# 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 + arr) = (-147 + 314) = 167.

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++ 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) ` `{ ` ` `  `    ``// Intializing 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; ` `        ``} ` ` `  `        ``// Conditon if the curent 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; ` `} `

Output:

```3 7
```

Time Complexity: O(N)

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