# Efficient for small data sets.
# Efficient for data sets that are already largely sorted.
# More efficient in practice than other simple quadratic algorithms
# (e.g. selection sort, bubble sort).
# Stable - does not change the relative order of elements with equal keys.
# In-place - only requires a constant amount O(1) of additional memory.
# Online - can sort a list as it receives it.
#
## References:
#
# Introduction to Algorithms, section 2.1, page 16.
#
## Code:
#
import lib
def insertion_sort(data):
for j in range(1, len(data)):
key = data[j]
# Insert data[j] into sorted sequence data[0..j-1].
i = j - 1
while i >= 0 and data[i] > key:
data[i + 1] = data[i]
i = i - 1
data[i + 1] = key
return data
if __name__ == "__main__":
lib.test_array_sort(insertion_sort)
largest = left
else:
largest = i
if right < heap_size and heap[right] > heap[largest]:
largest = right
if largest != i:
heap[i], heap[largest] = heap[largest], heap[i]
max_heapify(heap, heap_size, largest)
# Input an array and build into a max heap.
def build_max_heap(data):
for i in range(len(data) / 2 - 1, -1, -1):
max_heapify(data, len(data), i)
# The first step: build the entire array into a max heap.
build_max_heap(data)
# The second step: Continuously remove the largest object from the
# heap, and rebuild the max heap. Continue until there are no
# objects left in the heap.
for i in range(len(data) - 1, 0, -1):
data[0], data[i] = data[i], data[0]
max_heapify(data, i, 0)
return data
if __name__ == "__main__":
lib.test_array_sort(heap_sort)
if len(left) and len(right):
if right[0] < left[0]:
sorted.append(right[0])
right.pop(0)
else:
sorted.append(left[0])
left.pop(0)
# Else append the remainder of either list:
elif len(right):
sorted += right
right = []
else:
sorted += left
left = []
return sorted
# A list of 1 element or an empty list is considered sorted.
if len(data) <= 1:
return data
middle = int(len(data) / 2)
left = merge_sort(data[:middle])
right = merge_sort(data[middle:])
return merge(left, right)
if __name__ == "__main__":
lib.test_array_sort(merge_sort)
