如图：

 

 

public class App
{

    public static void main( String[] args )
    {
        int[][] checkerboard = new int[11][11]; //原始数组
        checkerboard[1][2]=1;
        checkerboard[2][3]=2;
        int [][] sparseArray=transtoSparseArray(checkerboard);
        System.out.println("原始数组。。。。。。。。。。");
        printArray(checkerboard);
        System.out.println("稀疏数组。。。。。。。。。。");
        printArray(sparseArray);
        System.out.println("稀疏数组转原始数组。。。。。。。。。。");
        printArray(transToPlainArray(sparseArray));


    }

    private static  void printArray(int[][] sparseArray){
        for (int[] arr : sparseArray) {
            for (int i : arr) {
                System.out.print(i);
                System.out.print(" ");
            }
            System.out.println("");
        }
    }

    private static int[][] transtoSparseArray(int[][] plainArray){
        int sum=0;
        for (int[] rows : plainArray) {
            for (int row : rows) {
                if(row!=0){
                    sum++;
                }
            }

        }
        //稀疏数组
        int[][] sparseArray = new int[sum + 1][3];
        sparseArray[0][0]=11;
        sparseArray[0][1]=11;
        sparseArray[0][2]=sum;
        int row=1;
        for (int i = 0; i < plainArray.length; i++) {
            int[] arr=plainArray[i];
            for (int j = 0; j < arr.length; j++) {
                int k=arr[j];
                if(k!=0){
                    sparseArray[row][0]=i;
                    sparseArray[row][1]=j;
                    sparseArray[row][2]=k;
                    row++;
                }

            }
        }
        return sparseArray;
    }

    private static int[][] transToPlainArray(int[][] sparseArray){ //稀疏数组转普通数组
        int row = sparseArray[0][0];
        int cl = sparseArray[0][1];
        int[][] plainArrays = new int[row][cl];
        for (int i = 1; i < sparseArray.length; i++) {
            int[] arr=sparseArray[i];
            for (int j = 0; j < arr.length; j++) {
                int r=arr[0];
                int c=arr[1];
                int v=arr[2];
                plainArrays[r][c]=v;
            }

        }
        return plainArrays;

    }

}

测试结果：