Split an Array A[] into Subsets having equal Sum and sizes equal to elements of Array B[]
Given an array A[] consisting of N integers, the task is to split the array A[] into subsets having equal sum and of length equal to elements in array B[].
Examples:
Input: A[] = {17, 13, 21, 20, 50, 29}, B[] = {2, 3, 1}
Output:
21 29
17 13 20
50Input: A[] = { 1, 2, 3, 4, 5, 6}, B[] = { 2, 2, 2}
Output:
1 6
2 5
3 4
Approach: Follow the steps below to solve the problem:
- Since the count of subsets is already given, calculate the sum of each subset.
- Traverse through each element of array B[], find each possible combination of length B[i] and check if the sum of the combination is equal to the desired sum or not.
- Repeat the above steps for every array element B[i] and print the final answer
Below is the implementation of the above approach:
Python
# Python Program to implement# the above approachfrom itertools import combinations # Function to split elements of first# array into subsets of size given as# elements in the second arraydef main(A, B): # Required sum of subsets req_sum = sum(A) // len(B) # Stores the subsets final = [] # Iterate the array B[] for i in B: # Generate all possible # combination of length B[i] temp = list(combinations(A, i)) # Iterate over all the combinations for j in temp: # If the sum is equal to the # required sum of subsets if(sum(j) == req_sum): # Store the subset temp = list(j) final.append(temp) for k in temp: # Removing the subset # from the array A.remove(k) break # Printing the final result print(final) # Driver Codeif __name__ == '__main__': # Value of array A and B A = [1, 2, 3, 4, 5, 6] B = [2, 2, 2] # Function call main(A, B) |
Output:
[[1, 6], [2, 5], [3, 4]]
Time Complexity: O(N3)
Auxiliary Space: O(2maxm), where maxm is the maximum element in array B[]
