167. Two Sum II - Input Array Is Sorted
Description
Given a 1-indexed array of integers numbers
that is already sorted in non-decreasing order, find two numbers such that they add up to a specific target
number. Let these two numbers be numbers[index1]
and numbers[index2]
where 1 <= index1 < index2 <= numbers.length
.
Return the indices of the two numbers, index1
and index2
, added by one as an integer array [index1, index2]
of length 2.
The tests are generated such that there is exactly one solution. You may not use the same element twice.
Your solution must use only constant extra space.
Example 1:
Input: numbers = [2,7,11,15], target = 9 Output: [1,2] Explanation: The sum of 2 and 7 is 9. Therefore, index1 = 1, index2 = 2. We return [1, 2].
Example 2:
Input: numbers = [2,3,4], target = 6 Output: [1,3] Explanation: The sum of 2 and 4 is 6. Therefore index1 = 1, index2 = 3. We return [1, 3].
Example 3:
Input: numbers = [-1,0], target = -1 Output: [1,2] Explanation: The sum of -1 and 0 is -1. Therefore index1 = 1, index2 = 2. We return [1, 2].
Constraints:
2 <= numbers.length <= 3 * 104
-1000 <= numbers[i] <= 1000
numbers
is sorted in non-decreasing order.-1000 <= target <= 1000
- The tests are generated such that there is exactly one solution.
Solutions
Solution 1: Binary Search
Note that the array is sorted in non-decreasing order, so for each numbers[i]
, we can find the position of target - numbers[i]
by binary search, and return $[i + 1, j + 1]$ if it exists.
The time complexity is $O(n \times \log n)$, where $n$ is the length of the array numbers
. The space complexity is $O(1)$.
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