What is Block Sort
Block sort is a family of sorting algorithms that operate on fixed-size blocks of elements rather than individual elements. In other words, instead of comparing and sorting individual elements, block sort algorithms compare and sort entire blocks of elements.
One popular block sort algorithm is called "merge sort". In merge sort, the list of elements to be sorted is recursively divided into smaller sub-lists until each sub-list consists of a single element. Then, these sub-lists are merged together in pairs, with each pair being sorted in the process. This process is repeated until the entire list is sorted.
Another example of a block sort algorithm is "quick sort with median-of-three partitioning", which works by selecting a "pivot" element from the block of elements and partitioning the block into two sub-blocks - one containing all elements less than the pivot, and the other containing all elements greater than or equal to the pivot. This process is then recursively applied to the two sub-blocks until the entire block is sorted.
Block sort algorithms are often used in situations where sorting large amounts of data is required, such as in database systems or data analysis applications.
One popular block sort algorithm is called "merge sort". In merge sort, the list of elements to be sorted is recursively divided into smaller sub-lists until each sub-list consists of a single element. Then, these sub-lists are merged together in pairs, with each pair being sorted in the process. This process is repeated until the entire list is sorted.
Another example of a block sort algorithm is "quick sort with median-of-three partitioning", which works by selecting a "pivot" element from the block of elements and partitioning the block into two sub-blocks - one containing all elements less than the pivot, and the other containing all elements greater than or equal to the pivot. This process is then recursively applied to the two sub-blocks until the entire block is sorted.
Block sort algorithms are often used in situations where sorting large amounts of data is required, such as in database systems or data analysis applications.
Who invented it?
There isn't a single person credited with inventing the block sort algorithm, as it is a general approach to sorting that has been developed and refined by many researchers and computer scientists over the years.
One early example of a block sort algorithm is the "tape sort" algorithm, which was developed in the 1950s for sorting data stored on magnetic tape. Tape sort operated on fixed-size blocks of data, rather than individual records, and was an early example of the block sort approach.
Other important contributions to the development of block sort algorithms include the work of Donald Knuth, who introduced the "Algorithm M" block sort algorithm in his book "The Art of Computer Programming", and the work of Robert Sedgewick, who developed several block sort algorithms for use in his book "Algorithms in C".
Today, block sort algorithms continue to be an important tool in computer science and are used in a wide range of applications, from sorting large data sets to implementing compression algorithms and other data processing tasks.
One early example of a block sort algorithm is the "tape sort" algorithm, which was developed in the 1950s for sorting data stored on magnetic tape. Tape sort operated on fixed-size blocks of data, rather than individual records, and was an early example of the block sort approach.
Other important contributions to the development of block sort algorithms include the work of Donald Knuth, who introduced the "Algorithm M" block sort algorithm in his book "The Art of Computer Programming", and the work of Robert Sedgewick, who developed several block sort algorithms for use in his book "Algorithms in C".
Today, block sort algorithms continue to be an important tool in computer science and are used in a wide range of applications, from sorting large data sets to implementing compression algorithms and other data processing tasks.
Pseudocode
function block_sort(list, block_size):
// Divide the list into blocks of size `block_size`
blocks = []
for i = 0 to length of list, increment by `block_size`:
block = list[i:i+block_size]
blocks.append(block)
// Sort each block using a comparison-based sorting algorithm (e.g. quicksort)
for i = 0 to length of blocks:
sort(blocks[i])
// Merge the sorted blocks back together into a single sorted list
result = []
while length of blocks > 0:
min_block = find_minimum_block(blocks)
result.append(min_block.pop(0))
if length of min_block > 0:
blocks.add(min_block)
else:
remove min_block from blocks
return result
function find_minimum_block(blocks):
min_block = blocks[0]
for block in blocks:
if block[0] < min_block[0]:
min_block = block
return min_block
This implementation divides the input list into blocks of size block_size, sorts each block using a comparison-based sorting algorithm (e.g. quicksort), and then merges the sorted blocks back together into a single sorted list. The find_minimum_block() function is used to identify the next smallest element to add to the sorted list, which is determined by comparing the first element of each block.
Sample Code
// C++ code snippet
vector block_sort(vector list, int block_size) {
// Divide the list into blocks of size `block_size`
vector> blocks;
for (int i = 0; i < list.size(); i += block_size) {
vector block(list.begin() + i, list.begin() + i + block_size);
blocks.push_back(block);
}
// Sort each block using a comparison-based sorting algorithm (e.g. quicksort)
for (int i = 0; i < blocks.size(); i++) {
sort(blocks[i].begin(), blocks[i].end());
}
// Merge the sorted blocks back together into a single sorted list
vector result;
while (blocks.size() > 0) {
vector min_block = blocks[0];
int min_index = 0;
for (int i = 1; i < blocks.size(); i++) {
if (blocks[i][0] < min_block[0]) {
min_block = blocks[i];
min_index = i;
}
}
result.push_back(min_block[0]);
min_block.erase(min_block.begin());
if (min_block.size() > 0) {
blocks[min_index] = min_block;
} else {
blocks.erase(blocks.begin() + min_index);
}
}
return result;
}
int main() {
vector list = { 5, 3, 8, 4, 2, 7, 1, 6 };
int block_size = 3;
vector sorted_list = block_sort(list, block_size);
// Print the sorted list
for (int i = 0; i < sorted_list.size(); i++) {
cout << sorted_list[i] << " ";
}
cout << endl;
return 0;
}
# Python code snippet
def block_sort(lst, block_size):
# Divide the list into blocks of size `block_size`
blocks = [lst[i:i+block_size] for i in range(0, len(lst), block_size)]
# Sort each block using a comparison-based sorting algorithm (e.g. quicksort)
for i in range(len(blocks)):
blocks[i].sort()
# Merge the sorted blocks back together into a single sorted list
result = []
while len(blocks) > 0:
min_block = blocks[0]
min_index = 0
for i in range(1, len(blocks)):
if blocks[i][0] < min_block[0]:
min_block = blocks[i]
min_index = i
result.append(min_block.pop(0))
if len(min_block) > 0:
blocks[min_index] = min_block
else:
blocks.pop(min_index)
return result
# Example usage
lst = [5, 3, 8, 4, 2, 7, 1, 6]
block_size = 3
sorted_lst = block_sort(lst, block_size)
print(sorted_lst)
import java.util.*;
public class BlockSort {
public static List blockSort(List list, int blockSize) {
// Divide the list into blocks of size `blockSize`
List> blocks = new ArrayList<>();
for (int i = 0; i < list.size(); i += blockSize) {
List block = list.subList(i, Math.min(i + blockSize, list.size()));
blocks.add(block);
}
// Sort each block using a comparison-based sorting algorithm (e.g. quicksort)
for (int i = 0; i < blocks.size(); i++) {
Collections.sort(blocks.get(i));
}
// Merge the sorted blocks back together into a single sorted list
List result = new ArrayList<>();
while (blocks.size() > 0) {
List minBlock = blocks.get(0);
int minIndex = 0;
for (int i = 1; i < blocks.size(); i++) {
if (blocks.get(i).get(0) < minBlock.get(0)) {
minBlock = blocks.get(i);
minIndex = i;
}
}
result.add(minBlock.get(0));
minBlock.remove(0);
if (minBlock.size() > 0) {
blocks.set(minIndex, minBlock);
} else {
blocks.remove(minIndex);
}
}
return result;
}
public static void main(String[] args) {
List list = Arrays.asList(5, 3, 8, 4, 2, 7, 1, 6);
int blockSize = 3;
List sortedList = blockSort(list, blockSize);
// Print the sorted list
System.out.println(sortedList);
}
}