Java: Declaring a multidimensional array without specifying the size of the array ( eg. new int[10][] )

Question

I've been trying to figure out what exactly is happening here. I'm just trying to figure out what the 2 lines are doing that I've commented on below. I found this program that doesn't declare the full dimensions of the array (instead of new int[10][5]; it just decides to not declare it by saying 'new int[10][];' It's like the 2nd array length doesn't matter (changing it to 1 or 100 doesn't affect the output).

int[][] tri = new int[10][];  //this lack of giving the size of the 2nd array is strange
 for (int r=0; r<tri.length; r++) {
 tri[r] = new int[r+1];   //I'm not sure what this line is doing really 
}
for (int r=0; r<tri.length; r++) {
 for (int a=0; a<tri[r].length; a++) {
     System.out.print(tri[r][a]);  
     }
 System.out.println();
 }

Answer 1

The first line makes an array of int arrays. There are 10 slots for int arrays created.

The third line creates a new int array and puts it in one of the slots you made at first. The new int array has r+1 spaces for ints in it.

So, the int array in position 0 will have 1 slot for an int. The int array in position 1 will have 2 slots for an int. The overall shape will be:

[
    [0],
    [0,0],
    [0,0,0],
    ...,
    [0,0,0,0,0,0,0,0,0,0]
]

which is hinted at with the variable name tri (it looks like a triangle)

Answer 2

All new int[10][] is declaring is an array of size 10, containing null arrays.

In the for loop, the null arrays are being instantiated into ever increasing array sizes.