Sort Counting The book's description of Counting Sort is different than what I presented in class. My algorithm is superior to the author's algorithm in a practical sense. But, the author's algorithm is specially designed to work with Radix sort. However, the author's version of Radix sort is not correct. Use this Counting Sort algorithm and not the one in the book:
c[] is an array of m zeros countsort(a[],m) { for i = 1 to n // n is a.size() c[a[i]]++; // uses the value of a[i] as the array index // increments c[index] k = 0; for i = 1 to m // m is the largest value in a[] for j = 1 to c[i] { // only loops if c[i] is non zero a[k] = i; // O(n) if n > m O(m) if m > n k++; // Or we can say its just O(n + m) } }
Radix Sort The book's description of Radix Sort uses Counting Sort, but it is not correct. I've sent a complaint to the authors. The problem with author's code is that Counting Sort is called with m = 10, which implies that the c[] array is of size 10. But, what happens if one of the values in a[] is greater than 10? Then, c[a[i]] not is a valid memory address. The author never shows that we need to take the remainder of a[i]/10 and use this as the array index. Also, on the next pass, we need to divide a[i] by 100, 1000, 10000, etc. and take the remainder to extract each progressive digit. Rather than use the authors incorrect code, use the algorithm I described below:
buckets[] is an array of 10 queues (first in first out). radixsort(a[], k) { // For each progressive digit x, bucket and un-bucket each value for x = 0 to k-1 { // Place each value in a bucket based on digit x for y = 1 to n { temp = a[y]/pow(10,x); // Divide by 1, 10, 100, 1000, etc. d = t...