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Code Backtracking

# Find all distinct combinations of k sum in array

The given problem deals with finding all distinct combinations of k-sum in an array. The problem essentially requires us to identify all possible combinations of k elements from the array that add up to a given target sum.

## Problem Statement

Given an array of integers and a target sum 'k', we need to find all distinct combinations of k elements from the array that sum up to 'k'. The combinations should not contain duplicates, and the order of elements in a combination doesn't matter.

## Example

Let's understand the problem using an example:

## Input

```Array: [5, 2, 2, 1, 6, 3, 4]
Target Sum: 7```

## Output

``````1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4``````

## Idea to Solve

To solve this problem, we can use a recursive approach that generates combinations by including and excluding elements from the array. We need to consider each element of the array and decide whether to include it in the current combination or not. While generating combinations, we keep track of the current sum and the elements included in the combination. We continue this process recursively until we reach the target sum 'k'.

## Pseudocode

``````function findCombinations(array, currentIndex, currentSum, currentCombination):
if currentSum == k:
add currentCombination to result
return

if currentIndex >= length of array or currentSum > k:
return

include current element:
findCombinations(array, currentIndex, currentSum + array[currentIndex], currentCombination + array[currentIndex])

exclude current element:
findCombinations(array, currentIndex + 1, currentSum, currentCombination)

result = []
findCombinations(array, 0, 0, [])
return result``````

## Algorithm Explanation

1. Initialize an empty array 'result' to store the distinct combinations.
2. Define a recursive function 'findCombinations' that takes four parameters: 'array', 'currentIndex', 'currentSum', and 'currentCombination'.
3. Inside the function:
• If 'currentSum' equals 'k', add 'currentCombination' to the 'result' array and return.
• If 'currentIndex' is greater than or equal to the length of the array or 'currentSum' exceeds 'k', return.
• Include the current element by recursively calling 'findCombinations' with the updated 'currentIndex', 'currentSum', and 'currentCombination' (include the current element in 'currentCombination').
• Exclude the current element by recursively calling 'findCombinations' with the next index ('currentIndex + 1'), the same 'currentSum', and 'currentCombination'.
4. Call 'findCombinations' initially with parameters ('array', 0, 0, []) to start generating combinations.
5. Return the 'result' array containing all distinct combinations.

## Code Solution

``````import java.util.Arrays;
import java.util.ArrayList;
/*
Java Program for
Find all distinct combinations of k sum in array
*/
public class Combinations
{
public void printArray(int[] arr, int n)
{
System.out.print("\n Array : ");
for (int i = 0; i < n; ++i)
{
System.out.print(" " + arr[i]);
}
}
public void printCombination(
ArrayList < Integer > data,
ArrayList < String > result,
int index,
int count,
int k,
int sum,
String ans)
{
if (sum == k)
{
result.add(ans);
}
if (index >= data.size() || count > data.size())
{
return;
}
int i = index;
while (i < data.size())
{
printCombination(data,
result, i,
count + 1,
k, data.get(i) + sum,
ans + " " + data.get(i));
i++;
}
}
public void distinctCombination(int[] arr, int n, int k)
{
if (n <= 0)
{
return;
}
printArray(arr, n);
// First sort given array
Arrays.sort(arr);
// Auxiliary space
ArrayList < Integer > data = new ArrayList < Integer > ();
ArrayList < String > result = new ArrayList < String > ();
// Add first element
data.add(arr[0]);
// Collect all distinct elements
for (int i = 1; i < n; ++i)
{
if (arr[i] != arr[i - 1])
{
data.add(arr[i]);
}
}
// Print combinations
printCombination(data, result, 0, 0, k, 0, "");
System.out.print("\n Given k : " + k);
System.out.print("\n Result : ");
if (result.size() == 0)
{
// When k sum  not exist
System.out.print(" None \n");
}
else
{
System.out.print("\n");
// Display combination
for (int i = 0; i < result.size(); ++i)
{
System.out.println(result.get(i));
}
}
}
public static void main(String[] args)
{
Combinations task = new Combinations();
int[] arr1 = {
5 , 2 , 2 , 1 , 6 , 3 , 4
};
int[] arr2 = {
6 , -3 , 2 , 3 , 1 , 4 , 1
};
// Test A
// Get the length of array
int n = arr1.length;
// Sum k
int k = 7;
// Test
task.distinctCombination(arr1, n, k);
// Test B
// Get the length of array
n = arr2.length;
// Sum k
k = -4;
// Test
task.distinctCombination(arr2, n, k);
}
}``````

#### Output

`````` Array :  5 2 2 1 6 3 4
Given k : 7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2``````
``````// Include header file
#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;
/*
C++ Program for
Find all distinct combinations of k sum in array
*/
class Combinations
{
public: void printArray(int arr[], int n)
{
cout << "\n Array : ";
for (int i = 0; i < n; ++i)
{
cout << " " << arr[i];
}
}
void printCombination(
vector < int > data,
vector < string > &result,
int index,
int count,
int k,
int sum,
string ans)
{
if (sum == k)
{
result.push_back(ans);
}
if (index >= data.size() || count > data.size())
{
return;
}
int i = index;
while (i < data.size())
{
this->printCombination(
data, result, i,
count + 1, k,
data.at(i) + sum, ans  +  " "
+  to_string(data.at(i))
);
i++;
}
}
void distinctCombination(int arr[], int n, int k)
{
if (n <= 0)
{
return;
}
this->printArray(arr, n);
// First sort given array
sort(arr, arr + n);
// Auxiliary space
vector < int > data;
vector < string > result;
// Add first element
data.push_back(arr[0]);
// Collect all distinct elements
for (int i = 1; i < n; ++i)
{
if (arr[i] != arr[i - 1])
{
data.push_back(arr[i]);
}
}
// Print combinations
this->printCombination(data, result, 0, 0, k, 0, "");
cout << "\n Given k : " << k;
cout << "\n Result : ";
if (result.size() == 0)
{
// When k sum  not exist
cout << " None \n";
}
else
{
cout << "\n";
// Display combination
for (int i = 0; i < result.size(); ++i)
{
cout << result.at(i) << endl;
}
}
}
};
int main()
{
Combinations *task = new Combinations();
int arr1[] = {
5 , 2 , 2 , 1 , 6 , 3 , 4
};
int arr2[] = {
6 , -3 , 2 , 3 , 1 , 4 , 1
};
// Test A
// Get the length of array
int n = sizeof(arr1) / sizeof(arr1[0]);
// Sum k
int k = 7;
// Test
task->distinctCombination(arr1, n, k);
// Test B
// Get the length of array
n = sizeof(arr2) / sizeof(arr2[0]);
// Sum k
k = -4;
// Test
task->distinctCombination(arr2, n, k);
return 0;
}``````

#### Output

`````` Array :  5 2 2 1 6 3 4
Given k : 7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2``````
``````// Include namespace system
using System;
using System.Collections.Generic;
/*
Csharp Program for
Find all distinct combinations of k sum in array
*/
public class Combinations
{
public void printArray(int[] arr, int n)
{
Console.Write("\n Array : ");
for (int i = 0; i < n; ++i)
{
Console.Write(" " + arr[i]);
}
}
public void printCombination(
List < int > data, List < string > result,
int index, int count,
int k, int sum, String ans)
{
if (sum == k)
{
result.Add(ans);
}
if (index >= data.Count || count > data.Count)
{
return;
}
int i = index;
while (i < data.Count)
{
this.printCombination(
data, result, i, count + 1,
k, data[i] + sum, ans + " " + data[i]);
i++;
}
}
public void distinctCombination(int[] arr, int n, int k)
{
if (n <= 0)
{
return;
}
this.printArray(arr, n);
// First sort given array
Array.Sort(arr);
// Auxiliary space
List < int > data = new List < int > ();
List < string > result = new List < string > ();
// Add first element
data.Add(arr[0]);
// Collect all distinct elements
for (int i = 1; i < n; ++i)
{
if (arr[i] != arr[i - 1])
{
data.Add(arr[i]);
}
}
// Print combinations
this.printCombination(data, result, 0, 0, k, 0, "");
Console.Write("\n Given k : " + k);
Console.Write("\n Result : ");
if (result.Count == 0)
{
// When k sum  not exist
Console.Write(" None \n");
}
else
{
Console.Write("\n");
// Display combination
for (int i = 0; i < result.Count; ++i)
{
Console.WriteLine(result[i]);
}
}
}
public static void Main(String[] args)
{
Combinations task = new Combinations();
int[] arr1 = {
5 , 2 , 2 , 1 , 6 , 3 , 4
};
int[] arr2 = {
6 , -3 , 2 , 3 , 1 , 4 , 1
};
// Test A
// Get the length of array
int n = arr1.Length;
// Sum k
int k = 7;
// Test
task.distinctCombination(arr1, n, k);
// Test B
// Get the length of array
n = arr2.Length;
// Sum k
k = -4;
// Test
task.distinctCombination(arr2, n, k);
}
}``````

#### Output

`````` Array :  5 2 2 1 6 3 4
Given k : 7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2``````
``````package main
import "strconv"
import "sort"
import "fmt"
/*
Go Program for
Find all distinct combinations of k sum in array
*/
type Combinations struct { result bool}
func getCombinations() * Combinations {
var me *Combinations = &Combinations {}
me.result = false
return me
}
func(this Combinations) printArray(arr[] int, n int) {
fmt.Print("\n Array : ")
for i := 0 ; i < n ; i++ {
fmt.Print(" ", arr[i])
}
}
func(this Combinations) printCombination(data []int, index int, count int, k int, sum int, ans string) {
if sum == k {
fmt.Print(ans,"\n");

}
if index >= len(data) || count > len(data) {
return
}
var i int = index
for (i < len(data)) {
this.printCombination(data, i, count + 1,
k, data[i] + sum, ans + " " + strconv.Itoa(data[i]))
i++
}
}
func(this Combinations) distinctCombination(arr[] int, n int, k int) {
if n <= 0 {
return
}
this.printArray(arr, n)
// First sort given array
sort.Ints(arr)
// Auxiliary space
var data = make([]int, 0)
this.result = false
// Add first element
data = append(data, arr[0])
// Collect all distinct elements
for i := 1 ; i < n ; i++ {
if arr[i] != arr[i - 1] {
data = append(data, arr[i])
}
}
fmt.Print("\n Given k : ", k)
fmt.Print("\n Result : ")
// Print combinations
this.printCombination(data, 0, 0, k, 0, "")

if this.result == true {
// When k sum  not exist
fmt.Print(" None \n")
}
}
func main() {
var task * Combinations = getCombinations()
var arr1 = [] int { 5 , 2 , 2 , 1 , 6 , 3 , 4 }
var arr2 = [] int { 6 , -3 , 2 , 3 , 1 , 4 , 1 }
// Test A
// Get the length of array
var n int = len(arr1)
// Sum k
var k int = 7
// Test
task.distinctCombination(arr1, n, k)
// Test B
// Get the length of array
n = len(arr2)
// Sum k
k = -4
// Test
task.distinctCombination(arr2, n, k)
}``````

#### Output

``````Array :  5 2 2 1 6 3 4
Given k : 7
Result :  1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :  -3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2
``````
``````<?php
/*
Php Program for
Find all distinct combinations of k sum in array
*/
class Combinations
{
public	function printArray(\$arr, \$n)
{
echo("\n Array : ");
for (\$i = 0; \$i < \$n; ++\$i)
{
echo(" ".\$arr[\$i]);
}
}
public	function printCombination(
\$data, &\$result, \$index,
\$count, \$k, \$sum, \$ans)
{
if (\$sum == \$k)
{
\$result[] = \$ans;
}
if (\$index >= count(\$data) || \$count > count(\$data))
{
return;
}
\$i = \$index;
while (\$i < count(\$data))
{
\$this->printCombination(
\$data, \$result, \$i,
\$count + 1, \$k,
\$data[\$i] + \$sum, \$ans." ".strval(\$data[\$i]));
\$i++;
}
}
public	function distinctCombination(\$arr, \$n, \$k)
{
if (\$n <= 0)
{
return;
}
\$this->printArray(\$arr, \$n);
// First sort given array
sort(\$arr);
// Auxiliary space
\$data = array();
\$result = array();
// Add first element
\$data[] = \$arr[0];
// Collect all distinct elements
for (\$i = 1; \$i < \$n; ++\$i)
{
if (\$arr[\$i] != \$arr[\$i - 1])
{
\$data[] = \$arr[\$i];
}
}
// Print combinations
\$this->printCombination(\$data, \$result, 0, 0, \$k, 0, "");
echo("\n Given k : ".\$k);
echo("\n Result : ");
if (count(\$result) == 0)
{
// When k sum  not exist
echo(" None \n");
}
else
{
echo("\n");
// Display combination
for (\$i = 0; \$i < count(\$result); ++\$i)
{
echo(\$result[\$i]."\n");
}
}
}
}

function main()
{
\$task = new Combinations();
\$arr1 = array(5, 2, 2, 1, 6, 3, 4);
\$arr2 = array(6, -3, 2, 3, 1, 4, 1);
// Test A
// Get the length of array
\$n = count(\$arr1);
// Sum k
\$k = 7;
// Test
\$task->distinctCombination(\$arr1, \$n, \$k);
// Test B
// Get the length of array
\$n = count(\$arr2);
// Sum k
\$k = -4;
// Test
\$task->distinctCombination(\$arr2, \$n, \$k);
}
main();``````

#### Output

`````` Array :  5 2 2 1 6 3 4
Given k : 7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2``````
``````/*
Node JS Program for
Find all distinct combinations of k sum in array
*/
class Combinations
{
printArray(arr, n)
{
process.stdout.write("\n Array : ");
for (var i = 0; i < n; ++i)
{
process.stdout.write(" " + arr[i]);
}
}
printCombination(data, result, index, count, k, sum, ans)
{
if (sum == k)
{
result.push(ans);
}
if (index >= data.length || count > data.length)
{
return;
}
var i = index;
while (i < data.length)
{
this.printCombination(
data, result, i, count + 1, k,
data[i] + sum, ans + " " + data[i]);
i++;
}
}
distinctCombination(arr, n, k)
{
if (n <= 0)
{
return;
}
this.printArray(arr, n);
// First sort given array
arr.sort(function(a, b)
{
return a - b;
});
// Auxiliary space
var data = [];
var result = [];
// Add first element
data.push(arr[0]);
// Collect all distinct elements
for (var i = 1; i < n; ++i)
{
if (arr[i] != arr[i - 1])
{
data.push(arr[i]);
}
}
// Print combinations
this.printCombination(data, result, 0, 0, k, 0, "");
process.stdout.write("\n Given k : " + k);
process.stdout.write("\n Result : ");
if (result.length == 0)
{
// When k sum  not exist
process.stdout.write(" None \n");
}
else
{
process.stdout.write("\n");
// Display combination
for (var i = 0; i < result.length; ++i)
{
console.log(result[i]);
}
}
}
}

function main()
{
var task = new Combinations();
var arr1 = [5, 2, 2, 1, 6, 3, 4];
var arr2 = [6, -3, 2, 3, 1, 4, 1];
// Test A
// Get the length of array
var n = arr1.length;
// Sum k
var k = 7;
// Test
task.distinctCombination(arr1, n, k);
// Test B
// Get the length of array
n = arr2.length;
// Sum k
k = -4;
// Test
task.distinctCombination(arr2, n, k);
}
main();``````

#### Output

`````` Array :  5 2 2 1 6 3 4
Given k : 7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2``````
``````#    Python 3 Program for
#    Find all distinct combinations of k sum in array
class Combinations :
def printArray(self, arr, n) :
print("\n Array : ", end = "")
i = 0
while (i < n) :
print(" ", arr[i], end = "")
i += 1

def printCombination(self, data, result,
index, count, k, sum, ans) :
if (sum == k) :
result.append(ans)

if (index >= len(data) or count > len(data)) :
return

i = index
while (i < len(data)) :
self.printCombination(data, result,
i, count + 1, k,
data[i] + sum, ans + " " + str(data[i]))
i += 1

def distinctCombination(self, arr, n, k) :
if (n <= 0) :
return

self.printArray(arr, n)
#  First sort given list
arr.sort()
#  Auxiliary space
data = []
result = []
#  Add first element
data.append(arr[0])
i = 1
#  Collect all distinct elements
while (i < n) :
if (arr[i] != arr[i - 1]) :
data.append(arr[i])

i += 1

#  Print combinations
self.printCombination(data, result, 0, 0, k, 0, "")
print("\n Given k : ", k, end = "")
print("\n Result : ", end = "")
if (len(result) == 0) :
#  When k sum  not exist
print(" None ")
else :
print(end = "\n")
i = 0
#  Display combination
while (i < len(result)) :
print(result[i])
i += 1

def main() :
task = Combinations()
arr1 = [5, 2, 2, 1, 6, 3, 4]
arr2 = [6, -3, 2, 3, 1, 4, 1]
#  Test A
#  Get the length of list
n = len(arr1)
#  Sum k
k = 7
#  Test
task.distinctCombination(arr1, n, k)
#  Test B
#  Get the length of list
n = len(arr2)
#  Sum k
k = -4
#  Test
task.distinctCombination(arr2, n, k)

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

#### Output

`````` Array :   5  2  2  1  6  3  4
Given k :  7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :   6  -3  2  3  1  4  1
Given k :  -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2``````
``````#    Ruby Program for
#    Find all distinct combinations of k sum in array
class Combinations
def printArray(arr, n)
print("\n Array : ")
i = 0
while (i < n)
print(" ", arr[i])
i += 1
end

end

def printCombination(data, result, index, count, k, sum, ans)
if (sum == k)
result.push(ans)
end

if (index >= data.length || count > data.length)
return
end

i = index
while (i < data.length)
self.printCombination(data, result, i,
count + 1, k,
data[i] + sum, ans + " " + data[i].to_s)
i += 1
end

end

def distinctCombination(arr, n, k)
if (n <= 0)
return
end

self.printArray(arr, n)
#  First sort given array
arr = arr.sort
#  Auxiliary space
data = []
result = []
#  Add first element
data.push(arr[0])
i = 1
#  Collect all distinct elements
while (i < n)
if (arr[i] != arr[i - 1])
data.push(arr[i])
end
i += 1
end

#  Print combinations
self.printCombination(data, result, 0, 0, k, 0, "")
print("\n Given k : ", k)
print("\n Result : ")
if (result.length == 0)
#  When k sum  not exist
print(" None \n")
else

print("\n")
i = 0
#  Display combination
while (i < result.length)
print(result[i], "\n")
i += 1
end

end

end

end

def main()
task = Combinations.new()
arr1 = [5, 2, 2, 1, 6, 3, 4]
arr2 = [6, -3, 2, 3, 1, 4, 1]
#  Test A
#  Get the length of array
n = arr1.length
#  Sum k
k = 7
#  Test
task.distinctCombination(arr1, n, k)
#  Test B
#  Get the length of array
n = arr2.length
#  Sum k
k = -4
#  Test
task.distinctCombination(arr2, n, k)
end

main()``````

#### Output

`````` Array :  5 2 2 1 6 3 4
Given k : 7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2
``````
``````import scala.collection.mutable._;
/*
Scala Program for
Find all distinct combinations of k sum in array
*/
class Combinations()
{
def printArray(arr: Array[Int], n: Int): Unit = {
print("\n Array : ");
var i: Int = 0;
while (i < n)
{
print(" " + arr(i));
i += 1;
}
}
def printCombination(
data: ArrayBuffer[Int],
result: ArrayBuffer[String],
index: Int, count: Int,
k: Int, sum: Int,
ans: String): Unit = {
if (sum == k)
{
result += ans;
}
if (index >= data.size || count > data.size)
{
return;
}
var i: Int = index;
while (i < data.size)
{
printCombination(data, result, i,
count + 1, k, data(i) + sum,
ans + " " + data(i).toString());
i += 1;
}
}
def distinctCombination(arr: Array[Int], n: Int, k: Int): Unit = {
if (n <= 0)
{
return;
}
printArray(arr, n);
// First sort given array
arr.sorted;
// Auxiliary space
var data: ArrayBuffer[Int] = new ArrayBuffer[Int]();
var result: ArrayBuffer[String] = new ArrayBuffer[String]();
// Add first element
data += arr(0);
var i: Int = 1;
// Collect all distinct elements
while (i < n)
{
if (arr(i) != arr(i - 1))
{
data += arr(i);
}
i += 1;
}
// Print combinations
printCombination(data, result, 0, 0, k, 0, "");
print("\n Given k : " + k);
print("\n Result : ");
if (result.size == 0)
{
// When k sum  not exist
print(" None \n");
}
else
{
print("\n");
var i: Int = 0;
// Display combination
while (i < result.size)
{
println(result(i));
i += 1;
}
}
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Combinations = new Combinations();
var arr1: Array[Int] = Array(5, 2, 2, 1, 6, 3, 4);
var arr2: Array[Int] = Array(6, -3, 2, 3, 1, 4, 1);
// Test A
// Get the length of array
var n: Int = arr1.length;
// Sum k
var k: Int = 7;
// Test
task.distinctCombination(arr1, n, k);
// Test B
// Get the length of array
n = arr2.length;
// Sum k
k = -4;
// Test
task.distinctCombination(arr2, n, k);
}
}``````

#### Output

`````` Array :  5 2 2 1 6 3 4
Given k : 7
Result :
5 2
5 1 1
2 2 2 1
2 2 1 1 1
2 2 3
2 1 1 1 1 1
2 1 1 3
2 1 4
1 1 1 1 1 1 1
1 1 1 1 3
1 1 1 4
1 6
1 3 3
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :
6 -3 -3 -3 -3 -3 2 3
6 -3 -3 -3 -3 -3 1 4
6 -3 -3 -3 -3 -3 4 1
6 -3 -3 -3 -3 2
6 -3 -3 -3 -3 1 1
6 -3 -3 -3 -3 1 1
6 -3 -3 -3 -3 1 1
-3 -3 -3 -3 -3 3 4 4
-3 -3 -3 -3 2 2 2 2
-3 -3 -3 -3 2 2 3 1
-3 -3 -3 -3 2 2 3 1
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 1 1 4
-3 -3 -3 -3 2 1 4 1
-3 -3 -3 -3 2 4 1 1
-3 -3 -3 -3 3 3 1 1
-3 -3 -3 -3 3 3 1 1
-3 -3 -3 -3 3 3 1 1
-3 -3 -3 -3 3 1 4
-3 -3 -3 -3 3 4 1
-3 -3 -3 -3 4 4
-3 -3 -3 2 2 1
-3 -3 -3 2 2 1
-3 -3 -3 2 3
-3 -3 -3 2 1 1 1
-3 -3 -3 2 1 1 1
-3 -3 -3 2 1 1 1
-3 -3 -3 2 1 1 1
-3 -3 -3 3 1 1
-3 -3 -3 3 1 1
-3 -3 -3 3 1 1
-3 -3 -3 1 1 1 1 1
-3 -3 -3 1 1 1 1 1
-3 -3 -3 1 1 1 1 1
-3 -3 -3 1 1 1 1 1
-3 -3 -3 1 4
-3 -3 -3 1 1 1 1 1
-3 -3 -3 4 1
-3 -3 -3 1 1 1 1 1
-3 -3 2
-3 -3 1 1
-3 -3 1 1
-3 -3 1 1``````
``````import Foundation;
/*
Swift 4 Program for
Find all distinct combinations of k sum in array
*/
class Combinations
{
func printArray(_ arr: [Int], _ n: Int)
{
print("\n Array : ", terminator: "");
var i: Int = 0;
while (i < n)
{
print(" ", arr[i], terminator: "");
i += 1;
}
}
func printCombination(
_ data: [Int],
_ result: inout[String],
_ index: Int,
_ count: Int,
_ k: Int,
_ sum: Int,
_ ans: String)
{
if (sum == k)
{
result.append(ans);
}
if (index >= data.count || count > data.count)
{
return;
}
var i: Int = index;
while (i < data.count)
{
self.printCombination(
data, &result, i, count + 1,
k, data[i] + sum, ans + " " + String(data[i]));
i += 1;
}
}
func distinctCombination(_ arr: [Int], _ n: Int, _ k: Int)
{
if (n <= 0)
{
return;
}
self.printArray(arr, n);
// First sort given array
var value = arr.sorted();
// Auxiliary space
var data: [Int] = [Int]();
var result: [String] = [String]();
// Add first element
data.append(value[0]);
var i: Int = 1;
// Collect all distinct elements
while (i < n)
{
if (value[i]  != value[i - 1])
{
data.append(value[i]);
}
i += 1;
}
// Print combinations
self.printCombination(data, &result, 0, 0, k, 0, "");
print("\n Given k : ", k, terminator: "");
print("\n Result : ", terminator: "");
if (result.count == 0)
{
// When k sum  not exist
print(" None ");
}
else
{
print(terminator: "\n");
var i: Int = 0;
// Display combination
while (i < result.count)
{
print(result[i]);
i += 1;
}
}
}
}
func main()
{
let task: Combinations = Combinations();
let arr1: [Int] = [5, 2, 2, 1, 6, 3, 4];
let arr2: [Int] = [6, -3, 2, 3, 1, 4, 1];
// Test A
// Get the length of array
var n: Int = arr1.count;
// Sum k
var k: Int = 7;
// Test
task.distinctCombination(arr1, n, k);
// Test B
// Get the length of array
n = arr2.count;
// Sum k
k = -4;
// Test
task.distinctCombination(arr2, n, k);
}
main();``````

#### Output

`````` Array :   5  2  2  1  6  3  4
Given k :  7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :   6  -3  2  3  1  4  1
Given k :  -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2``````
``````/*
Kotlin Program for
Find all distinct combinations of k sum in array
*/
class Combinations
{
fun printArray(arr: Array < Int > , n: Int): Unit
{
print("\n Array : ");
var i: Int = 0;
while (i < n)
{
print(" " + arr[i]);
i += 1;
}
}
fun printCombination(
data: MutableList < Int >  ,
result : MutableList < String >  ,
index : Int, count: Int,
k: Int, sum: Int,
ans: String): Unit
{
if (sum == k)
{
result.add(ans);
}
if (index >= data.size || count > data.size)
{
return;
}
var i: Int = index;
while (i < data.size)
{
this.printCombination(
data, result, i,
count + 1, k,
data[i] + sum,
ans + " " + data[i].toString());
i += 1;
}
}
fun distinctCombination(arr: Array < Int > , n: Int, k: Int): Unit
{
if (n <= 0)
{
return;
}
this.printArray(arr, n);
// First sort given array
arr.sort();
// Auxiliary space
var data: MutableList < Int > = mutableListOf < Int > ();
var result: MutableList < String > = mutableListOf < String > ();
// Add first element
data.add(arr[0]);
var i: Int = 1;
// Collect all distinct elements
while (i < n)
{
if (arr[i] != arr[i - 1])
{
data.add(arr[i]);
}
i += 1;
}
// Print combinations
this.printCombination(data, result, 0, 0, k, 0, "");
print("\n Given k : " + k);
print("\n Result : ");
if (result.size == 0)
{
// When k sum  not exist
print(" None \n");
}
else
{
print("\n");
i = 0;
// Display combination
while (i < result.size)
{
println(result[i]);
i += 1;
}
}
}
}
fun main(args: Array < String > ): Unit
{
val task: Combinations = Combinations();
val arr1: Array < Int > = arrayOf(5, 2, 2, 1, 6, 3, 4);
val arr2: Array < Int > = arrayOf(6, -3, 2, 3, 1, 4, 1);
// Test A
// Get the length of array
var n: Int = arr1.count();
// Sum k
var k: Int = 7;
// Test
task.distinctCombination(arr1, n, k);
// Test B
// Get the length of array
n = arr2.count();
// Sum k
k = -4;
// Test
task.distinctCombination(arr2, n, k);
}``````

#### Output

`````` Array :  5 2 2 1 6 3 4
Given k : 7
Result :
1 1 1 1 1 1 1
1 1 1 1 1 2
1 1 1 1 3
1 1 1 2 2
1 1 1 4
1 1 2 3
1 1 5
1 2 2 2
1 2 4
1 3 3
1 6
2 2 3
2 5
3 4

Array :  6 -3 2 3 1 4 1
Given k : -4
Result :
-3 -3 -3 -3 1 1 6
-3 -3 -3 -3 1 3 4
-3 -3 -3 -3 2 2 4
-3 -3 -3 -3 2 3 3
-3 -3 -3 -3 2 6
-3 -3 -3 -3 4 4
-3 -3 -3 1 1 1 2
-3 -3 -3 1 1 3
-3 -3 -3 1 2 2
-3 -3 -3 1 4
-3 -3 -3 2 3
-3 -3 1 1
-3 -3 2``````

## Time Complexity Analysis

The time complexity of this approach depends on the number of valid combinations. In the worst case, when there are many valid combinations, the algorithm can take exponential time. Let's denote 'n' as the length of the input array. Since we are exploring all possible combinations, the time complexity could be O(2^n) in the worst case.

## Comment

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