The pair sum of a pair (a,b)
is equal to a + b
. The maximum pair sum is the largest pair sum in a list of pairs.
- For example, if we have pairs
(1,5)
,(2,3)
, and(4,4)
, the maximum pair sum would bemax(1+5, 2+3, 4+4) = max(6, 5, 8) = 8
.
Given an array nums
of even length n
, pair up the elements of nums
into n / 2
pairs such that:
- Each element of
nums
is in exactly one pair, and - The maximum pair sum is minimized.
Return the minimized maximum pair sum after optimally pairing up the elements.
Example 1:
Input: nums = [3,5,2,3]
Output: 7
Explanation: The elements can be paired up into pairs (3,3) and (5,2).
The maximum pair sum is max(3+3, 5+2) = max(6, 7) = 7.
Example 2:
Input: nums = [3,5,4,2,4,6]
Output: 8
Explanation: The elements can be paired up into pairs (3,5), (4,4), and (6,2).
The maximum pair sum is max(3+5, 4+4, 6+2) = max(8, 8, 8) = 8.
Constraints:
-
n == nums.length
-
2 <= n <= 105
-
n
is even. -
1 <= nums[i] <= 105
SOLUTION:
import heapq
class Solution:
def minPairSum(self, nums: List[int]) -> int:
minheap = []
maxheap = []
for num in nums:
heapq.heappush(minheap, num)
heapq.heappush(maxheap, -num)
n = len(nums)
smallest = heapq.nlargest(n // 2, minheap)
biggest = heapq.nlargest(n // 2, maxheap)
return max(smallest[i] - biggest[i] for i in range(n // 2))
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