The code for the array is shown below:
Python
def partition(arr):
"""
Partition the array into two subsets A and B such that:
- The intersection of A and B is null
- The union A and B is equal to the original array
- The number of elements in subset A is minimal
- The sum of A's elements is greater than the sum of B's elements
Args:
arr (list[int]): The input array
Returns:
list[int], list[int]: The subsets A and B
"""
n = len(arr)
arr.sort()
# Initialize the subsets
A = []
B = []
# Calculate the target sum for subset A
target_sum = (sum(arr) + 1) // 2
# Initialize the current sum and index
current_sum = 0
i = n - 1
# Add elements to subset A until the target sum is reached
while current_sum < target_sum and i >= 0:
current_sum += arr[i]
A.append(arr[i])
i -= 1
# Add remaining elements to subset B
for j in range(i + 1, n):
B.append(arr[j])
return A, B
# Example usage
arr = [1, 2, 3, 4, 5]
A, B = partition(arr)
print(f"Subset A: {A}")
print(f"Subset B: {B}")
So, the code outputs will be:
Subset A: [5, 4]
Subset B: [4, 5]
Hence, Given an integer array, divide the array into 2 subsets A and B while respecting the conditions of :
A. The intersection of A and B is null
B. The union A and B is equal to the original array
C. The number of elements in subset A is minimal
D. The sum of A's elements is greater than the sum of B's elements.