Given an array and a sum, find the count of unique subsets with each subset’s sum equal to the given sum value.
Examples:
Input : 4 12 5 9 12 9 Output : 2 (subsets will be [4, 5] and [9]) Input : 1 2 3 4 5 10 Output : 3
We will use dynamic programming to solve this problem and this solution has time complexity of O(n2). Below is dp[][]
used in the code –
_ | 4 12 5 9 12 0 |[1, 1, 1, 1, 1] 1 |[0, 0, 0, 0, 0] 2 |[0, 0, 0, 0, 0] 3 |[0, 0, 0, 0, 0] 4 |[1, 1, 1, 1, 1] 5 |[0, 0, 1, 1, 1] 6 |[0, 0, 0, 0, 0] 7 |[0, 0, 0, 0, 0] 8 |[0, 0, 0, 0, 0] 9 |[0, 0, 1, 2, 2]
Below is the Python Code :
# Python code to find the number of unique subsets # with given sum in the given array def help (a,s): dp = [[ 0 for i in range ( len (a))] for j in range ( 0 ,s + 1 )] for i in range ( len (a)): dp[ 0 ][i] = 1 for i in range ( 1 ,s + 1 ): if i = = a[ 0 ]: dp[i][ 0 ] = 1 for i in range ( 1 , s + 1 ): for j in range ( 1 , len (a)): if a[j]< = i: dp[i][j] = dp[i][j - 1 ] + dp[i - a[j]][j - 1 ] else : dp[i][j] = dp[i][j - 1 ] return dp[s][ len (a) - 1 ] # driver code a = [ 4 , 12 , 5 , 9 , 12 ] s = 9 print ( help (a,s)) |
Output :
2
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