The basic idea of the algorithm 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 (Rosetta code). Merge sort follows divide-and-conquer approach.
Worst case performance - O(n log n)
Source - Wikipedia |
C++
void merge_sort(int array[], int low, int high)
{
if (low < high)
{
int middle = (low + high) / 2;
merge_sort(array,low, middle);
merge_sort(array,middle + 1, high);
merge(array, low, middle, high);
}
}
void merge(int array[], int low, int middle, int high)
{
int size1 = middle - low + 1;
int size2 = high - middle;
int left[size1 + 1];
int right[size2 + 1];
for (int i = 0; i < size1; i++)
{
left[i] = array[low + i];
}
for (int j = 0; j < size2; j++)
{
right[j] = array[middle + j + 1];
}
left[size1] = numeric_limits<int>::max();;
right[size2] = numeric_limits<int>::max();;
int i = 0;
int j = 0;
for (int k = low; k <= high; k++)
{
if (left[i] <= right[j])
{
array[k] = left[i];
i++;
}
else
{
array[k] = right[j];
j++;
}
}
}
Java
static int[] array = {5, 4, 8, 3, 1, 2, 9, 6, 7, 10};
static void merge_sort(int[] array, int low, int high) {
if (low < high) {
int middle = (low + high) / 2;
merge_sort(array, low, middle);
merge_sort(array, middle + 1, high);
merge(array, low, middle, high);
}
}
static void merge(int[] array, int low, int middle, int high) {
int size1 = middle - low + 1;
int size2 = high - middle;
int[] left = new int[size1 + 1];
int[] right = new int[size2 + 1];
for (int i = 0; i < size1; i++) {
left[i] = array[low + i];
}
for (int j = 0; j < size2; j++) {
right[j] = array[middle + j + 1];
}
left[size1] = Integer.MAX_VALUE;
right[size2] = Integer.MAX_VALUE;
int i = 0;
int j = 0;
for (int k = low; k <= high; k++) {
if (left[i] <= right[j]) {
array[k] = left[i];
i++;
} else {
array[k] = right[j];
j++;
}
}
}
Matlab
function array = merge_sort(array,low,high)
if(low < high)
middle = floor((low + high)/2);
array = merge_sort(array,low, middle);
array = merge_sort(array,middle + 1, high);
array = merge(array, low, middle, high);
end
end
function array = merge(array,low,middle,high)
size1 = middle - low + 1;
size2 = high - middle;
left = zeros(1,size1+1);
right = zeros(1,size2+1);
for i=1:size1
left(i) = array(low+i-1);
end
for j=1:size2
right(j) = array(middle+j);
end
left(size1+1) = inf;
right(size2+1) = inf;
i = 1;
j = 1;
for k=low:high
if left(i)<= right(j)
array(k) = left(i);
i = i + 1;
else
array(k) = right(j);
j = j + 1;
end
end
end
Python
import math
def merge(array,low,middle,high):
size1 = middle - low + 1
size2 = high - middle
left = [0]* (size1+1)
right = [0]* (size2+1)
for i in range(size1):
left[i] = array[low+i]
for j in range(size2):
right[j] = array[middle+j+1]
left[size1] = float("inf")
right[size2] = float("inf")
i = 0
j = 0
for k in range(low,high+1):
if left[i]<= right[j]:
array[k] = left[i]
i = i + 1
else:
array[k] = right[j]
j = j + 1
def merge_sort(array,low,high):
if low<high:
middle = int(math.floor((low+high)/2))
merge_sort(array,low,middle)
merge_sort(array,middle+1,high)
merge(array,low,middle,high)
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