Problem 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.
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].
Python Solution
def twoSum(numbers: List[int], target: int) -> List[int]:
left, right = 0, len(numbers) - 1
while left < right:
current_sum = numbers[left] + numbers[right]
if current_sum == target:
return [left + 1, right + 1]
elif current_sum < target:
left += 1
else:
right -= 1
return [] # No solution found
Java Solution
class Solution {
public int[] twoSum(int[] numbers, int target) {
int left = 0;
int right = numbers.length - 1;
while (left < right) {
int currentSum = numbers[left] + numbers[right];
if (currentSum == target) {
return new int[]{left + 1, right + 1};
} else if (currentSum < target) {
left++;
} else {
right--;
}
}
return new int[]{}; // No solution found
}
}
C++ Solution
class Solution {
public:
vector twoSum(vector& numbers, int target) {
int left = 0;
int right = numbers.size() - 1;
while (left < right) {
int currentSum = numbers[left] + numbers[right];
if (currentSum == target) {
return {left + 1, right + 1};
} else if (currentSum < target) {
left++;
} else {
right--;
}
}
return {}; // No solution found
}
};
JavaScript Solution
/**
* @param {number[]} numbers
* @param {number} target
* @return {number[]}
*/
var twoSum = function(numbers, target) {
let left = 0;
let right = numbers.length - 1;
while (left < right) {
const currentSum = numbers[left] + numbers[right];
if (currentSum === target) {
return [left + 1, right + 1];
} else if (currentSum < target) {
left++;
} else {
right--;
}
}
return []; // No solution found
};
C# Solution
public class Solution {
public int[] TwoSum(int[] numbers, int target) {
int left = 0;
int right = numbers.Length - 1;
while (left < right) {
int currentSum = numbers[left] + numbers[right];
if (currentSum == target) {
return new int[]{left + 1, right + 1};
} else if (currentSum < target) {
left++;
} else {
right--;
}
}
return new int[]{}; // No solution found
}
}
Complexity Analysis
- Time Complexity: O(n) where n is the length of the input array
- Space Complexity: O(1) as we only use two pointers
Solution Explanation
This solution uses the two-pointer technique:
- Key concept:
- Two pointers
- Sorted array
- Binary search
- Algorithm steps:
- Initialize pointers
- Calculate sum
- Move pointers
- Find target
Key points:
- Linear time
- Constant space
- One solution exists
- 1-based indexing