Two Sum - Pair sum in sorted array

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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.

Examples:

Input: arr[] = {2, 7, 11, 15}, target = 9
Output: 1 2
Explanation: Since the array is 1-indexed, arr[1] + arr[2] = 2 + 7 = 9

Input: {1, 3, 4, 6, 8, 11} target = 10
Output: 3 4
Explanation: Since the array is 1-indexed, arr[3] + arr[5] = 4 + 6 = 10

Approach: To solve the problem, follow the below idea:

The problem can be solved using two pointers technique. We can maintain two pointers, left = 0 and right = n - 1, and calculate their sum S = arr[left] + arr[right].

• If S = target, then return left and right.
• If S < target, then we need to increase sum S, so we will increment left = left + 1.
• If S > target, then we need to decrease sum S, so we will decrement right = right - 1.

If at any point left >= right, then no pair with sum = target is found.

Step-by-step algorithm:

• We need to initialize two pointers as left and right with position at the beginning and at the end of the array respectively.
• Need to calculate the sum of the elements in the array at these two positions of the pointers.
• If the sum equals to target value, return the 1-indexed positions of the two elements.
• If the sum comes out to be less than the target, move the left pointer to the right to the increase the sum.
• If the sum is greater than the target, move the right pointer to the left to decrease the sum.
• Repeat the following steps till both the pointers meet.

Below is the implementation of the algorithm:

#include <vector>
using namespace std;

vector<int> twoSum(vector<int>& numbers, int target)
{
    int left = 0, right = numbers.size() - 1;

    while (left < right) {
        int current_sum = numbers[left] + numbers[right];
        // If current sum = target, return left and right
        if (current_sum == target) {
            return { left + 1, right + 1 };
        }
        // If current sum < target, then increase the
        // current sum by moving the left pointer by 1
        else if (current_sum < target) {
            left++;
        }
        else {
            // If current sum > target, then decrease the
            // current sum by moving the right pointer by 1
            right--;
        }
    }

    return {};
}

// Example usage
#include <iostream>
int main()
{
    vector<int> numbers = { 2, 7, 11, 15 };
    int target = 9;
    vector<int> result = twoSum(numbers, target);
    for (int num : result) {
        cout << num << " ";
    }
    cout << endl;
    return 0;
}

// This code is contributed by Shivam Gupta

import java.util.*;

public class TwoSum {
    public static List<Integer> twoSum(List<Integer> numbers, int target) {
        int left = 0, right = numbers.size() - 1;

        while (left < right) {
            int current_sum = numbers.get(left) + numbers.get(right);
            // If current sum = target, return left and right
            if (current_sum == target) {
                return Arrays.asList(left + 1, right + 1);
            }
            // If current sum < target, then increase the
            // current sum by moving the left pointer by 1
            else if (current_sum < target) {
                left++;
            } else {
                // If current sum > target, then decrease the
                // current sum by moving the right pointer by 1
                right--;
            }
        }

        return Collections.emptyList();
    }

    public static void main(String[] args) {
        List<Integer> numbers = Arrays.asList(2, 7, 11, 15);
        int target = 9;
        List<Integer> result = twoSum(numbers, target);
        for (int num : result) {
            System.out.print(num + " ");
        }
        System.out.println();
    }
}
// This code is contributed by Ayush Mishra

def twoSum(numbers, target):
    left, right = 0, len(numbers) - 1

    while left < right:
        current_sum = numbers[left] + numbers[right]
        # If current sum = target, return left and right
        if current_sum == target:
            return [left + 1, right + 1]
        # If current sum < target, then increase the current sum by moving the left 
        # pointer by 1
        elif current_sum < target:
            left += 1
        else:
            # If current sum > target, then decrease the current sum by 
            # moving the right pointer by 1
            right -= 1

    return []


# Example usage
numbers = [2, 7, 11, 15]
target = 9
print(twoSum(numbers, target))

// Function to find two numbers such that they add up to a specific target
function twoSum(numbers, target) {
    let left = 0;
    let right = numbers.length - 1;

    // Continue searching while the left index is less than the right index
    while (left < right) {
        let currentSum = numbers[left] + numbers[right];
        
        // If the current sum equals the target, return the indices (1-indexed)
        if (currentSum === target) {
            return [left + 1, right + 1];
        }
        // If the current sum is less than the target, move the left index to the right
        else if (currentSum < target) {
            left++;
        }
        // If the current sum is greater than the target, move the right index to the left
        else {
            right--;
        }
    }

    // Return an empty array if no two numbers sum up to the target
    return [];
}

const numbers = [2, 7, 11, 15];
const target = 9;
const result = twoSum(numbers, target);

// Output the result
result.forEach(num => {
    console.log(num);
});

[1, 2]

Time Complexity: O(n), where n is declared to be as length of array because elements of array is traced only once.
Auxiliary Space: O(1)