We have seen that it is possible to initialize an array in its declaration. For example a one dimensional array would be declared as follows:

int arr[] = {1, 4, 5};

Now with a two dimensional array we would do something similar:

int arr[][3] = { {1, 4, 5}, {2, 3, 6}, {4, 2, 5} };

In a two-dimensional array all of the rows be the same number of columns wide. For this reason, you must include a size between each pair of brackets except the first, which is optional. If you look at the syntax, what we are actually doing is declaring a one dimensional array of one dimensional arrays.

Now we will cover why all of the columns need to be of the same width when we explain what actually happens when you index into an array. If it is a one dimensional array, the indexing step is simple. It can be thought of through pointer arithmetic. To get arr[2] you just dereference the pointer plus two: *(arr + 2). The process gets more complicated when dealing with multi-dimensional arrays because each of the dimensions will affect the pointer arithmetic differently. Specifically, the index in the row position should be multiplied by the column width. So arr2[2][1] is the same as *(arr + 2 * 3 + 1) which is the pointer plus the row number times the column width plus the column number. If the number of columns were not fixed it would be impossible to do this sort of pointer arithmetic to arrive at the correct cell. One way to think about this is that a two dimensional array looks the same as a one dimensional array in memory. It is just one chunk of memory. The column width is necessary to know how to fold this chunk of memory into rows.

Another significant implication of arrays really just being a pointer to a chunk of memory is that when you pass an array into a function, the function can modify it and have those modifications affect the array in the place that the function was called. In other words, there is not local copy of the entire array passed into a function. The reason for this is that only a pointer to the array gets passed in, which means that when you assign to the array you are affecting the same memory that the array from the calling function refers to. This feature can be very useful for processing large amounts of data in functions, but can also create some confusing bugs if you forget that only a pointer to an array gets passed to functions.