In one embodiment, a data recovery system sorts data elements of a data array by representation. The data recovery system allocates a representation array corresponding to a position of a corresponding data array element after sorting. A scan module of the data recovery system assigns index values to the representation elements of the representation array based on the values of the data elements of the data array without moving the data elements of the data array. A sort module of the data recovery system swaps the data elements of the data array based on the index values of the representation elements of the representation array corresponding to the data elements. The sort module swaps representation elements of the representation array corresponding to the swapped data elements of the data array.