# Given an absolute sorted array and a number K, find the pair whose sum is K

Given an absolute sorted array arr[] and a number K, the task is to find a pair of elements in the given array that sum to K. An absolute sorted array is an array of numbers in which |arr[i]| ? |arr[j]| whenever i < j.

Examples:

Input: arr[] = {-49, 75, 103, -147, 164, -197, -238, 314, 348, -422}, K = 167
Output: 3 7
(arr[3] + arr[7]) = (-147 + 314) = 167.

Input: arr[] = {-8, 10, -15, 12, 24}, K = 22
Output: 1 3

Naive Approach:- The simple approach to find a pair is to check for each element in the array for another element. If no pair found then returning -1,-1

Algorithm:

1. Create a function FindPair which takes the array A and integer K as input
2. Create a pair of integers ans to store the indices of the pair which sums to K
3. Iterate over the array A from index 0 to size-2 (outer loop)
4. For each iteration of outer loop, iterate over the array A from index i+1 to size-1 (inner loop)
5. If the sum of A[i] and A[j] is equal to K, store the indices i and j in ans
6. Return ans
7. If no pair is found, return {-1,-1}
8. In the main function, create an array A with the given elements and an integer K with the given value
9. Call the FindPair function with A and K as input arguments
10. Print the indices returned by the function.

Implementation:-

## C++

 `// C++ implementation of above approach` `#include ``using` `namespace` `std;` `//function to return answer``pair<``int``,``int``> FindPair(vector<``int``> A,``int` `K)``{``      ``//pair to store answer``      ``pair<``int``,``int``> ans;``      ` `      ``//iterating over array``      ``for``(``int` `i=0;i A;``    ``A.push_back(-49);``    ``A.push_back(75);``    ``A.push_back(103);``    ``A.push_back(-147);``    ``A.push_back(164);``    ``A.push_back(-197);``    ``A.push_back(-238);``    ``A.push_back(314);``    ``A.push_back(348);``    ``A.push_back(-422);``    ``int` `K = 167;``    ``pair<``int``,``int``> result = FindPair(A, K);` `    ``cout << result.first << ``' '``         ``<< result.second;` `    ``return` `0;``}` `//This code contributed by shubhamrajput6156`

## Java

 `// Java implementation of above approach``import` `java.util.ArrayList;``import` `java.util.List;` `public` `class` `Main {``    ``// Function to return answer``    ``static` `int``[] FindPair(List A, ``int` `K)``    ``{``        ``// int array to store answer``        ``int``[] ans = ``new` `int``[``2``];` `        ``// iterating over array``        ``for` `(``int` `i = ``0``; i < A.size() - ``1``; i++) {``            ``for` `(``int` `j = i + ``1``; j < A.size(); j++) {``                ``// if found such pair``                ``if` `(A.get(i) + A.get(j) == K) {``                    ``ans[``0``] = i;``                    ``ans[``1``] = j;``                    ``// returning answer``                    ``return` `ans;``                ``}``            ``}``        ``}` `        ``// if no pair exist``        ``return` `new` `int``[] { -``1``, -``1` `};``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``List A = ``new` `ArrayList<>();``        ``A.add(-``49``);``        ``A.add(``75``);``        ``A.add(``103``);``        ``A.add(-``147``);``        ``A.add(``164``);``        ``A.add(-``197``);``        ``A.add(-``238``);``        ``A.add(``314``);``        ``A.add(``348``);``        ``A.add(-``422``);``        ``int` `K = ``167``;``        ``int``[] result = FindPair(A, K);` `        ``System.out.println(result[``0``] + ``" "` `+ result[``1``]);``    ``}``}`

## Python3

 `# Python implementation of above approach` `# function to return answer``def` `find_pair(A, K):``    ``for` `i ``in` `range``(``len``(A) ``-` `1``):``        ``for` `j ``in` `range``(i ``+` `1``, ``len``(A)):``          ` `              ``# if found such pair``            ``if` `A[i] ``+` `A[j] ``=``=` `K:``              ` `                ``# returning answer``                ``return` `(i, j)``              ` `    ``# if no pair exist``    ``return` `(``-``1``, ``-``1``)` `# driver code``A ``=` `[]``A.append(``-``49``)``A.append(``75``)``A.append(``103``)``A.append(``-``147``)``A.append(``164``)``A.append(``-``197``)``A.append(``-``238``)``A.append(``314``)``A.append(``348``)``A.append(``-``422``)``K ``=` `167``result ``=` `find_pair(A, K)` `print``(result)` `# This code is contributed by redmoonz.`

## C#

 `// C# implementation of above approach``using` `System;``using` `System.Collections.Generic;` `namespace` `ConsoleApp``{``  ``class` `Program``  ``{``    ``// Function to return answer``    ``static` `int``[] FindPair(List<``int``> A, ``int` `K)``    ``{``      ``// int array to store answer``      ``int``[] ans = ``new` `int``[2];` `      ``// iterating over array``      ``for` `(``int` `i = 0; i < A.Count - 1; i++)``      ``{``        ``for` `(``int` `j = i + 1; j < A.Count; j++)``        ``{``          ``// if found such pair``          ``if` `(A[i] + A[j] == K)``          ``{``            ``ans[0] = i;``            ``ans[1] = j;``            ``// returning answer``            ``return` `ans;``          ``}``        ``}``      ``}` `      ``// if no pair exist``      ``return` `new` `int``[] { -1, -1 };``    ``}` `    ``// Driver Code``    ``static` `void` `Main(``string``[] args)``    ``{``      ``List<``int``> A = ``new` `List<``int``>() { -49, 75, 103, -147, 164, -197, -238, 314, 348, -422 };``      ``int` `K = 167;``      ``int``[] result = FindPair(A, K);` `      ``Console.WriteLine(result[0] + ``" "` `+ result[1]);``      ``Console.ReadLine();``    ``}``  ``}``}` `// This code is contributed by vinayetbi1.`

## Javascript

 ``

Output:-  3 7

Time Complexity:- O(N^2) where N is size of array

Space Complexity:- O(1)

Efficient Approach: For a sorted array, use the approach discussed in this article. In case of an absolute sorted array, there are generally three cases for pairs according to their property:

1. Both the numbers in the pair are negative.
2. Both the numbers in the pair are positive.
3. One is negative and the other is positive.

For cases (1) and (2), use the Two Pointer Approach separately by just limiting to consider either positive or negative numbers.
For case (3), use the same Two pointer approach where we have one index for positive numbers and one index for negative numbers, and they both start from the highest possible index and then go down.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of above approach` `#include ``using` `namespace` `std;` `// Index Pair Structure``struct` `indexPair {``    ``int` `index_1, index_2;``};` `// Function to find positive and``// Negative pairs``indexPair findPositiveNegativePairs(``    ``const` `vector<``int``>& arr, ``int` `k)``{` `    ``// result.index_1 for positive number &``    ``// result.index_2 for negative number``    ``indexPair result = indexPair{``        ``static_cast``<``int``>(arr.size() - 1),``        ``static_cast``<``int``>(arr.size() - 1)``    ``};` `    ``// Find the last positive or zero number``    ``while` `(result.index_1 >= 0``           ``&& arr[result.index_1] < 0) {``        ``--result.index_1;``    ``}` `    ``// Find the last negative number``    ``while` `(result.index_2 >= 0``           ``&& arr[result.index_2] >= 0) {``        ``--result.index_2;``    ``}` `    ``// Loop to find the pair with``    ``// Desired Sum``    ``while` `(result.index_1 >= 0``           ``&& result.index_2 >= 0) {` `        ``// Condition if the current index pair``        ``// have the desired sum``        ``if` `(arr[result.index_1]``                ``+ arr[result.index_2]``            ``== k) {``            ``return` `result;``        ``}` `        ``// Condition if the current index pairs``        ``// sum is greater than desired sum``        ``else` `if` `(arr[result.index_1]``                     ``+ arr[result.index_2]``                 ``> k) {` `            ``// Loop to find the next``            ``// negative element from last``            ``do` `{``                ``--result.index_1;``            ``} ``while` `(result.index_1 >= 0``                     ``&& arr[result.index_1] < 0);``        ``}` `        ``// Condition if the current index pairs``        ``// sum is less than desired sum``        ``else` `{` `            ``// Loop to find the next``            ``// positive or zero number from last``            ``do` `{``                ``--result.index_2;``            ``} ``while` `(result.index_2 >= 0``                     ``&& arr[result.index_2] >= 0);``        ``}``    ``}``    ``return` `{ -1, -1 };``}` `// Function to find positive-positive number``// pairs or negative-negative number pairs``template` `<``typename` `T>``indexPair findPairsOfSameSign(``    ``const` `vector<``int``>& arr, ``int` `k, T compare)``{` `    ``// Initializing the index pairs with``    ``// 0 and the end of array length - 1``    ``indexPair result``        ``= indexPair{``              ``0,``              ``static_cast``<``int``>(arr.size() - 1)``          ``};` `    ``// Loop to find the first positive or negative``    ``// number in the array according to the given``    ``// comparison template function``    ``while` `(result.index_1 < result.index_2``           ``&& compare(arr[result.index_1], 0)) {``        ``++result.index_1;``    ``}` `    ``// Loop to find the last positive or negative``    ``// number in the array according to the given``    ``// comparison template function``    ``while` `(result.index_1 < result.index_2``           ``&& compare(arr[result.index_2], 0)) {``        ``--result.index_2;``    ``}` `    ``// Loop to find the desired pairs``    ``while` `(result.index_1 < result.index_2) {` `        ``// Condition if the current index pair``        ``// have the desired sum``        ``if` `(arr[result.index_1]``                ``+ arr[result.index_2]``            ``== k) {``            ``return` `result;``        ``}` `        ``// Condition if the current index pair``        ``// is greater than or equal to the desired``        ``// sum according to the compare function``        ``else` `if` `(compare(arr[result.index_1]``                             ``+ arr[result.index_2],``                         ``k)) {` `            ``// Loop to find the next positive-positive``            ``// or negative-negative pairs``            ``do` `{``                ``++result.index_1;``            ``} ``while` `(result.index_1 < result.index_2``                     ``&& compare(arr[result.index_1], 0));``        ``}` `        ``// Condition if the current index pair is``        ``// greater than or equal to the desired``        ``// sum according to the compare function``        ``else` `{` `            ``// Loop to find the next positive-positive``            ``// or negative-negative pairs``            ``do` `{``                ``--result.index_2;``            ``} ``while` `(result.index_1 < result.index_2``                     ``&& compare(arr[result.index_2], 0));``        ``}``    ``}``    ``return` `{ -1, -1 };``}` `// Function to find the pairs whose sum``// is equal to the given desired sum K``indexPair FindPairs(``const` `vector<``int``>& arr, ``int` `k)``{``    ``// Find the positive-negative pairs``    ``indexPair result = findPositiveNegativePairs(arr, k);` `    ``// Condition to check if positive-negative``    ``// pairs not found in the array``    ``if` `(result.index_1 == -1``        ``&& result.index_2 == -1) {` `        ``return` `k >= 0``                   ``? findPairsOfSameSign(``                         ``arr, k, less<``int``>())``                   ``: findPairsOfSameSign(``                         ``arr, k, greater_equal<``int``>());``    ``}``    ``return` `result;``}` `// Driver Code``int` `main()``{``    ``vector<``int``> A;``    ``A.push_back(-49);``    ``A.push_back(75);``    ``A.push_back(103);``    ``A.push_back(-147);``    ``A.push_back(164);``    ``A.push_back(-197);``    ``A.push_back(-238);``    ``A.push_back(314);``    ``A.push_back(348);``    ``A.push_back(-422);``    ``int` `K = 167;``    ``indexPair result = FindPairs(A, K);` `    ``cout << result.index_2 << ``' '``         ``<< result.index_1;` `    ``return` `0;``}`

## Java

 `// Java implementation of above approach``import` `java.util.*;` `// Index Pair Structure``class` `IndexPair {``    ``int` `index_1, index_2;``}` `class` `GFG {``    ` `    ``// Function to find positive and``    ``// Negative pairs``    ``static` `IndexPair findPositiveNegativePairs(``        ``final` `List arr, ``final` `int` `k)``    ``{``        ` `        ``// result.index_1 for positive number &``        ``// result.index_2 for negative number``        ``final` `IndexPair result = ``new` `IndexPair();``        ``result.index_1 = arr.size() - ``1``;``        ``result.index_2 = arr.size() - ``1``;``        ` `        ``// Find the last positive or zero number``        ``while` `(result.index_1 >= ``0``               ``&& arr.get(result.index_1) < ``0``) {``            ``--result.index_1;``        ``}``        ` `        ``// Find the last negative number``        ``while` `(result.index_2 >= ``0``               ``&& arr.get(result.index_2) >= ``0``) {``            ``--result.index_2;``        ``}``        ` `        ``// Loop to find the pair with``        ``// Desired Sum``        ``while` `(result.index_1 >= ``0``               ``&& result.index_2 >= ``0``) {``            ``// Condition if the current index pair``        ``// have the desired sum``            ``if` `(arr.get(result.index_1)``                    ``+ arr.get(result.index_2)``                ``== k) {``                ``return` `result;``            ``}``            ` `        ``// Condition if the current index pairs``         ``// sum is greater than desired sum``            ``else` `if` `(arr.get(result.index_1)``                         ``+ arr.get(result.index_2)``                     ``> k) {``                ` `            ``// Loop to find the next``            ``// negative element from last``                ``do` `{``                    ``--result.index_1;``                ``} ``while` `(result.index_1 >= ``0``                         ``&& arr.get(result.index_1) < ``0``);``            ``}``            ` `        ``// Condition if the current index pairs``        ``// sum is less than desired sum``            ``else` `{``            ` `            ``// Loop to find the next``            ``// positive or zero number from last``                ``do` `{``                    ``--result.index_2;``                ``} ``while` `(result.index_2 >= ``0``                         ``&& arr.get(result.index_2) >= ``0``);``            ``}``        ``}``        ``return` `new` `IndexPair();``    ``}``    ` `    ` `// Function to find positive-positive number``// pairs or negative-negative number pairs``    ``static` `IndexPair findPairsOfSameSign(``        ``final` `List arr, ``final` `int` `k)``    ``{``    ` `    ` `    ``// Initializing the index pairs with``    ``// 0 and the end of array length - 1``        ``final` `IndexPair result = ``new` `IndexPair();``        ``result.index_1 = ``0``;``        ``result.index_2 = arr.size() - ``1``;``    ``// Loop to find the first positive or negative``    ``// number in the array according to the given``    ``// comparison template function``        ``while` `(result.index_1 < result.index_2``               ``&& arr.get(result.index_1) < ``0``) {``            ``++result.index_1;``        ``}``    ` `     ``// Loop to find the last positive or negative``    ``// number in the array according to the given``    ``// comparison template function``        ``while` `(result.index_1 < result.index_2``               ``&& arr.get(result.index_2) >= ``0``) {``            ``--result.index_2;``        ``}``    ` `    ``// Loop to find the desired pairs``        ``while` `(result.index_1 < result.index_2) {``            ``// Condition if the current index pair``            ``// have the desired sum``            ``if` `(arr.get(result.index_1)``                    ``+ arr.get(result.index_2)``                ``== k) {``                ``return` `result;``            ``}``            ` `            ``// Condition if the current index pair``            ``// is greater than or equal to the desired``            ``// sum according to the compare function``            ``else` `if` `(arr.get(result.index_1)``                         ``+ arr.get(result.index_2)``                     ``> k) {``                ` `            ``// Loop to find the next positive-positive``            ``// or negative-negative pairs``                ``do` `{``                    ``++result.index_1;``                ``} ``while` `(result.index_1 < result.index_2``                         ``&& arr.get(result.index_1) < ``0``);``            ``}``        ` `         ``// Condition if the current index pair is``        ``// greater than or equal to the desired``        ``// sum according to the compare function``            ``else` `{``                 ``// Loop to find the next positive-positive``                ``// or negative-negative pairs``                ``do` `{``                    ``--result.index_2;``                ``} ``while` `(result.index_1 < result.index_2``                         ``&& arr.get(result.index_2) >= ``0``);``            ``}``        ``}``        ``return` `new` `IndexPair();``    ``}``    ` `    ``// Function to find the pairs whose sum``    ``// is equal to the given desired sum K``    ``static` `IndexPair FindPairs(``final` `List arr, ``final` `int` `k)``    ``{``        ` `        ``// Find the positive-negative pairs``        ``final` `IndexPair result = findPositiveNegativePairs(arr, k);``        ` `         ``// Condition to check if positive-negative``        ``// pairs not found in the array``        ``if` `(result.index_1 == -``1``            ``&& result.index_2 == -``1``) {` `            ``return` `k >= ``0``                       ``? findPairsOfSameSign(``                             ``arr, k)``                       ``: findPairsOfSameSign(``                             ``arr, k);``        ``}``        ``return` `result;``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args) {``        ``List A = ``new` `ArrayList<>();``        ``A.add(-``49``);``        ``A.add(``75``);``        ``A.add(``103``);``        ``A.add(-``147``);``        ``A.add(``164``);``        ``A.add(-``197``);``        ``A.add(-``238``);``        ``A.add(``314``);``        ``A.add(``348``);``        ``A.add(-``422``);``        ``int` `K = ``167``;``        ``IndexPair result = FindPairs(A, K);``        ``System.out.println(result.index_2 + ``" "` `+ result.index_1);``    ``}` `}` `//this code is contributed by bhardwajji`

## Python3

 `def` `find_pairs_with_sum(arr, k):``    ``seen ``=` `{}  ``# Dictionary to store elements seen so far and their indices` `    ``for` `i, num ``in` `enumerate``(arr):``        ``complement ``=` `k ``-` `num  ``# Calculate the complement needed to reach the target sum` `        ``# Check if the complement is in the dictionary (i.e., we've seen it before)``        ``if` `complement ``in` `seen:``            ``return` `[seen[complement], i]` `        ``# Store the current number in the dictionary with its index``        ``seen[num] ``=` `i` `    ``return` `None`  `# No pair with the desired sum found` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ``A ``=` `[``-``49``, ``75``, ``103``, ``-``147``, ``164``, ``-``197``, ``-``238``, ``314``, ``348``, ``-``422``]``    ``K ``=` `167``    ``result ``=` `find_pairs_with_sum(A, K)` `    ``if` `result:``        ``print``(result[``0``], result[``1``])``    ``else``:``        ``print``(``"No pair found with the desired sum"``)`

## C#

 `using` `System;``using` `System.Collections.Generic;` `class` `MainClass``{``    ``// Function to find pairs in the array with the desired sum``    ``static` `int``[] FindPairsWithSum(``int``[] arr, ``int` `k)``    ``{``        ``Dictionary<``int``, ``int``> seen = ``new` `Dictionary<``int``, ``int``>();` `        ``for` `(``int` `i = 0; i < arr.Length; i++)``        ``{``            ``int` `num = arr[i];``            ``int` `complement = k - num;` `            ``// Check if the complement is in the dictionary (i.e., we've seen it before)``            ``if` `(seen.ContainsKey(complement))``            ``{``                ``return` `new` `int``[] { seen[complement], i };``            ``}` `            ``// Store the current number in the dictionary with its index``            ``seen[num] = i;``        ``}` `        ``return` `null``; ``// No pair with the desired sum found``    ``}` `    ``public` `static` `void` `Main(``string``[] args)``    ``{``        ``int``[] A = { -49, 75, 103, -147, 164, -197, -238, 314, 348, -422 };``        ``int` `K = 167;``        ``int``[] result = FindPairsWithSum(A, K);` `        ``if` `(result != ``null``)``        ``{``            ``Console.WriteLine(result[0] + ``" "` `+ result[1]);``        ``}``        ``else``        ``{``            ``Console.WriteLine(``"No pair found with the desired sum"``);``        ``}``    ``}``}`

## Javascript

 `function` `findPairsWithSum(arr, k) {``  ``const seen = ``new` `Map(); ``// Map to store elements seen so far and their indices` `  ``for` `(let i = 0; i < arr.length; i++) {``    ``const num = arr[i];``    ``const complement = k - num; ``// Calculate the complement needed to reach the target sum` `    ``// Check if the complement is in the Map (i.e., we've seen it before)``    ``if` `(seen.has(complement)) {``      ``return` `[seen.get(complement), i];``    ``}` `    ``// Store the current number in the Map with its index``    ``seen.set(num, i);``  ``}` `  ``return` `null``; ``// No pair with the desired sum found``}` `// Driver Code``const A = [-49, 75, 103, -147, 164, -197, -238, 314, 348, -422];``const K = 167;``const result = findPairsWithSum(A, K);` `if` `(result) {``  ``console.log(result[0], result[1]);``} ``else` `{``  ``console.log(``"No pair found with the desired sum"``);``}` `// This code is contributed by Dwaipayan Bandyopadhyay`

Output
```3 7

```

Time Complexity: O(N)

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