Question

python code

The power set of a list L is a list containing all possible combinations of the elements of L. For example, the power set of [1, 2, 3] is [[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]. Section 9.3 of your textbook describes a (subtle) algorithm for generating the power set.

• Read and understand the structure of the code in Figure 9.6

• Write (your own) function powerset(L) that generates and returns the power set of a list;

• What is the complexity of your algorithm?

Answer 1

def powerset(L):
    # set_size of power set of a set
    pow_set_size = (int)(math.pow(2, len(L)))
    counter = 0;
    j = 0;
    print("[]")
   
    for counter in range(1, pow_set_size):
        print("[",end=" ")
        for j in range(0, len(L)):

            # Check if jth bit in the
            # counter is set If set then
            # print jth element from set
            if ((counter & (1 << j)) > 0):
                print(L[j], end=" ")
        print("]")

    # Driver program to test printPowerSet


L = [1, 2, 3]
powerset(L)

Complexity is O(n²).

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