Insertion sort is used when number of elements is small. It can also be useful when input array is almost sorted, only few elements are misplaced in complete big array.
- If we have log2n bits for every digit, the running time of Radix appears to be better than Quick Sort for a wide range of input numbers. The constant factors hidden in asymptotic notation are higher for Radix Sort and Quick-Sort uses hardware caches more effectively. Also, Radix sort uses counting sort as a subroutine and counting sort takes extra space to sort numbers.
- An example is when creating a “suffix array” using the skew DC3 algorithm (Kärkkäinen-Sanders-Burkhardt). The algorithm is only linear-time if the sorting algorithm is linear-time, and radix sort is necessary and useful here because the keys are short by construction (3-tuples of integers).