0167. Two Sum II

0167. Two Sum II#

Problem#

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.

Examples#

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.

Analysis#

For the two-sum problem in 0001, hashing table results in a time complexiy to \(O(n)\), and a space complexity to \(O(n)\) due to the introduction of extra hashing table.

This problem requires the space complexity to be \(O(1)\). We can solve it using two-pointer algorithms.

Solution#

# Solution: naive solution O(m+n) - two-pointers
def solution(nums, target):
    l ,r = 0, len(nums)-1
    while l < r:
        a = nums[l]
        b = nums[r]
        if a + b == target:
            return [l+1, r+1]
        elif a + b > target:
            r += -1
        else:
            l += 1

# test
nums = [2, 7, 11, 15]
target = 9
print(solution(nums, target))

nums = [2, 3, 4]
target = 6
print(solution(nums, target))

nums = [-1, 0]
target = -1
print(solution(nums, target))

[1, 2]
[1, 3]
[1, 2]
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