How to resolve the algorithm Sorting algorithms/Merge sort step by step in the Eiffel programming language
How to resolve the algorithm Sorting algorithms/Merge sort step by step in the Eiffel programming language
Table of Contents
Problem Statement
The merge sort is a recursive sort of order nlog(n). It is notable for having a worst case and average complexity of O(nlog(n)), and a best case complexity of O(n) (for pre-sorted input). The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements (which are both entirely sorted groups). Then merge the groups back together so that their elements are in order. This is how the algorithm gets its divide and conquer description.
Write a function to sort a collection of integers using the merge sort.
The merge sort algorithm comes in two parts: The functions in pseudocode look like this:
Note: better performance can be expected if, rather than recursing until length(m) ≤ 1, an insertion sort is used for length(m) smaller than some threshold larger than 1. However, this complicates the example code, so it is not shown here.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Sorting algorithms/Merge sort step by step in the Eiffel programming language
Source code in the eiffel programming language
class
MERGE_SORT [G -> COMPARABLE]
create
sort
feature
sort (ar: ARRAY [G])
-- Sorted array in ascending order.
require
ar_not_empty: not ar.is_empty
do
create sorted_array.make_empty
mergesort (ar, 1, ar.count)
sorted_array := ar
ensure
sorted_array_not_empty: not sorted_array.is_empty
sorted: is_sorted (sorted_array, 1, sorted_array.count)
end
sorted_array: ARRAY [G]
feature {NONE}
mergesort (ar: ARRAY [G]; l, r: INTEGER)
-- Sorting part of mergesort.
local
m: INTEGER
do
if l < r then
m := (l + r) // 2
mergesort (ar, l, m)
mergesort (ar, m + 1, r)
merge (ar, l, m, r)
end
end
merge (ar: ARRAY [G]; l, m, r: INTEGER)
-- Merge part of mergesort.
require
positive_index_l: l >= 1
positive_index_m: m >= 1
positive_index_r: r >= 1
ar_not_empty: not ar.is_empty
local
merged: ARRAY [G]
h, i, j, k: INTEGER
do
i := l
j := m + 1
k := l
create merged.make_filled (ar [1], 1, ar.count)
from
until
i > m or j > r
loop
if ar.item (i) <= ar.item (j) then
merged.force (ar.item (i), k)
i := i + 1
elseif ar.item (i) > ar.item (j) then
merged.force (ar.item (j), k)
j := j + 1
end
k := k + 1
end
if i > m then
from
h := j
until
h > r
loop
merged.force (ar.item (h), k + h - j)
h := h + 1
end
elseif j > m then
from
h := i
until
h > m
loop
merged.force (ar.item (h), k + h - i)
h := h + 1
end
end
from
h := l
until
h > r
loop
ar.item (h) := merged.item (h)
h := h + 1
end
ensure
is_partially_sorted: is_sorted (ar, l, r)
end
is_sorted (ar: ARRAY [G]; l, r: INTEGER): BOOLEAN
-- Is 'ar' sorted in ascending order?
require
ar_not_empty: not ar.is_empty
l_in_range: l >= 1
r_in_range: r <= ar.count
local
i: INTEGER
do
Result := True
from
i := l
until
i = r
loop
if ar [i] > ar [i + 1] then
Result := False
end
i := i + 1
end
end
end
class
APPLICATION
create
make
feature
make
do
test := <<2, 5, 66, -2, 0, 7>>
io.put_string ("unsorted" + "%N")
across
test as ar
loop
io.put_string (ar.item.out + "%T")
end
io.put_string ("%N" + "sorted" + "%N")
create merge.sort (test)
across
merge.sorted_array as ar
loop
io.put_string (ar.item.out + "%T")
end
end
test: ARRAY [INTEGER]
merge: MERGE_SORT [INTEGER]
end
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