We know that radix sort's run time is $\Theta (d(n +k))$ where n is the no. of elements to be sorted, k is the range of individual digit of the elements ($k =O(n)$) and $d$ is the no. of digits in every element, which is assumed to be constant.
I am wondering that if we re-arrange any random list of elements to contain same constant no. of digits we will be able to achieve a $\Theta(n)$ time.
For eg.
5, 72, 99, 343, 2, 8999, 1765, 57, 554, 12
can be rearranged to
0005, 0072, 0099, 0343, 0002, 8999, 1765, 0057, 0554, 0012
now, here $d = 4$ (constant) and also $k= O(n)$ (0 to 9)
We can do this with any random arrangement of numbers and achieve a linear time,
Where am I wrong $?$
