Given an array of non-negative integers and a value sum, determine if there is a subset of the given set with sum equal to given sum.

Examples:

Input : arr[] = {4, 1, 10, 12, 5, 2}, sum = 9 Output : TRUE {4, 5} is a subset with sum 9. Input : arr[] = {1, 8, 2, 5}, sum = 4 Output : FALSE There exists no subset with sum 4.

We have discussed a Dynamic Programming based solution in below post.

Dynamic Programming | Set 25 (Subset Sum Problem)

The solution discussed above requires O(n * sum) space and O(n * sum) time. We cab optimize space. We create a boolean 2D array subset[2][sum+1]. Using bottom up manner we can fill up this table. The idea behind using **2 in “subset[2][sum+1]”** is that for filling a row only the values from previous row is required. So alternate rows are used either making the first one as current and second as previous or the first as previous and second as current.

## C++

[sourcecode language=”C” highlight=””]

// Returns true if there exists a subset

// with given sum in arr[]

#include <stdio.h>

#include <stdbool.h>

bool isSubsetSum(int arr[], int n, int sum)

{

// The value of subset[i%2][j] will be true

// if there exists a subset of sum j in

// arr[0, 1, …., i-1]

bool subset[2][sum + 1];

for (int i = 0; i <= n; i++) {

for (int j = 0; j <= sum; j++) {

// A subset with sum 0 is always possible

if (j == 0)

subset[i % 2][j] = true;

// If there exists no element no sum

// is possible

else if (i == 0)

subset[i % 2][j] = false;

else if (arr[i – 1] <= j)

subset[i % 2][j] = subset[(i + 1) % 2]

[j – arr[i – 1]] || subset[(i + 1) % 2][j];

else

subset[i % 2][j] = subset[(i + 1) % 2][j];

}

}

return subset[n % 2][sum];

}

// Driver code

int main()

{

int arr[] = { 6, 2, 5 };

int sum = 7;

int n = sizeof(arr) / sizeof(arr[0]);

if (isSubsetSum(arr, n, sum) == true)

printf("There exists a subset with given sum");

else

printf("No subset exists with given sum");

return 0;

}

[/sourcecode]

## Java

[sourcecode language=”Java” highlight=””]

// Java Program to get a subset with a

// with a sum provided by the user

public class Subset_sum {

// Returns true if there exists a subset

// with given sum in arr[]

static boolean isSubsetSum(int arr[], int n, int sum)

{

// The value of subset[i%2][j] will be true

// if there exists a subset of sum j in

// arr[0, 1, …., i-1]

boolean subset[][] = new boolean[2][sum + 1];

for (int i = 0; i <= n; i++) {

for (int j = 0; j <= sum; j++) {

// A subset with sum 0 is always possible

if (j == 0)

subset[i % 2][j] = true;

// If there exists no element no sum

// is possible

else if (i == 0)

subset[i % 2][j] = false;

else if (arr[i – 1] <= j)

subset[i % 2][j] = subset[(i + 1) % 2]

[j – arr[i – 1]] || subset[(i + 1) % 2][j];

else

subset[i % 2][j] = subset[(i + 1) % 2][j];

}

}

return subset[n % 2][sum];

}

// Driver code

public static void main(String args[])

{

int arr[] = { 1, 2, 5 };

int sum = 7;

int n = arr.length;

if (isSubsetSum(arr, n, sum) == true)

System.out.println("There exists a subset with" +

"given sum");

else

System.out.println("No subset exists with" +

"given sum");

}

}

// This code is contributed by Sumit Ghosh

[/sourcecode]

## Python

[sourcecode language=”Python”]

# Returns true if there exists a subset

# with given sum in arr[]

def isSubsetSum(arr, n, sum):

# The value of subset[i%2][j] will be true

# if there exists a subset of sum j in

# arr[0, 1, …., i-1]

subset = [ [False for j in range(sum + 1)] for i in range(3) ]

for i in range(n + 1):

for j in range(sum + 1):

# A subset with sum 0 is always possible

if (j == 0):

subset[i % 2][j] = True

# If there exists no element no sum

# is possible

elif (i == 0):

subset[i % 2][j] = False

elif (arr[i – 1] <= j):

subset[i % 2][j] = subset[(i + 1) % 2][j – arr[i – 1]] or subset[(i + 1)

% 2][j]

else:

subset[i % 2][j] = subset[(i + 1) % 2][j]

return subset[n % 2][sum]

# Driver code

arr = [ 6, 2, 5 ]

sum = 7

n = len(arr)

if (isSubsetSum(arr, n, sum) == True):

print ("There exists a subset with given sum")

else:

print ("No subset exists with given sum")

# This code is contributed by Sachin Bisht

[/sourcecode]

Output:

There exists a subset with given sum

This article is contributed by Neelesh (Neelesh_Sinha). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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