Ds sorting

Sorting
 Sorting is the process of placing elements from a
collection in some kind of order.
Types
 Bubble Sort.
 Insertion Sort.
 Selection Sort.
 Quick Sort.
 Merge Sort.

Bubble sort
 Bubble sort is a simple sorting algorithm. This sorting
algorithm is comparison-based algorithm in which each
pair of adjacent elements is compared and the elements
are swapped if they are not in order.

Insertion Sort
Insertion sort is a sorting algorithm in which the elements are
transferred one at a time to the right position by comparison
but with left values.
This is an in-place comparison-based sorting
Algorithm.

Insertion Sort passes
11 2 1 9 6
Array[0] Array[1] Array[2] Array[3] Array[4]
11 2 1 9 6
2 11 1 9 6

2 11 1 9 6
2 1 11 9 6
2 1 11 9 6

1 2 11 9 6
1 2 9 11 6
1 2 11 9 6
1 2 9 11 6

1 2 9 6 11
1 2 9 6 11
1 2 6 9 11

Insertion Sort Algorithm & Program
Class assignment to write algorithm for this.

Selection Sort
 In selection sort, the smallest element is selected from the
unsorted array and swapped with the leftmost element,
and that element becomes a part of the sorted array. This
process continues moving unsorted array boundary by one
element to the right.
 Step 1 − Set MIN to location 0.
 Step 2 − Search the minimum element in the list.
 Step 3 − Swap with value at location MIN.
 Step 4 − Increment MIN to point to next element.
 Step 5 − Repeat until list is sorted.

Selection Sort Algorithm & Program
 Class assignment to write Code for this.

Merge Sort
 Merge sort is a sorting technique based on divide and
conquer technique.
 Merge sort first divides the array into equal halves and
then combines them in a sorted manner.

void MergeSort(int *a, int low, int high)
{
int mid;
if (low < high)
{
mid=(low+high)/2;
MergeSort(a, low, mid);
MergeSort(a, mid+1, high);
Merge(a, low, high, mid);
}
}
Low = 1,high= 8,1<8,mid = 4
Stack and PC
MergeSort(a, mid+1, high); [array,5,8]
Merge(a, low, high, mid); [array,1,8,4]
{
int mid;
if (low < high)
{
mid=(low+high)/2;
}
}
Low = 1,high= 4,1<4,mid = 2
Stack and PC
Array,low= 1Mid=4 => low=1 and high =4

{
int mid;
if (low < high)
{
mid=(low+high)/2;
}
}
Low = 1,high= 2,1<2,mid = 1
Stack and PC
{
int mid;
if (low < high)
{
mid=(low+high)/2;
}
}
Low = 1,high= 1,1<1(false)

Stack and PC
{
int mid;
if (low < high)
{
mid=(low+high)/2;
}
}
Low = 2,high= 2,<2,false
Array,Mid=2,high=2 => low=2 and high =2
{
int mid;
if (low < high)
{
mid=(low+high)/2;
}
}
low =3 ,high= 4,3<4,mid = 3
Array,mid+1[3] ,high 4 => low=3 and high =4

{
int mid;
if (low < high)
{
mid=(low+high)/2;
}
}
low =3 ,high= 4,3<4,mid = 3
Array,mid+1[3] ,high 4 => low=3 and high =4
Stack and PC
{
int mid;
if (low < high)
{
mid=(low+high)/2;
}
}
Array,low=3,Mid=3 => low=3 and high =3
low =3 ,high= 3,3<3,false

Stack and PC
{
int mid;
if (low < high)
{
mid=(low+high)/2;
}
}
Low = 4,high= 2,4<4,false
Array,Mid=3+1[4] high=4 => low=4 and high =4

void Merge(int *a, int low, int high, int mid)
{// We have low to mid and mid+1 to high already
sorted.
int i, j, k, temp[high-low+1];
i = low;
k = 0;
j = mid + 1;
// Merge the two parts into temp[].
while (i <= mid && j <= high)
{ if (a[i] < a[j])
{ temp[k] = a[i];
k++; i++; }
else
{ temp[k] = a[j];
k++; j++; }}
// Insert all the remaining values from i to mid
into temp[].
while (i <= mid)
{ temp[k] = a[i];
k++; i++; }
// Insert all the remaining values from j to high
into temp[].
while (j <= high)
{ temp[k] = a[j];
k++;j++;} // Assign sorted data stored in temp[] to
a[].
for (i = low; i <= high; i++)
{ a[i] = temp[i-low]; } }
i = low=1; k = 0; j = mid + 1=2;
{ if (a[i] < a[j])
{ temp[k] = a[i];
k++; i++; }
else
{ temp[k] = a[j];
k++; j++; }}
while (i <= mid)
{ temp[k] = a[i];
k++; i++; }
// Insert all the remaining values from j to
high into temp[].
while (j <= high)
{ temp[k] = a[j];
k++;j++;}
while (j <= high)
{ temp[k] = a[j];
k++;j++;}
// Assign sorted data stored in temp[] to a[].
i = low=3; k = 0; j = mid + 1=3;
{ if (a[i] < a[j])
{ temp[k] = a[i];
k++; i++; }
else
{ temp[k] = a[j];
k++; j++; }}
while (i <= mid)
{ temp[k] = a[i];
k++; i++; }
high into temp[].
while (j <= high)
{ temp[k] = a[j];
k++;j++;}
while (j <= high)
{ temp[k] = a[j];
k++;j++;}
i = low=1; k = 0; j = mid + 1=3;
{ if (a[i] < a[j])
{ temp[k] = a[i];
k++; i++; }
else
{ temp[k] = a[j];
k++; j++; }}
while (i <= mid)
{ temp[k] = a[i];
k++; i++; }
high into temp[].
while (j <= high)
{ temp[k] = a[j];
k++;j++;}
while (j <= high)
{ temp[k] = a[j];
k++;j++;}

#include <iostream>
using namespace std;
// A function to merge the two half into a sorted data.
void Merge(int *a, int low, int high, int mid)
{
// We have low to mid and mid+1 to high already sorted.
int i, j, k, temp[high-low+1];
i = low;
k = 0;
j = mid + 1;
{
if (a[i] < a[j])
{
temp[k] = a[i];
k++;
i++;
}
else
{
temp[k] = a[j];
k++;
j++;
}
}
// Insert all the remaining values from i to mid into temp[].
while (i <= mid)
{
temp[k] = a[i];
k++;
i++;
}
// Insert all the remaining values from j to high into temp[].
while (j <= high)
{
temp[k] = a[j];
k++;
j++;
}
{
a[i] = temp[i-low];
}
}

After sorting of remaining elements we will get

Quick Sort Algorithm & Program
• Assignment
Submission time Friday till 12:00AM

Ds sorting

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