Posted on by Kalkicode
Code Backtracking

# Print all subsequences of given size

Here given code implementation process.

``````// C program
// Print all subsequences of given size

#include <stdio.h>

//Print all subsequences in a given size k
void print_subsequences(int collection[],
int output[],
int n,
int k,
int next,
int location)
{

if(location == k)
{
// When get new subsequence of k size
printf(" [");

for (int i = 0; i < k; ++i)
{
printf(" %d ",collection[output[i]]);
}

printf("]\n");

return;
}
else
{
for (int i = next; i < n ; ++i)
{
// Get location of subset collection
output[location] = i;

print_subsequences(collection,output,n,k,i+1,location+1);
}
}
}

// Handles the request to print subsequence element
void subsequences(int collection[],int n, int length)
{

if(n <= 0 || length <= 0 && length >= n)
{
//if not a valid inputs
return;
}

//Used to display result
int output[length];

printf("\n Subsequences of size %d \n",length);

print_subsequences(collection,output,n,length,0,0);
}

int main()
{

//Define the element of integers
int arr[] = { 4, 7, 8, 1, 3, 5, 6, 2};

int length   = 4;

//Get the size
int size = sizeof(arr)/sizeof(arr[0]);

//Test Case 1
subsequences(arr,size,length);

length   = 6;

//Test Case 2
subsequences(arr,size,length);

return 0;
}``````

#### Output

`````` Subsequences of size 4
[ 4  7  8  1 ]
[ 4  7  8  3 ]
[ 4  7  8  5 ]
[ 4  7  8  6 ]
[ 4  7  8  2 ]
[ 4  7  1  3 ]
[ 4  7  1  5 ]
[ 4  7  1  6 ]
[ 4  7  1  2 ]
[ 4  7  3  5 ]
[ 4  7  3  6 ]
[ 4  7  3  2 ]
[ 4  7  5  6 ]
[ 4  7  5  2 ]
[ 4  7  6  2 ]
[ 4  8  1  3 ]
[ 4  8  1  5 ]
[ 4  8  1  6 ]
[ 4  8  1  2 ]
[ 4  8  3  5 ]
[ 4  8  3  6 ]
[ 4  8  3  2 ]
[ 4  8  5  6 ]
[ 4  8  5  2 ]
[ 4  8  6  2 ]
[ 4  1  3  5 ]
[ 4  1  3  6 ]
[ 4  1  3  2 ]
[ 4  1  5  6 ]
[ 4  1  5  2 ]
[ 4  1  6  2 ]
[ 4  3  5  6 ]
[ 4  3  5  2 ]
[ 4  3  6  2 ]
[ 4  5  6  2 ]
[ 7  8  1  3 ]
[ 7  8  1  5 ]
[ 7  8  1  6 ]
[ 7  8  1  2 ]
[ 7  8  3  5 ]
[ 7  8  3  6 ]
[ 7  8  3  2 ]
[ 7  8  5  6 ]
[ 7  8  5  2 ]
[ 7  8  6  2 ]
[ 7  1  3  5 ]
[ 7  1  3  6 ]
[ 7  1  3  2 ]
[ 7  1  5  6 ]
[ 7  1  5  2 ]
[ 7  1  6  2 ]
[ 7  3  5  6 ]
[ 7  3  5  2 ]
[ 7  3  6  2 ]
[ 7  5  6  2 ]
[ 8  1  3  5 ]
[ 8  1  3  6 ]
[ 8  1  3  2 ]
[ 8  1  5  6 ]
[ 8  1  5  2 ]
[ 8  1  6  2 ]
[ 8  3  5  6 ]
[ 8  3  5  2 ]
[ 8  3  6  2 ]
[ 8  5  6  2 ]
[ 1  3  5  6 ]
[ 1  3  5  2 ]
[ 1  3  6  2 ]
[ 1  5  6  2 ]
[ 3  5  6  2 ]

Subsequences of size 6
[ 4  7  8  1  3  5 ]
[ 4  7  8  1  3  6 ]
[ 4  7  8  1  3  2 ]
[ 4  7  8  1  5  6 ]
[ 4  7  8  1  5  2 ]
[ 4  7  8  1  6  2 ]
[ 4  7  8  3  5  6 ]
[ 4  7  8  3  5  2 ]
[ 4  7  8  3  6  2 ]
[ 4  7  8  5  6  2 ]
[ 4  7  1  3  5  6 ]
[ 4  7  1  3  5  2 ]
[ 4  7  1  3  6  2 ]
[ 4  7  1  5  6  2 ]
[ 4  7  3  5  6  2 ]
[ 4  8  1  3  5  6 ]
[ 4  8  1  3  5  2 ]
[ 4  8  1  3  6  2 ]
[ 4  8  1  5  6  2 ]
[ 4  8  3  5  6  2 ]
[ 4  1  3  5  6  2 ]
[ 7  8  1  3  5  6 ]
[ 7  8  1  3  5  2 ]
[ 7  8  1  3  6  2 ]
[ 7  8  1  5  6  2 ]
[ 7  8  3  5  6  2 ]
[ 7  1  3  5  6  2 ]
[ 8  1  3  5  6  2 ]``````
``````/*
Java program
Print all subsequences of given size
*/
class Subsequence
{
//Print all subsequences in a given size k
public void print_subsequences(int[] collection, int[] output, int n, int k, int next, int location)
{
if (location == k)
{
// When get new subsequence of k size
System.out.print(" [");
for (int i = 0; i < k; ++i)
{
System.out.print(" " + collection[output[i]] + " ");
}
System.out.print("]\n");
return;
}
else
{
for (int i = next; i < n; ++i)
{
// Get location of subset collection
output[location] = i;
print_subsequences(collection, output, n, k, i + 1, location + 1);
}
}
}
// Handles the request to print subsequence element
public void subsequences(int[] collection, int n, int size)
{
if (n <= 0 || size <= 0 && size >= n)
{
//if not a valid inputs
return;
}
//Used to display result
int[] output = new int[size];
System.out.print("\n Subsequences of size " + size + " \n");
print_subsequences(collection, output, n, size, 0, 0);
}
public static void main(String[] args)
{
Subsequence obj = new Subsequence();
//Define the element of integers
int[] arr = {
4 , 7 , 8 , 1 , 3 , 5 , 6 , 2
};
int size = 4;
//Get the size
int n = arr.length;
//Test Case 1
obj.subsequences(arr, n, size);
size = 6;
//Test Case 2
obj.subsequences(arr, n, size);
}
}``````

#### Output

`````` Subsequences of size 4
[ 4  7  8  1 ]
[ 4  7  8  3 ]
[ 4  7  8  5 ]
[ 4  7  8  6 ]
[ 4  7  8  2 ]
[ 4  7  1  3 ]
[ 4  7  1  5 ]
[ 4  7  1  6 ]
[ 4  7  1  2 ]
[ 4  7  3  5 ]
[ 4  7  3  6 ]
[ 4  7  3  2 ]
[ 4  7  5  6 ]
[ 4  7  5  2 ]
[ 4  7  6  2 ]
[ 4  8  1  3 ]
[ 4  8  1  5 ]
[ 4  8  1  6 ]
[ 4  8  1  2 ]
[ 4  8  3  5 ]
[ 4  8  3  6 ]
[ 4  8  3  2 ]
[ 4  8  5  6 ]
[ 4  8  5  2 ]
[ 4  8  6  2 ]
[ 4  1  3  5 ]
[ 4  1  3  6 ]
[ 4  1  3  2 ]
[ 4  1  5  6 ]
[ 4  1  5  2 ]
[ 4  1  6  2 ]
[ 4  3  5  6 ]
[ 4  3  5  2 ]
[ 4  3  6  2 ]
[ 4  5  6  2 ]
[ 7  8  1  3 ]
[ 7  8  1  5 ]
[ 7  8  1  6 ]
[ 7  8  1  2 ]
[ 7  8  3  5 ]
[ 7  8  3  6 ]
[ 7  8  3  2 ]
[ 7  8  5  6 ]
[ 7  8  5  2 ]
[ 7  8  6  2 ]
[ 7  1  3  5 ]
[ 7  1  3  6 ]
[ 7  1  3  2 ]
[ 7  1  5  6 ]
[ 7  1  5  2 ]
[ 7  1  6  2 ]
[ 7  3  5  6 ]
[ 7  3  5  2 ]
[ 7  3  6  2 ]
[ 7  5  6  2 ]
[ 8  1  3  5 ]
[ 8  1  3  6 ]
[ 8  1  3  2 ]
[ 8  1  5  6 ]
[ 8  1  5  2 ]
[ 8  1  6  2 ]
[ 8  3  5  6 ]
[ 8  3  5  2 ]
[ 8  3  6  2 ]
[ 8  5  6  2 ]
[ 1  3  5  6 ]
[ 1  3  5  2 ]
[ 1  3  6  2 ]
[ 1  5  6  2 ]
[ 3  5  6  2 ]

Subsequences of size 6
[ 4  7  8  1  3  5 ]
[ 4  7  8  1  3  6 ]
[ 4  7  8  1  3  2 ]
[ 4  7  8  1  5  6 ]
[ 4  7  8  1  5  2 ]
[ 4  7  8  1  6  2 ]
[ 4  7  8  3  5  6 ]
[ 4  7  8  3  5  2 ]
[ 4  7  8  3  6  2 ]
[ 4  7  8  5  6  2 ]
[ 4  7  1  3  5  6 ]
[ 4  7  1  3  5  2 ]
[ 4  7  1  3  6  2 ]
[ 4  7  1  5  6  2 ]
[ 4  7  3  5  6  2 ]
[ 4  8  1  3  5  6 ]
[ 4  8  1  3  5  2 ]
[ 4  8  1  3  6  2 ]
[ 4  8  1  5  6  2 ]
[ 4  8  3  5  6  2 ]
[ 4  1  3  5  6  2 ]
[ 7  8  1  3  5  6 ]
[ 7  8  1  3  5  2 ]
[ 7  8  1  3  6  2 ]
[ 7  8  1  5  6  2 ]
[ 7  8  3  5  6  2 ]
[ 7  1  3  5  6  2 ]
[ 8  1  3  5  6  2 ]``````
``````//Include namespace system
using System;
/*
C# program
Print all subsequences of given size
*/
class Subsequence
{
//Print all subsequences in a given size k
public void print_subsequences(int[] collection, int[] output, int n, int k, int next, int location)
{
int i = 0;
if (location == k)
{
// When get new subsequence of k size
Console.Write(" [");
while (i < k)
{
Console.Write(" " + collection[output[i]] + " ");
++i;
}
Console.Write("]\n");
return;
}
else
{
i = next;
while (i < n)
{
// Get location of subset collection
output[location] = i;
print_subsequences(collection, output, n, k, i + 1, location + 1);
++i;
}
}
}
// Handles the request to print subsequence element
public void subsequences(int[] collection, int n, int size)
{
if (n <= 0 || size <= 0 && size >= n)
{
//if not a valid inputs
return;
}
//Used to display result
int[] output = new int[size];
Console.Write("\n Subsequences of size " + size + " \n");
print_subsequences(collection, output, n, size, 0, 0);
}
public static void Main(String[] args)
{
Subsequence obj = new Subsequence();
//Define the element of integers
int[] arr = {
4 , 7 , 8 , 1 , 3 , 5 , 6 , 2
};
int size = 4;
//Get the size
int n = arr.Length;
//Test Case 1
obj.subsequences(arr, n, size);
size = 6;
//Test Case 2
obj.subsequences(arr, n, size);
}
}``````

#### Output

`````` Subsequences of size 4
[ 4  7  8  1 ]
[ 4  7  8  3 ]
[ 4  7  8  5 ]
[ 4  7  8  6 ]
[ 4  7  8  2 ]
[ 4  7  1  3 ]
[ 4  7  1  5 ]
[ 4  7  1  6 ]
[ 4  7  1  2 ]
[ 4  7  3  5 ]
[ 4  7  3  6 ]
[ 4  7  3  2 ]
[ 4  7  5  6 ]
[ 4  7  5  2 ]
[ 4  7  6  2 ]
[ 4  8  1  3 ]
[ 4  8  1  5 ]
[ 4  8  1  6 ]
[ 4  8  1  2 ]
[ 4  8  3  5 ]
[ 4  8  3  6 ]
[ 4  8  3  2 ]
[ 4  8  5  6 ]
[ 4  8  5  2 ]
[ 4  8  6  2 ]
[ 4  1  3  5 ]
[ 4  1  3  6 ]
[ 4  1  3  2 ]
[ 4  1  5  6 ]
[ 4  1  5  2 ]
[ 4  1  6  2 ]
[ 4  3  5  6 ]
[ 4  3  5  2 ]
[ 4  3  6  2 ]
[ 4  5  6  2 ]
[ 7  8  1  3 ]
[ 7  8  1  5 ]
[ 7  8  1  6 ]
[ 7  8  1  2 ]
[ 7  8  3  5 ]
[ 7  8  3  6 ]
[ 7  8  3  2 ]
[ 7  8  5  6 ]
[ 7  8  5  2 ]
[ 7  8  6  2 ]
[ 7  1  3  5 ]
[ 7  1  3  6 ]
[ 7  1  3  2 ]
[ 7  1  5  6 ]
[ 7  1  5  2 ]
[ 7  1  6  2 ]
[ 7  3  5  6 ]
[ 7  3  5  2 ]
[ 7  3  6  2 ]
[ 7  5  6  2 ]
[ 8  1  3  5 ]
[ 8  1  3  6 ]
[ 8  1  3  2 ]
[ 8  1  5  6 ]
[ 8  1  5  2 ]
[ 8  1  6  2 ]
[ 8  3  5  6 ]
[ 8  3  5  2 ]
[ 8  3  6  2 ]
[ 8  5  6  2 ]
[ 1  3  5  6 ]
[ 1  3  5  2 ]
[ 1  3  6  2 ]
[ 1  5  6  2 ]
[ 3  5  6  2 ]

Subsequences of size 6
[ 4  7  8  1  3  5 ]
[ 4  7  8  1  3  6 ]
[ 4  7  8  1  3  2 ]
[ 4  7  8  1  5  6 ]
[ 4  7  8  1  5  2 ]
[ 4  7  8  1  6  2 ]
[ 4  7  8  3  5  6 ]
[ 4  7  8  3  5  2 ]
[ 4  7  8  3  6  2 ]
[ 4  7  8  5  6  2 ]
[ 4  7  1  3  5  6 ]
[ 4  7  1  3  5  2 ]
[ 4  7  1  3  6  2 ]
[ 4  7  1  5  6  2 ]
[ 4  7  3  5  6  2 ]
[ 4  8  1  3  5  6 ]
[ 4  8  1  3  5  2 ]
[ 4  8  1  3  6  2 ]
[ 4  8  1  5  6  2 ]
[ 4  8  3  5  6  2 ]
[ 4  1  3  5  6  2 ]
[ 7  8  1  3  5  6 ]
[ 7  8  1  3  5  2 ]
[ 7  8  1  3  6  2 ]
[ 7  8  1  5  6  2 ]
[ 7  8  3  5  6  2 ]
[ 7  1  3  5  6  2 ]
[ 8  1  3  5  6  2 ]``````
``````//Include header file
#include <iostream>
using namespace std;

/*
C++ program
Print all subsequences of given size
*/

class Subsequence
{
public:
//Print all subsequences in a given size k
void print_subsequences(int collection[], int output[], int n, int k, int next, int location)
{
if (location == k)
{
// When get new subsequence of k size
cout << " [";
for (int i = 0; i < k; ++i)
{
cout << " " << collection[output[i]] << " ";
}
cout << "]\n";
return;
}
else
{
for (int i = next; i < n; ++i)
{
// Get location of subset collection
output[location] = i;
this->print_subsequences(collection, output, n, k, i + 1, location + 1);
}
}
}
// Handles the request to print subsequence element
void subsequences(int collection[], int n, int size)
{
if (n <= 0 || size <= 0 && size >= n)
{
//if not a valid inputs
return;
}
//Used to display result
int output[size];
cout << "\n Subsequences of size " << size << " \n";
this->print_subsequences(collection, output, n, size, 0, 0);
}
};
int main()
{
Subsequence obj = Subsequence();
//Define the element of integers
int arr[] = {
4 , 7 , 8 , 1 , 3 , 5 , 6 , 2
};
int size = 4;
//Get the size
int n = sizeof(arr) / sizeof(arr[0]);
//Test Case 1
obj.subsequences(arr, n, size);
size = 6;
//Test Case 2
obj.subsequences(arr, n, size);
return 0;
}``````

#### Output

`````` Subsequences of size 4
[ 4  7  8  1 ]
[ 4  7  8  3 ]
[ 4  7  8  5 ]
[ 4  7  8  6 ]
[ 4  7  8  2 ]
[ 4  7  1  3 ]
[ 4  7  1  5 ]
[ 4  7  1  6 ]
[ 4  7  1  2 ]
[ 4  7  3  5 ]
[ 4  7  3  6 ]
[ 4  7  3  2 ]
[ 4  7  5  6 ]
[ 4  7  5  2 ]
[ 4  7  6  2 ]
[ 4  8  1  3 ]
[ 4  8  1  5 ]
[ 4  8  1  6 ]
[ 4  8  1  2 ]
[ 4  8  3  5 ]
[ 4  8  3  6 ]
[ 4  8  3  2 ]
[ 4  8  5  6 ]
[ 4  8  5  2 ]
[ 4  8  6  2 ]
[ 4  1  3  5 ]
[ 4  1  3  6 ]
[ 4  1  3  2 ]
[ 4  1  5  6 ]
[ 4  1  5  2 ]
[ 4  1  6  2 ]
[ 4  3  5  6 ]
[ 4  3  5  2 ]
[ 4  3  6  2 ]
[ 4  5  6  2 ]
[ 7  8  1  3 ]
[ 7  8  1  5 ]
[ 7  8  1  6 ]
[ 7  8  1  2 ]
[ 7  8  3  5 ]
[ 7  8  3  6 ]
[ 7  8  3  2 ]
[ 7  8  5  6 ]
[ 7  8  5  2 ]
[ 7  8  6  2 ]
[ 7  1  3  5 ]
[ 7  1  3  6 ]
[ 7  1  3  2 ]
[ 7  1  5  6 ]
[ 7  1  5  2 ]
[ 7  1  6  2 ]
[ 7  3  5  6 ]
[ 7  3  5  2 ]
[ 7  3  6  2 ]
[ 7  5  6  2 ]
[ 8  1  3  5 ]
[ 8  1  3  6 ]
[ 8  1  3  2 ]
[ 8  1  5  6 ]
[ 8  1  5  2 ]
[ 8  1  6  2 ]
[ 8  3  5  6 ]
[ 8  3  5  2 ]
[ 8  3  6  2 ]
[ 8  5  6  2 ]
[ 1  3  5  6 ]
[ 1  3  5  2 ]
[ 1  3  6  2 ]
[ 1  5  6  2 ]
[ 3  5  6  2 ]

Subsequences of size 6
[ 4  7  8  1  3  5 ]
[ 4  7  8  1  3  6 ]
[ 4  7  8  1  3  2 ]
[ 4  7  8  1  5  6 ]
[ 4  7  8  1  5  2 ]
[ 4  7  8  1  6  2 ]
[ 4  7  8  3  5  6 ]
[ 4  7  8  3  5  2 ]
[ 4  7  8  3  6  2 ]
[ 4  7  8  5  6  2 ]
[ 4  7  1  3  5  6 ]
[ 4  7  1  3  5  2 ]
[ 4  7  1  3  6  2 ]
[ 4  7  1  5  6  2 ]
[ 4  7  3  5  6  2 ]
[ 4  8  1  3  5  6 ]
[ 4  8  1  3  5  2 ]
[ 4  8  1  3  6  2 ]
[ 4  8  1  5  6  2 ]
[ 4  8  3  5  6  2 ]
[ 4  1  3  5  6  2 ]
[ 7  8  1  3  5  6 ]
[ 7  8  1  3  5  2 ]
[ 7  8  1  3  6  2 ]
[ 7  8  1  5  6  2 ]
[ 7  8  3  5  6  2 ]
[ 7  1  3  5  6  2 ]
[ 8  1  3  5  6  2 ]``````
``````<?php
/*
Php program
Print all subsequences of given size
*/
class Subsequence
{
//Print all subsequences in a given size k
public	function print_subsequences( & \$collection, & \$output, \$n, \$k, \$next, \$location)
{
if (\$location == \$k)
{
// When get new subsequence of k size
echo " [";
for (\$i = 0; \$i < \$k; ++\$i)
{
echo " ". \$collection[\$output[\$i]] ." ";
}
echo "]\n";
return;
}
else
{
for (\$i = \$next; \$i < \$n; ++\$i)
{
// Get location of subset collection
\$output[\$location] = \$i;
\$this->print_subsequences(\$collection, \$output, \$n, \$k, \$i + 1, \$location + 1);
}
}
}
// Handles the request to print subsequence element
public	function subsequences( & \$collection, \$n, \$size)
{
if (\$n <= 0 || \$size <= 0 && \$size >= \$n)
{
//if not a valid inputs
return;
}
//Used to display result
\$output = array_fill(0, \$size, 0);
echo "\n Subsequences of size ". \$size ." \n";
\$this->print_subsequences(\$collection, \$output, \$n, \$size, 0, 0);
}
}

function main()
{
\$obj = new Subsequence();
//Define the element of integers
\$arr = array(4, 7, 8, 1, 3, 5, 6, 2);
\$size = 4;
//Get the size
\$n = count(\$arr);
//Test Case 1
\$obj->subsequences(\$arr, \$n, \$size);
\$size = 6;
//Test Case 2
\$obj->subsequences(\$arr, \$n, \$size);
}
main();``````

#### Output

`````` Subsequences of size 4
[ 4  7  8  1 ]
[ 4  7  8  3 ]
[ 4  7  8  5 ]
[ 4  7  8  6 ]
[ 4  7  8  2 ]
[ 4  7  1  3 ]
[ 4  7  1  5 ]
[ 4  7  1  6 ]
[ 4  7  1  2 ]
[ 4  7  3  5 ]
[ 4  7  3  6 ]
[ 4  7  3  2 ]
[ 4  7  5  6 ]
[ 4  7  5  2 ]
[ 4  7  6  2 ]
[ 4  8  1  3 ]
[ 4  8  1  5 ]
[ 4  8  1  6 ]
[ 4  8  1  2 ]
[ 4  8  3  5 ]
[ 4  8  3  6 ]
[ 4  8  3  2 ]
[ 4  8  5  6 ]
[ 4  8  5  2 ]
[ 4  8  6  2 ]
[ 4  1  3  5 ]
[ 4  1  3  6 ]
[ 4  1  3  2 ]
[ 4  1  5  6 ]
[ 4  1  5  2 ]
[ 4  1  6  2 ]
[ 4  3  5  6 ]
[ 4  3  5  2 ]
[ 4  3  6  2 ]
[ 4  5  6  2 ]
[ 7  8  1  3 ]
[ 7  8  1  5 ]
[ 7  8  1  6 ]
[ 7  8  1  2 ]
[ 7  8  3  5 ]
[ 7  8  3  6 ]
[ 7  8  3  2 ]
[ 7  8  5  6 ]
[ 7  8  5  2 ]
[ 7  8  6  2 ]
[ 7  1  3  5 ]
[ 7  1  3  6 ]
[ 7  1  3  2 ]
[ 7  1  5  6 ]
[ 7  1  5  2 ]
[ 7  1  6  2 ]
[ 7  3  5  6 ]
[ 7  3  5  2 ]
[ 7  3  6  2 ]
[ 7  5  6  2 ]
[ 8  1  3  5 ]
[ 8  1  3  6 ]
[ 8  1  3  2 ]
[ 8  1  5  6 ]
[ 8  1  5  2 ]
[ 8  1  6  2 ]
[ 8  3  5  6 ]
[ 8  3  5  2 ]
[ 8  3  6  2 ]
[ 8  5  6  2 ]
[ 1  3  5  6 ]
[ 1  3  5  2 ]
[ 1  3  6  2 ]
[ 1  5  6  2 ]
[ 3  5  6  2 ]

Subsequences of size 6
[ 4  7  8  1  3  5 ]
[ 4  7  8  1  3  6 ]
[ 4  7  8  1  3  2 ]
[ 4  7  8  1  5  6 ]
[ 4  7  8  1  5  2 ]
[ 4  7  8  1  6  2 ]
[ 4  7  8  3  5  6 ]
[ 4  7  8  3  5  2 ]
[ 4  7  8  3  6  2 ]
[ 4  7  8  5  6  2 ]
[ 4  7  1  3  5  6 ]
[ 4  7  1  3  5  2 ]
[ 4  7  1  3  6  2 ]
[ 4  7  1  5  6  2 ]
[ 4  7  3  5  6  2 ]
[ 4  8  1  3  5  6 ]
[ 4  8  1  3  5  2 ]
[ 4  8  1  3  6  2 ]
[ 4  8  1  5  6  2 ]
[ 4  8  3  5  6  2 ]
[ 4  1  3  5  6  2 ]
[ 7  8  1  3  5  6 ]
[ 7  8  1  3  5  2 ]
[ 7  8  1  3  6  2 ]
[ 7  8  1  5  6  2 ]
[ 7  8  3  5  6  2 ]
[ 7  1  3  5  6  2 ]
[ 8  1  3  5  6  2 ]``````
``````/*
Node Js program
Print all subsequences of given size
*/
class Subsequence
{
//Print all subsequences in a given size k
print_subsequences(collection, output, n, k, next, location)
{
if (location == k)
{
// When get new subsequence of k size
process.stdout.write(" [");
for (var i = 0; i < k; ++i)
{
process.stdout.write(" " + collection[output[i]] + " ");
}
process.stdout.write("]\n");
return;
}
else
{
for (var i = next; i < n; ++i)
{
// Get location of subset collection
output[location] = i;
this.print_subsequences(collection, output, n, k, i + 1, location + 1);
}
}
}
// Handles the request to print subsequence element
subsequences(collection, n, size)
{
if (n <= 0 || size <= 0 && size >= n)
{
//if not a valid inputs
return;
}
//Used to display result
var output = Array(size).fill(0);
process.stdout.write("\n Subsequences of size " + size + " \n");
this.print_subsequences(collection, output, n, size, 0, 0);
}
}

function main()
{
var obj = new Subsequence();
//Define the element of integers
var arr = [4, 7, 8, 1, 3, 5, 6, 2];
var size = 4;
//Get the size
var n = arr.length;
//Test Case 1
obj.subsequences(arr, n, size);
size = 6;
//Test Case 2
obj.subsequences(arr, n, size);
}
main();``````

#### Output

`````` Subsequences of size 4
[ 4  7  8  1 ]
[ 4  7  8  3 ]
[ 4  7  8  5 ]
[ 4  7  8  6 ]
[ 4  7  8  2 ]
[ 4  7  1  3 ]
[ 4  7  1  5 ]
[ 4  7  1  6 ]
[ 4  7  1  2 ]
[ 4  7  3  5 ]
[ 4  7  3  6 ]
[ 4  7  3  2 ]
[ 4  7  5  6 ]
[ 4  7  5  2 ]
[ 4  7  6  2 ]
[ 4  8  1  3 ]
[ 4  8  1  5 ]
[ 4  8  1  6 ]
[ 4  8  1  2 ]
[ 4  8  3  5 ]
[ 4  8  3  6 ]
[ 4  8  3  2 ]
[ 4  8  5  6 ]
[ 4  8  5  2 ]
[ 4  8  6  2 ]
[ 4  1  3  5 ]
[ 4  1  3  6 ]
[ 4  1  3  2 ]
[ 4  1  5  6 ]
[ 4  1  5  2 ]
[ 4  1  6  2 ]
[ 4  3  5  6 ]
[ 4  3  5  2 ]
[ 4  3  6  2 ]
[ 4  5  6  2 ]
[ 7  8  1  3 ]
[ 7  8  1  5 ]
[ 7  8  1  6 ]
[ 7  8  1  2 ]
[ 7  8  3  5 ]
[ 7  8  3  6 ]
[ 7  8  3  2 ]
[ 7  8  5  6 ]
[ 7  8  5  2 ]
[ 7  8  6  2 ]
[ 7  1  3  5 ]
[ 7  1  3  6 ]
[ 7  1  3  2 ]
[ 7  1  5  6 ]
[ 7  1  5  2 ]
[ 7  1  6  2 ]
[ 7  3  5  6 ]
[ 7  3  5  2 ]
[ 7  3  6  2 ]
[ 7  5  6  2 ]
[ 8  1  3  5 ]
[ 8  1  3  6 ]
[ 8  1  3  2 ]
[ 8  1  5  6 ]
[ 8  1  5  2 ]
[ 8  1  6  2 ]
[ 8  3  5  6 ]
[ 8  3  5  2 ]
[ 8  3  6  2 ]
[ 8  5  6  2 ]
[ 1  3  5  6 ]
[ 1  3  5  2 ]
[ 1  3  6  2 ]
[ 1  5  6  2 ]
[ 3  5  6  2 ]

Subsequences of size 6
[ 4  7  8  1  3  5 ]
[ 4  7  8  1  3  6 ]
[ 4  7  8  1  3  2 ]
[ 4  7  8  1  5  6 ]
[ 4  7  8  1  5  2 ]
[ 4  7  8  1  6  2 ]
[ 4  7  8  3  5  6 ]
[ 4  7  8  3  5  2 ]
[ 4  7  8  3  6  2 ]
[ 4  7  8  5  6  2 ]
[ 4  7  1  3  5  6 ]
[ 4  7  1  3  5  2 ]
[ 4  7  1  3  6  2 ]
[ 4  7  1  5  6  2 ]
[ 4  7  3  5  6  2 ]
[ 4  8  1  3  5  6 ]
[ 4  8  1  3  5  2 ]
[ 4  8  1  3  6  2 ]
[ 4  8  1  5  6  2 ]
[ 4  8  3  5  6  2 ]
[ 4  1  3  5  6  2 ]
[ 7  8  1  3  5  6 ]
[ 7  8  1  3  5  2 ]
[ 7  8  1  3  6  2 ]
[ 7  8  1  5  6  2 ]
[ 7  8  3  5  6  2 ]
[ 7  1  3  5  6  2 ]
[ 8  1  3  5  6  2 ]``````
``````#   Python 3 program
#   Print all subsequences of given size

class Subsequence :
# Print all subsequences in a given size k
def print_subsequences(self, collection, output, n, k, next, location) :
i = 0
if (location == k) :
#  When get new subsequence of k size
print(" [", end = "")
while (i < k) :
print(" ", collection[output[i]] ," ", end = "")
i += 1

print("]\n", end = "")
return
else :
i = next
while (i < n) :
#  Get location of subset collection
output[location] = i
self.print_subsequences(collection, output, n, k, i + 1, location + 1)
i += 1

#  Handles the request to print subsequence element
def subsequences(self, collection, n, size) :
if (n <= 0 or size <= 0 and size >= n) :
# if not a valid inputs
return

# Used to display result
output = [0] * (size)
print("\n Subsequences of size ", size ," \n", end = "")
self.print_subsequences(collection, output, n, size, 0, 0)

def main() :
obj = Subsequence()
# Define the element of integers
arr = [4, 7, 8, 1, 3, 5, 6, 2]
size = 4
# Get the size
n = len(arr)
# Test Case 1
obj.subsequences(arr, n, size)
size = 6
# Test Case 2
obj.subsequences(arr, n, size)

if __name__ == "__main__": main()``````

#### Output

`````` Subsequences of size  4
[  4    7    8    1  ]
[  4    7    8    3  ]
[  4    7    8    5  ]
[  4    7    8    6  ]
[  4    7    8    2  ]
[  4    7    1    3  ]
[  4    7    1    5  ]
[  4    7    1    6  ]
[  4    7    1    2  ]
[  4    7    3    5  ]
[  4    7    3    6  ]
[  4    7    3    2  ]
[  4    7    5    6  ]
[  4    7    5    2  ]
[  4    7    6    2  ]
[  4    8    1    3  ]
[  4    8    1    5  ]
[  4    8    1    6  ]
[  4    8    1    2  ]
[  4    8    3    5  ]
[  4    8    3    6  ]
[  4    8    3    2  ]
[  4    8    5    6  ]
[  4    8    5    2  ]
[  4    8    6    2  ]
[  4    1    3    5  ]
[  4    1    3    6  ]
[  4    1    3    2  ]
[  4    1    5    6  ]
[  4    1    5    2  ]
[  4    1    6    2  ]
[  4    3    5    6  ]
[  4    3    5    2  ]
[  4    3    6    2  ]
[  4    5    6    2  ]
[  7    8    1    3  ]
[  7    8    1    5  ]
[  7    8    1    6  ]
[  7    8    1    2  ]
[  7    8    3    5  ]
[  7    8    3    6  ]
[  7    8    3    2  ]
[  7    8    5    6  ]
[  7    8    5    2  ]
[  7    8    6    2  ]
[  7    1    3    5  ]
[  7    1    3    6  ]
[  7    1    3    2  ]
[  7    1    5    6  ]
[  7    1    5    2  ]
[  7    1    6    2  ]
[  7    3    5    6  ]
[  7    3    5    2  ]
[  7    3    6    2  ]
[  7    5    6    2  ]
[  8    1    3    5  ]
[  8    1    3    6  ]
[  8    1    3    2  ]
[  8    1    5    6  ]
[  8    1    5    2  ]
[  8    1    6    2  ]
[  8    3    5    6  ]
[  8    3    5    2  ]
[  8    3    6    2  ]
[  8    5    6    2  ]
[  1    3    5    6  ]
[  1    3    5    2  ]
[  1    3    6    2  ]
[  1    5    6    2  ]
[  3    5    6    2  ]

Subsequences of size  6
[  4    7    8    1    3    5  ]
[  4    7    8    1    3    6  ]
[  4    7    8    1    3    2  ]
[  4    7    8    1    5    6  ]
[  4    7    8    1    5    2  ]
[  4    7    8    1    6    2  ]
[  4    7    8    3    5    6  ]
[  4    7    8    3    5    2  ]
[  4    7    8    3    6    2  ]
[  4    7    8    5    6    2  ]
[  4    7    1    3    5    6  ]
[  4    7    1    3    5    2  ]
[  4    7    1    3    6    2  ]
[  4    7    1    5    6    2  ]
[  4    7    3    5    6    2  ]
[  4    8    1    3    5    6  ]
[  4    8    1    3    5    2  ]
[  4    8    1    3    6    2  ]
[  4    8    1    5    6    2  ]
[  4    8    3    5    6    2  ]
[  4    1    3    5    6    2  ]
[  7    8    1    3    5    6  ]
[  7    8    1    3    5    2  ]
[  7    8    1    3    6    2  ]
[  7    8    1    5    6    2  ]
[  7    8    3    5    6    2  ]
[  7    1    3    5    6    2  ]
[  8    1    3    5    6    2  ]``````
``````#   Ruby program
#   Print all subsequences of given size

class Subsequence
# Print all subsequences in a given size k
def print_subsequences(collection, output, n, k, next_element, location)
i = 0
if (location == k)
#  When get new subsequence of k size
print(" [")
while (i < k)
print(" ", collection[output[i]] ," ")
i += 1
end

print("]\n")
return
else
i = next_element
while (i < n)
#  Get location of subset collection
output[location] = i
self.print_subsequences(collection, output, n, k, i + 1, location + 1)
i += 1
end

end

end

#  Handles the request to print subsequence element
def subsequences(collection, n, size)
if (n <= 0 || size <= 0 && size >= n)
# if not a valid inputs
return
end

# Used to display result
output = Array.new(size) {0}
print("\n Subsequences of size ", size ," \n")
self.print_subsequences(collection, output, n, size, 0, 0)
end

end

def main()
obj = Subsequence.new()
# Define the element of integers
arr = [4, 7, 8, 1, 3, 5, 6, 2]
size = 4
# Get the size
n = arr.length
# Test Case 1
obj.subsequences(arr, n, size)
size = 6
# Test Case 2
obj.subsequences(arr, n, size)
end

main()``````

#### Output

`````` Subsequences of size 4
[ 4  7  8  1 ]
[ 4  7  8  3 ]
[ 4  7  8  5 ]
[ 4  7  8  6 ]
[ 4  7  8  2 ]
[ 4  7  1  3 ]
[ 4  7  1  5 ]
[ 4  7  1  6 ]
[ 4  7  1  2 ]
[ 4  7  3  5 ]
[ 4  7  3  6 ]
[ 4  7  3  2 ]
[ 4  7  5  6 ]
[ 4  7  5  2 ]
[ 4  7  6  2 ]
[ 4  8  1  3 ]
[ 4  8  1  5 ]
[ 4  8  1  6 ]
[ 4  8  1  2 ]
[ 4  8  3  5 ]
[ 4  8  3  6 ]
[ 4  8  3  2 ]
[ 4  8  5  6 ]
[ 4  8  5  2 ]
[ 4  8  6  2 ]
[ 4  1  3  5 ]
[ 4  1  3  6 ]
[ 4  1  3  2 ]
[ 4  1  5  6 ]
[ 4  1  5  2 ]
[ 4  1  6  2 ]
[ 4  3  5  6 ]
[ 4  3  5  2 ]
[ 4  3  6  2 ]
[ 4  5  6  2 ]
[ 7  8  1  3 ]
[ 7  8  1  5 ]
[ 7  8  1  6 ]
[ 7  8  1  2 ]
[ 7  8  3  5 ]
[ 7  8  3  6 ]
[ 7  8  3  2 ]
[ 7  8  5  6 ]
[ 7  8  5  2 ]
[ 7  8  6  2 ]
[ 7  1  3  5 ]
[ 7  1  3  6 ]
[ 7  1  3  2 ]
[ 7  1  5  6 ]
[ 7  1  5  2 ]
[ 7  1  6  2 ]
[ 7  3  5  6 ]
[ 7  3  5  2 ]
[ 7  3  6  2 ]
[ 7  5  6  2 ]
[ 8  1  3  5 ]
[ 8  1  3  6 ]
[ 8  1  3  2 ]
[ 8  1  5  6 ]
[ 8  1  5  2 ]
[ 8  1  6  2 ]
[ 8  3  5  6 ]
[ 8  3  5  2 ]
[ 8  3  6  2 ]
[ 8  5  6  2 ]
[ 1  3  5  6 ]
[ 1  3  5  2 ]
[ 1  3  6  2 ]
[ 1  5  6  2 ]
[ 3  5  6  2 ]

Subsequences of size 6
[ 4  7  8  1  3  5 ]
[ 4  7  8  1  3  6 ]
[ 4  7  8  1  3  2 ]
[ 4  7  8  1  5  6 ]
[ 4  7  8  1  5  2 ]
[ 4  7  8  1  6  2 ]
[ 4  7  8  3  5  6 ]
[ 4  7  8  3  5  2 ]
[ 4  7  8  3  6  2 ]
[ 4  7  8  5  6  2 ]
[ 4  7  1  3  5  6 ]
[ 4  7  1  3  5  2 ]
[ 4  7  1  3  6  2 ]
[ 4  7  1  5  6  2 ]
[ 4  7  3  5  6  2 ]
[ 4  8  1  3  5  6 ]
[ 4  8  1  3  5  2 ]
[ 4  8  1  3  6  2 ]
[ 4  8  1  5  6  2 ]
[ 4  8  3  5  6  2 ]
[ 4  1  3  5  6  2 ]
[ 7  8  1  3  5  6 ]
[ 7  8  1  3  5  2 ]
[ 7  8  1  3  6  2 ]
[ 7  8  1  5  6  2 ]
[ 7  8  3  5  6  2 ]
[ 7  1  3  5  6  2 ]
[ 8  1  3  5  6  2 ]
``````
``````/*
Scala program
Print all subsequences of given size
*/
class Subsequence
{
//Print all subsequences in a given size k
def print_subsequences(collection: Array[Int], output: Array[Int], n: Int, k: Int, next: Int, location: Int): Unit = {
var i: Int = 0;
if (location == k)
{
// When get new subsequence of k size
print(" [");
while (i < k)
{
print(" " + collection(output(i)) + " ");
i += 1;
}
print("]\n");
return;
}
else
{
i = next;
while (i < n)
{
// Get location of subset collection
output(location) = i;
print_subsequences(collection, output, n, k, i + 1, location + 1);
i += 1;
}
}
}
// Handles the request to print subsequence element
def subsequences(collection: Array[Int], n: Int, size: Int): Unit = {
if (n <= 0 || size <= 0 && size >= n)
{
//if not a valid inputs
return;
}
//Used to display result
var output: Array[Int] = Array.fill[Int](size)(0);
print("\n Subsequences of size " + size + " \n");
print_subsequences(collection, output, n, size, 0, 0);
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: Subsequence = new Subsequence();
//Define the element of integers
var arr: Array[Int] = Array(4, 7, 8, 1, 3, 5, 6, 2);
var size: Int = 4;
//Get the size
var n: Int = arr.length;
//Test Case 1
obj.subsequences(arr, n, size);
size = 6;
//Test Case 2
obj.subsequences(arr, n, size);
}
}``````

#### Output

`````` Subsequences of size 4
[ 4  7  8  1 ]
[ 4  7  8  3 ]
[ 4  7  8  5 ]
[ 4  7  8  6 ]
[ 4  7  8  2 ]
[ 4  7  1  3 ]
[ 4  7  1  5 ]
[ 4  7  1  6 ]
[ 4  7  1  2 ]
[ 4  7  3  5 ]
[ 4  7  3  6 ]
[ 4  7  3  2 ]
[ 4  7  5  6 ]
[ 4  7  5  2 ]
[ 4  7  6  2 ]
[ 4  8  1  3 ]
[ 4  8  1  5 ]
[ 4  8  1  6 ]
[ 4  8  1  2 ]
[ 4  8  3  5 ]
[ 4  8  3  6 ]
[ 4  8  3  2 ]
[ 4  8  5  6 ]
[ 4  8  5  2 ]
[ 4  8  6  2 ]
[ 4  1  3  5 ]
[ 4  1  3  6 ]
[ 4  1  3  2 ]
[ 4  1  5  6 ]
[ 4  1  5  2 ]
[ 4  1  6  2 ]
[ 4  3  5  6 ]
[ 4  3  5  2 ]
[ 4  3  6  2 ]
[ 4  5  6  2 ]
[ 7  8  1  3 ]
[ 7  8  1  5 ]
[ 7  8  1  6 ]
[ 7  8  1  2 ]
[ 7  8  3  5 ]
[ 7  8  3  6 ]
[ 7  8  3  2 ]
[ 7  8  5  6 ]
[ 7  8  5  2 ]
[ 7  8  6  2 ]
[ 7  1  3  5 ]
[ 7  1  3  6 ]
[ 7  1  3  2 ]
[ 7  1  5  6 ]
[ 7  1  5  2 ]
[ 7  1  6  2 ]
[ 7  3  5  6 ]
[ 7  3  5  2 ]
[ 7  3  6  2 ]
[ 7  5  6  2 ]
[ 8  1  3  5 ]
[ 8  1  3  6 ]
[ 8  1  3  2 ]
[ 8  1  5  6 ]
[ 8  1  5  2 ]
[ 8  1  6  2 ]
[ 8  3  5  6 ]
[ 8  3  5  2 ]
[ 8  3  6  2 ]
[ 8  5  6  2 ]
[ 1  3  5  6 ]
[ 1  3  5  2 ]
[ 1  3  6  2 ]
[ 1  5  6  2 ]
[ 3  5  6  2 ]

Subsequences of size 6
[ 4  7  8  1  3  5 ]
[ 4  7  8  1  3  6 ]
[ 4  7  8  1  3  2 ]
[ 4  7  8  1  5  6 ]
[ 4  7  8  1  5  2 ]
[ 4  7  8  1  6  2 ]
[ 4  7  8  3  5  6 ]
[ 4  7  8  3  5  2 ]
[ 4  7  8  3  6  2 ]
[ 4  7  8  5  6  2 ]
[ 4  7  1  3  5  6 ]
[ 4  7  1  3  5  2 ]
[ 4  7  1  3  6  2 ]
[ 4  7  1  5  6  2 ]
[ 4  7  3  5  6  2 ]
[ 4  8  1  3  5  6 ]
[ 4  8  1  3  5  2 ]
[ 4  8  1  3  6  2 ]
[ 4  8  1  5  6  2 ]
[ 4  8  3  5  6  2 ]
[ 4  1  3  5  6  2 ]
[ 7  8  1  3  5  6 ]
[ 7  8  1  3  5  2 ]
[ 7  8  1  3  6  2 ]
[ 7  8  1  5  6  2 ]
[ 7  8  3  5  6  2 ]
[ 7  1  3  5  6  2 ]
[ 8  1  3  5  6  2 ]``````
``````/*
Swift 4 program
Print all subsequences of given size
*/
class Subsequence
{
//Print all subsequences in a given size k
func print_subsequences(_ collection: [Int], _ output: inout[Int], _ n: Int, _ k: Int, _ next: Int, _ location: Int)
{
var i: Int = 0;
if (location == k)
{
// When get new subsequence of k size
print(" [", terminator: "");
while (i < k)
{
print(" ", collection[output[i]]," ", terminator: "");
i += 1;
}
print("]\n", terminator: "");
return;
}
else
{
i = next;
while (i < n)
{
// Get location of subset collection
output[location] = i;
self.print_subsequences(collection, &output, n, k, i + 1, location + 1);
i += 1;
}
}
}
// Handles the request to print subsequence element
func subsequences(_ collection: [Int], _ n: Int, _ size: Int)
{
if (n <= 0 || size <= 0 && size >= n)
{
//if not a valid inputs
return;
}
//Used to display result
var output: [Int] = Array(repeating: 0, count: size);
print("\n Subsequences of size ", size ," \n", terminator: "");
self.print_subsequences(collection, &output, n, size, 0, 0);
}
}
func main()
{
let obj: Subsequence = Subsequence();
//Define the element of integers
let arr: [Int] = [4, 7, 8, 1, 3, 5, 6, 2];
var size: Int = 4;
//Get the size
let n: Int = arr.count;
//Test Case 1
obj.subsequences(arr, n, size);
size = 6;
//Test Case 2
obj.subsequences(arr, n, size);
}
main();``````

#### Output

`````` Subsequences of size  4
[  4    7    8    1  ]
[  4    7    8    3  ]
[  4    7    8    5  ]
[  4    7    8    6  ]
[  4    7    8    2  ]
[  4    7    1    3  ]
[  4    7    1    5  ]
[  4    7    1    6  ]
[  4    7    1    2  ]
[  4    7    3    5  ]
[  4    7    3    6  ]
[  4    7    3    2  ]
[  4    7    5    6  ]
[  4    7    5    2  ]
[  4    7    6    2  ]
[  4    8    1    3  ]
[  4    8    1    5  ]
[  4    8    1    6  ]
[  4    8    1    2  ]
[  4    8    3    5  ]
[  4    8    3    6  ]
[  4    8    3    2  ]
[  4    8    5    6  ]
[  4    8    5    2  ]
[  4    8    6    2  ]
[  4    1    3    5  ]
[  4    1    3    6  ]
[  4    1    3    2  ]
[  4    1    5    6  ]
[  4    1    5    2  ]
[  4    1    6    2  ]
[  4    3    5    6  ]
[  4    3    5    2  ]
[  4    3    6    2  ]
[  4    5    6    2  ]
[  7    8    1    3  ]
[  7    8    1    5  ]
[  7    8    1    6  ]
[  7    8    1    2  ]
[  7    8    3    5  ]
[  7    8    3    6  ]
[  7    8    3    2  ]
[  7    8    5    6  ]
[  7    8    5    2  ]
[  7    8    6    2  ]
[  7    1    3    5  ]
[  7    1    3    6  ]
[  7    1    3    2  ]
[  7    1    5    6  ]
[  7    1    5    2  ]
[  7    1    6    2  ]
[  7    3    5    6  ]
[  7    3    5    2  ]
[  7    3    6    2  ]
[  7    5    6    2  ]
[  8    1    3    5  ]
[  8    1    3    6  ]
[  8    1    3    2  ]
[  8    1    5    6  ]
[  8    1    5    2  ]
[  8    1    6    2  ]
[  8    3    5    6  ]
[  8    3    5    2  ]
[  8    3    6    2  ]
[  8    5    6    2  ]
[  1    3    5    6  ]
[  1    3    5    2  ]
[  1    3    6    2  ]
[  1    5    6    2  ]
[  3    5    6    2  ]

Subsequences of size  6
[  4    7    8    1    3    5  ]
[  4    7    8    1    3    6  ]
[  4    7    8    1    3    2  ]
[  4    7    8    1    5    6  ]
[  4    7    8    1    5    2  ]
[  4    7    8    1    6    2  ]
[  4    7    8    3    5    6  ]
[  4    7    8    3    5    2  ]
[  4    7    8    3    6    2  ]
[  4    7    8    5    6    2  ]
[  4    7    1    3    5    6  ]
[  4    7    1    3    5    2  ]
[  4    7    1    3    6    2  ]
[  4    7    1    5    6    2  ]
[  4    7    3    5    6    2  ]
[  4    8    1    3    5    6  ]
[  4    8    1    3    5    2  ]
[  4    8    1    3    6    2  ]
[  4    8    1    5    6    2  ]
[  4    8    3    5    6    2  ]
[  4    1    3    5    6    2  ]
[  7    8    1    3    5    6  ]
[  7    8    1    3    5    2  ]
[  7    8    1    3    6    2  ]
[  7    8    1    5    6    2  ]
[  7    8    3    5    6    2  ]
[  7    1    3    5    6    2  ]
[  8    1    3    5    6    2  ]``````

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