subset generation Algorithm
The subset generation algorithm is a popular combinatorial method used to generate all possible subsets of a given set. This algorithm is often utilized in a variety of applications, including data analysis, pattern recognition, and problem-solving, where the exploration of different combinations of elements is essential. The algorithm works by iterating through each element in the set and either including or excluding it in the current subset, which leads to the creation of numerous subsets with varying combinations of elements. The process is repeated until all possible subsets, including the empty set and the complete set, have been generated.
One of the most common ways to implement the subset generation algorithm is through a binary counting method, where each subset is represented as a binary number with digits corresponding to the presence or absence of an element in the subset. For example, given a set with three elements, the binary numbers 000, 001, 010, 011, 100, 101, 110, and 111 represent all possible subsets. The algorithm can also be implemented using recursive methods or by employing backtracking techniques. Regardless of the implementation, the subset generation algorithm is an invaluable tool in combinatorial mathematics and computer science for exploring the vast space of possible combinations and finding optimal solutions to complex problems.
# Python program to print all subset combinations of n element in given set of r element.
def combination_util(arr, n, r, index, data, i):
"""
Current combination is ready to be printed, print it
arr[] ---> Input Array
data[] ---> Temporary array to store current combination
start & end ---> Staring and Ending indexes in arr[]
index ---> Current index in data[]
r ---> Size of a combination to be printed
"""
if index == r:
for j in range(r):
print(data[j], end=" ")
print(" ")
return
# When no more elements are there to put in data[]
if i >= n:
return
# current is included, put next at next location
data[index] = arr[i]
combination_util(arr, n, r, index + 1, data, i + 1)
# current is excluded, replace it with
# next (Note that i+1 is passed, but
# index is not changed)
combination_util(arr, n, r, index, data, i + 1)
# The main function that prints all combinations
# of size r in arr[] of size n. This function
# mainly uses combinationUtil()
def print_combination(arr, n, r):
# A temporary array to store all combination one by one
data = [0] * r
# Print all combination using temporary array 'data[]'
combination_util(arr, n, r, 0, data, 0)
# Driver function to check for above function
arr = [10, 20, 30, 40, 50]
print_combination(arr, len(arr), 3)
# This code is contributed by Ambuj sahu
