Subsets of size K with product equal to difference of two perfect squares
Given a distinct integers array arr[] of size N and an integer K, the task is to count the number of subsets of size K of array whose product of elements can be represented as a2 – b2.
Examples:
Input: arr[] = {1, 2, 3} K = 2
Output: 2
Explaination:
All possible subsets of length 2 with their products are given below:
{1, 2} = 2
{2, 3} = 6
{1, 3} = 3
Since, only 3 can be expressed as (22 – 12, therefore only one such subset exists.Input: arr[] = {2, 5, 6} K = 2
Output: 2
Explaination:
All possible contiguous sub-sequences with their products given below:
{2, 5} = 10
{2, 6} = 12
{5, 6} = 30
Since, only 12 can be expressed as (42 – 22), only one such subset exists.
Approach:
- Generate all subsets of size K.
- Calculate the products of all subsets.
- A number can be represented as the difference of square of two numbers only if it is odd or divisible by 4.
- Hence, count all subsets with with product that satisfies this condition.
Below is the implementation of the above approach:
Python3
# Python3 implementation of the approach import itertools # Function to return the# Count of required sub-sequencesdef count_seq(arr, n, k): # ans is Count variable ans = 0 for seq in itertools.combinations(arr, k): # product of seq pro = 1 for ele in seq: pro *= ele # checking form of a2-b2 if ((pro % 4) != 2): ans += 1 return ans # Driver codeif __name__ == "__main__": arr = [2, 5, 6] n = len(arr) k = 2 print(count_seq(arr, n, k)) |
1
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