A good meal contains exactly two different food items with a sum of deliciousness equal to a power of two. You can pick any two different foods to make a good meal.
Let us suppose we have given an array of integers arr where arr[i] is the deliciousness of the ith item of food, return the number of different good meals you can make from this list.
For example,
Input-1 −
arr[ ] = {1, 3, 5, 7, 9}Output −
4
Explanation − The good meals are (1,3), (1,7), (3,5) and, (7,9). Their respective sums are 4, 8, 8, and 16, all of which are powers of 2.
Input-2 −
arr[ ]= {1,1,1,3,3,3,7}Output −
15
Explanation − The good meals are (1,1) in 3 ways, (1,3) in 9 ways, and (1,7) in 3 ways.
The approach used to solve this problem
Take input as an array of positive integers.
A function count pairs take all the array elements as a list of integers.
Sort the input array element in increasing order.
For every element of the array, find the maximum sum such that every element is in the power of ‘2’.
Example
class Solution: def countpairs(self, arr: List[int]) -> int: """ elem1 + elem2 == 1 << i elem1 = 2 << i - elem2 """ result = 0 seen = defaultdict(int) arr.sort() for d in arr: n = 1 while n <= d + d: ans = (ans + seen[n-d]) % (10 ** 9 + 7) n = n << 1 seen[d] += 1 return ans sol1= Solution() print(sol1.countpairs([1,1,1,3,3,3,7]))
Output
4