8]
[2, 5]
[2, 6]
[2, 7]
[2, 8]
[3, 5]
[3, 6]
[3, 7]
[3, 8]
[4, 5]
[4, 6]
[4, 7]
[4, 8]
counter = 16

matrix length: 3
[1, 4, 7]
[1, 4, 8]
[1, 4, 9]
[1, 5, 7]
[1, 5, 8]
[1, 5, 9]
[1, 6, 7]
[1, 6, 8]
[1, 6, 9]
[2, 4, 7]
[2, 4, 8]
[2, 4, 9]
[2, 5, 7]
[2, 5, 8]
[2, 5, 9]
[2, 6, 7]
[2, 6, 8]
[2, 6, 9]
[3, 4, 7]
[3, 4, 8]
[3, 4, 9]
[3, 5, 7]
[3, 5, 8]
[3, 5, 9]
[3, 6, 7]
[3, 6, 8]
[3, 6, 9]
counter = 27

matrix length: 4
[1, 4, 7, 10]
[1, 4, 7, 11]
[1, 4, 7, 12]
[1, 4, 8, 10]
[1, 4, 8, 11]
[1, 4, 8, 12]
[1, 4, 9, 10]
[1, 4, 9, 11]
[1, 4, 9, 12]
[1, 5, 7, 10]
[1, 5, 7, 11]
[1, 5, 7, 12]
[1, 5, 8, 10]
[1, 5, 8, 11]
[1, 5, 8, 12]
[1, 5, 9, 10]
[1, 5, 9, 11]
[1, 5, 9, 12]
[1, 6, 7, 10]
[1, 6, 7, 11]
[1, 6, 7, 12]
[1, 6, 8, 10]
[1, 6, 8, 11]
[1, 6, 8, 12]
[1, 6, 9, 10]
[1, 6, 9, 11]
[1, 6, 9, 12]
[2, 4, 7, 10]
[2, 4, 7, 11]
[2, 4, 7, 12]
[2, 4, 8, 10]
[2, 4, 8, 11]
[2, 4, 8, 12]
[2, 4, 9, 10]
[2, 4, 9, 11]
[2, 4, 9, 12]
[2, 5, 7, 10]
[2, 5, 7, 11]
[2, 5, 7, 12]
[2, 5, 8, 10]
[2, 5, 8, 11]
[2, 5, 8, 12]
[2, 5, 9, 10]
[2, 5, 9, 11]
[2, 5, 9, 12]
[2, 6, 7, 10]
[2, 6, 7, 11]
[2, 6, 7, 12]
[2, 6, 8, 10]
[2, 6, 8, 11]
[2, 6, 8, 12]
[2, 6, 9, 10]
[2, 6, 9, 11]
[2, 6, 9, 12]
[3, 4, 7, 10]
[3, 4, 7, 11]
[3, 4, 7, 12]
[3, 4, 8, 10]
[3, 4, 8, 11]
[3, 4, 8, 12]
[3, 4, 9, 10]
[3, 4, 9, 11]
[3, 4, 9, 12]
[3, 5, 7, 10]
[3, 5, 7, 11]
[3, 5, 7, 12]
[3, 5, 8, 10]
[3, 5, 8, 11]
[3, 5, 8, 12]
[3, 5, 9, 10]
[3, 5, 9, 11]
[3, 5, 9, 12]
[3, 6, 7, 10]
[3, 6, 7, 11]
[3, 6, 7, 12]
[3, 6, 8, 10]
[3, 6, 8, 11]
[3, 6, 8, 12]
[3, 6, 9, 10]
[3, 6, 9, 11]
[3, 6, 9, 12]
counter = 81