Subset Sum Equal To K | Coding Ninja Solution | CodeStudio

 Subset Sum Equal To K | CodingNinja Solution | CodeStudio

You are given an array/list ‘ARR’ of ‘N’ positive integers and an integer ‘K’. Your task is to check if there exists a subset in ‘ARR’ with a sum equal to ‘K’.

Note: Return true if there exists a subset with sum equal to ‘K’. Otherwise, return false.

For Example :

If ‘ARR’ is {1,2,3,4} and ‘K’ = 4, then there exists 2 subsets with sum = 4. These are {1,3} and {4}. Hence, return true.

Input Format :

The first line contains a single integer T representing the number of test cases.

The first line of each test case contains two space-separated integers ‘N’ and ‘K’ representing the size of the input ‘ARR’ and the required sum as discussed above.

The next line of each test case contains ‘N’ single space-separated integers that represent the elements of the ‘ARR’.

Output Format :

For each test case, return true or false as discussed above.
Output for each test case will be printed in a separate line.

Note:

You don’t need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 5
1 <= N <= 10^3
0 <= ARR[i] <= 10^9
0 <= K <= 10^9

Time Limit: 1 sec

Sample Input 1:

2
4 5
4 3 2 1
5 4
2 5 1 6 7

Sample Output 1:

true
false

Explanation For Sample Input 1:

In example 1, ‘ARR’ is {4,3,2,1} and ‘K’ = 5. There exist 2 subsets with sum = 5. These are {4,1} and {3,2}. Hence, return true.
In example 2, ‘ARR’ is {2,5,1,6,7} and ‘K’ = 4. There are no subsets with sum = 4. Hence, return false.

Sample Input 2:

2
4 4
6 1 2 1
5 6
1 7 2 9 10

Sample Output 2:

true
false

Explanation For Sample Input 2:

In example 1, ‘ARR’ is {6,1,2,1} and ‘K’ = 4. There exist 1 subset with sum = 4. That is {1,2,1}. Hence, return true.
In example 2, ‘ARR’ is {1,7,2,9,10} and ‘K’ = 6. There are no subsets with sum = 6. Hence, return false.

bool subsetSumToK(int n, int k, vector<int> &arr)
{
  vector<vector<bool>> dp(n, vector<bool>(k + 1, 0));
  for (int i = 0; i < n; i++)
    dp[i][0] = true;
  dp[0][arr[0]] = true;
  for (int i = 1; i < n; i++)
  {
    for (int j = 1; j <= k; j++)
    {
      bool nottake = dp[i - 1][j];
      bool take = false;
      if (arr[i] <= j)
        take = dp[i - 1][j - arr[i]];
      dp[i][j] = take | nottake;
    }
  }
  return dp[n - 1][k];
}

bool subsetSumToK(int n, int k, vector<int> &arr)
{
  vector<bool> pre(k + 1, 0);
  vector<bool> curr(k + 1, 0);
  pre[arr[0]] = true;
  pre[0] = curr[0] = true;
  for (int i = 1; i < n; i++)
  {
    for (int j = 1; j <= k; j++)
    {
      bool nottake = pre[j];
      bool take = false;
      if (arr[i] <= j)
        take = pre[j - arr[i]];
      curr[j] = take | nottake;
    }
    pre = curr;
  }
  return pre[k];
}