Python Program for Subset Sum Problem | DP-25
Given a set of non-negative integers, and a value sum, determine if there is a subset of the given set with sum equal to given sum.
Example:
Input: set[] = {3, 34, 4, 12, 5, 2}, sum = 9
Output: True //There is a subset (4, 5) with sum 9.
Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.
Following is naive recursive implementation that simply follows the recursive structure mentioned above.
Python3
# A recursive solution for subset sum# problem # Returns true if there is a subset # of set[] with sun equal to given sumdef isSubsetSum(set, n, sum) : # Base Cases if (sum == 0) : return True if (n == 0 and sum != 0) : return False # If last element is greater than # sum, then ignore it if (set[n - 1] > sum) : return isSubsetSum(set, n - 1, sum); # else, check if sum can be obtained # by any of the following # (a) including the last element # (b) excluding the last element return isSubsetSum(set, n-1, sum) or isSubsetSum(set, n-1, sum-set[n-1]) # Driver program to test above functionset = [3, 34, 4, 12, 5, 2]sum = 9n = len(set)if (isSubsetSum(set, n, sum) == True) : print("Found a subset with given sum")else : print("No subset with given sum") # This code is contributed by Nikita Tiwari. |
Output:
Found a subset with given sum
We can solve the problem in Pseudo-polynomial time using Dynamic programming.
Python3
# A Dynamic Programming solution for subset sum problem# Returns true if there is a subset of # set[] with sun equal to given sum # Returns true if there is a subset of set[] # with sun equal to given sumdef isSubsetSum(set, n, sum): # The value of subset[i][j] will be # true if there is a # subset of set[0..j-1] with sum equal to i subset =([[False for i in range(sum + 1)] for i in range(n + 1)]) # If sum is 0, then answer is true for i in range(n + 1): subset[i][0] = True # If sum is not 0 and set is empty, # then answer is false for i in range(1, sum + 1): subset[0][i]= False # Fill the subset table in bottom up manner for i in range(1, n + 1): for j in range(1, sum + 1): if j<set[i-1]: subset[i][j] = subset[i-1][j] if j>= set[i-1]: subset[i][j] = (subset[i-1][j] or subset[i - 1][j-set[i-1]]) # uncomment this code to print table # for i in range(n + 1): # for j in range(sum + 1): # print (subset[i][j], end =" ") # print() return subset[n][sum] # Driver program to test above functionif __name__=='__main__': set = [3, 34, 4, 12, 5, 2] sum = 9 n = len(set) if (isSubsetSum(set, n, sum) == True): print("Found a subset with given sum") else: print("No subset with given sum") # This code is contributed by # sahil shelangia. |
Output:
Found a subset with given sum
Please refer complete article on Subset Sum Problem | DP-25 for more details!
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