A good meal is a meal that 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.
Given an array of integers deliciousness
where deliciousness[i]
is the deliciousness of the i​​​​​​th​​​​
​​​​ item of food, return the number of different good meals you can make from this list modulo 109 + 7
.
Note that items with different indices are considered different even if they have the same deliciousness value.
Example 1:
Input: deliciousness = [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.
Example 2:
Input: deliciousness = [1,1,1,3,3,3,7]
Output: 15
Explanation: The good meals are (1,1) with 3 ways, (1,3) with 9 ways, and (1,7) with 3 ways.
Constraints:
-
1 <= deliciousness.length <= 105
-
0 <= deliciousness[i] <= 220
SOLUTION:
from collections import Counter
class Solution:
def countPairs(self, deliciousness: List[int]) -> int:
deliciousness = Counter(deliciousness)
ctr = 0
for i in range(22):
total = 1 << i
for d in deliciousness:
if total - d in deliciousness:
if 2 * d != total:
ctr += deliciousness[d] * deliciousness[total - d] / 2
else:
ctr += deliciousness[d] * (deliciousness[d] - 1) // 2
return int(ctr) % (10 ** 9 + 7)
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