# Count pairs with given sum

• Difficulty Level : Medium
• Last Updated : 18 Jun, 2022

Given an array of integers, and a number ‘sum’, find the number of pairs of integers in the array whose sum is equal to ‘sum’.

Examples:

Input:  arr[] = {1, 5, 7, -1}, sum = 6
Output:  2
Explanation: Pairs with sum 6 are (1, 5) and (7, -1)

Input:  arr[] = {1, 5, 7, -1, 5}, sum = 6
Output:  3
Explanation: Pairs with sum 6 are (1, 5), (7, -1) & (1, 5)

Input:  arr[] = {1, 1, 1, 1}, sum = 2
Output:  6
Explanation: There are 3! pairs with sum 2.

Input:  arr[] = {10, 12, 10, 15, -1, 7, 6, 5, 4, 2, 1, 1, 1}, sum = 11
Output:  9

Expected time complexity O(n)

Naive Solution – A simple solution is to traverse each element and check if there’s another number in the array which can be added to it to give sum.

## C++

 `// C++ implementation of simple method to find count of` `// pairs with given sum.` `#include ` `using` `namespace` `std;`   `// Returns number of pairs in arr[0..n-1] with sum equal` `// to 'sum'` `int` `getPairsCount(``int` `arr[], ``int` `n, ``int` `sum)` `{` `    ``int` `count = 0; ``// Initialize result`   `    ``// Consider all possible pairs and check their sums` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``for` `(``int` `j = i + 1; j < n; j++)` `            ``if` `(arr[i] + arr[j] == sum)` `                ``count++;`   `    ``return` `count;` `}`   `// Driver function to test the above function` `int` `main()` `{` `    ``int` `arr[] = { 1, 5, 7, -1, 5 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``int` `sum = 6;` `    ``cout << ``"Count of pairs is "` `         ``<< getPairsCount(arr, n, sum);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## C

 `// C implementation of simple method to find count of` `// pairs with given sum.` `#include `   `// Returns number of pairs in arr[0..n-1] with sum equal` `// to 'sum'` `int` `getPairsCount(``int` `arr[], ``int` `n, ``int` `sum)` `{` `    ``int` `count = 0; ``// Initialize result`   `    ``// Consider all possible pairs and check their sums` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``for` `(``int` `j = i + 1; j < n; j++)` `            ``if` `(arr[i] + arr[j] == sum)` `                ``count++;`   `    ``return` `count;` `}`   `// Driver function to test the above function` `int` `main()` `{` `    ``int` `arr[] = { 1, 5, 7, -1, 5 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``int` `sum = 6;` `    ``printf``(``"Count of pairs is %d"``,getPairsCount(arr, n, sum));` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## Java

 `// Java implementation of simple method to find count of` `// pairs with given sum.` `public` `class` `find {` `    ``public` `static` `void` `main(String args[])` `    ``{` `        ``int``[] arr = { ``1``, ``5``, ``7``, -``1``, ``5` `};` `        ``int` `sum = ``6``;` `        ``getPairsCount(arr, sum);` `    ``}`   `    ``// Prints number of pairs in arr[0..n-1] with sum equal` `    ``// to 'sum'` `    ``public` `static` `void` `getPairsCount(``int``[] arr, ``int` `sum)` `    ``{`   `        ``int` `count = ``0``; ``// Initialize result`   `        ``// Consider all possible pairs and check their sums` `        ``for` `(``int` `i = ``0``; i < arr.length; i++)` `            ``for` `(``int` `j = i + ``1``; j < arr.length; j++)` `                ``if` `((arr[i] + arr[j]) == sum)` `                    ``count++;`   `        ``System.out.printf(``"Count of pairs is %d"``, count);` `    ``}` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## Python3

 `# Python3 implementation of simple method` `# to find count of pairs with given sum.`   `# Returns number of pairs in arr[0..n-1]` `# with sum equal to 'sum'`     `def` `getPairsCount(arr, n, ``sum``):`   `    ``count ``=` `0`  `# Initialize result`   `    ``# Consider all possible pairs` `    ``# and check their sums` `    ``for` `i ``in` `range``(``0``, n):` `        ``for` `j ``in` `range``(i ``+` `1``, n):` `            ``if` `arr[i] ``+` `arr[j] ``=``=` `sum``:` `                ``count ``+``=` `1`   `    ``return` `count`     `# Driver function` `arr ``=` `[``1``, ``5``, ``7``, ``-``1``, ``5``]` `n ``=` `len``(arr)` `sum` `=` `6` `print``(``"Count of pairs is"``,` `      ``getPairsCount(arr, n, ``sum``))`   `# This code is contributed by Smitha Dinesh Semwal`

## C#

 `// C# implementation of simple` `// method to find count of` `// pairs with given sum.` `using` `System;`   `class` `GFG {` `    ``public` `static` `void` `getPairsCount(``int``[] arr, ``int` `sum)` `    ``{`   `        ``int` `count = 0; ``// Initialize result`   `        ``// Consider all possible pairs` `        ``// and check their sums` `        ``for` `(``int` `i = 0; i < arr.Length; i++)` `            ``for` `(``int` `j = i + 1; j < arr.Length; j++)` `                ``if` `((arr[i] + arr[j]) == sum)` `                    ``count++;`   `        ``Console.WriteLine(``"Count of pairs is "` `+ count);` `    ``}`   `    ``// Driver Code` `    ``static` `public` `void` `Main()` `    ``{` `        ``int``[] arr = { 1, 5, 7, -1, 5 };` `        ``int` `sum = 6;` `        ``getPairsCount(arr, sum);` `    ``}` `}`   `// This code is contributed` `// by Sach_Code`

## PHP

 ``

## Javascript

 ``

Output

`Count of pairs is 3`

Time Complexity: O(n2
Auxiliary Space: O(1)

Efficient Approach: This approach is based on the following idea:

If the array is sorted then for each array element arr[i] we can find the number of pairs by finding all the values (sum – arr[i]) which are situated after ith index.

Follow the steps below to implement this approach:

• Sort the array arr[] in increasing order.
• Loop from i = 0 to N-1.
• Find the index of the first element having value same or just greater than (sum – arr[i]) using lower bound.
• Find the index of the first element having value just greater than (sum – arr[i]) using upper bound.
• The gap between these two indices is the number of elements with value same as (sum – arr[i]).
• Add this with the final count of pairs.
• Return the final count after the iteration is over.

Below is the implementation of the above approach.

## C++

 `// C++ code to implement the approach`   `#include ` `using` `namespace` `std;`   `// Function to find the count of pairs` `int` `getPairsCount(``int` `arr[], ``int` `n, ``int` `k)` `{` `    ``sort(arr, arr + n);` `    ``int` `x = 0, c = 0, y, z;` `    ``for` `(``int` `i = 0; i < n - 1; i++) {` `        ``x = k - arr[i];` `      `  `        ``// Lower bound from i+1` `        ``int` `y = lower_bound(arr + i + 1,` `                            ``arr + n, x) - arr;` `        `  `        ``// Upper bound from i+1` `        ``int` `z = upper_bound(arr + i + 1, ` `                            ``arr + n, x) - arr;` `        ``c = c + z - y;` `    ``}` `    ``return` `c;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 1, 5, 7, -1, 5 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``int` `k = 6;` `  `  `    ``// Function call` `    ``cout << ``"Count of pairs is "` `         ``<< getPairsCount(arr, n, k);` `    ``return` `0;` `}`

Output

`Count of pairs is 3`

Time Complexity: O(n * log(n) )
Auxiliary Space: O(1)

This approach is contributed by tene2902

Most Efficient Approach:
A better solution is possible in O(n) time. Below is the Algorithm –

1. Create a map to store frequency of each number in the array. (Single traversal is required)
2. In the next traversal, for every element check if it can be combined with any other element (other than itself!) to give the desired sum. Increment the counter accordingly.
3. After completion of second traversal, we’d have twice the required value stored in counter because every pair is counted two times. Hence divide count by 2 and return.

Below is the implementation of above idea :

## C++

 `// C++ implementation of simple method to find count of` `// pairs with given sum.` `#include ` `using` `namespace` `std;`   `// Returns number of pairs in arr[0..n-1] with sum equal` `// to 'sum'` `int` `getPairsCount(``int` `arr[], ``int` `n, ``int` `sum)` `{` `    ``unordered_map<``int``, ``int``> m;`   `    ``// Store counts of all elements in map m` `    ``for` `(``int` `i = 0; i < n; i++)` `        ``m[arr[i]]++;`   `    ``int` `twice_count = 0;`   `    ``// iterate through each element and increment the` `    ``// count (Notice that every pair is counted twice)` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``twice_count += m[sum - arr[i]];`   `        ``// if (arr[i], arr[i]) pair satisfies the condition,` `        ``// then we need to ensure that the count is` `        ``// decreased by one such that the (arr[i], arr[i])` `        ``// pair is not considered` `        ``if` `(sum - arr[i] == arr[i])` `            ``twice_count--;` `    ``}`   `    ``// return the half of twice_count` `    ``return` `twice_count / 2;` `}`   `// Driver function to test the above function` `int` `main()` `{` `    ``int` `arr[] = { 1, 5, 7, -1, 5 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``int` `sum = 6;` `    ``cout << ``"Count of pairs is "` `         ``<< getPairsCount(arr, n, sum);` `    ``return` `0;` `}`

## Java

 `/* Java implementation of simple method to find count of` `pairs with given sum*/`   `import` `java.util.HashMap;`   `class` `Test {` `    ``static` `int` `arr[] = ``new` `int``[] { ``1``, ``5``, ``7``, -``1``, ``5` `};`   `    ``// Returns number of pairs in arr[0..n-1] with sum equal` `    ``// to 'sum'` `    ``static` `int` `getPairsCount(``int` `n, ``int` `sum)` `    ``{` `        ``HashMap hm = ``new` `HashMap<>();`   `        ``// Store counts of all elements in map hm` `        ``for` `(``int` `i = ``0``; i < n; i++) {`   `            ``// initializing value to 0, if key not found` `            ``if` `(!hm.containsKey(arr[i]))` `                ``hm.put(arr[i], ``0``);`   `            ``hm.put(arr[i], hm.get(arr[i]) + ``1``);` `        ``}` `        ``int` `twice_count = ``0``;`   `        ``// iterate through each element and increment the` `        ``// count (Notice that every pair is counted twice)` `        ``for` `(``int` `i = ``0``; i < n; i++) {` `            ``if` `(hm.get(sum - arr[i]) != ``null``)` `                ``twice_count += hm.get(sum - arr[i]);`   `            ``// if (arr[i], arr[i]) pair satisfies the` `            ``// condition, then we need to ensure that the` `            ``// count is decreased by one such that the` `            ``// (arr[i], arr[i]) pair is not considered` `            ``if` `(sum - arr[i] == arr[i])` `                ``twice_count--;` `        ``}`   `        ``// return the half of twice_count` `        ``return` `twice_count / ``2``;` `    ``}`   `    ``// Driver method to test the above function` `    ``public` `static` `void` `main(String[] args)` `    ``{`   `        ``int` `sum = ``6``;` `        ``System.out.println(` `            ``"Count of pairs is "` `            ``+ getPairsCount(arr.length, sum));` `    ``}` `}` `// This code is contributed by Gaurav Miglani`

## Python3

 `# Python 3 implementation of simple method` `# to find count of pairs with given sum.` `import` `sys`   `# Returns number of pairs in arr[0..n-1]` `# with sum equal to 'sum'`     `def` `getPairsCount(arr, n, ``sum``):`   `    ``m ``=` `[``0``] ``*` `1000`   `    ``# Store counts of all elements in map m` `    ``for` `i ``in` `range``(``0``, n):` `        ``m[arr[i]] ``+``=` `1`   `    ``twice_count ``=` `0`   `    ``# Iterate through each element and increment` `    ``# the count (Notice that every pair is` `    ``# counted twice)` `    ``for` `i ``in` `range``(``0``, n):`   `        ``twice_count ``+``=` `m[``sum` `-` `arr[i]]`   `        ``# if (arr[i], arr[i]) pair satisfies the` `        ``# condition, then we need to ensure that` `        ``# the count is  decreased by one such` `        ``# that the (arr[i], arr[i]) pair is not` `        ``# considered` `        ``if` `(``sum` `-` `arr[i] ``=``=` `arr[i]):` `            ``twice_count ``-``=` `1`   `    ``# return the half of twice_count` `    ``return` `int``(twice_count ``/` `2``)`     `# Driver function` `arr ``=` `[``1``, ``5``, ``7``, ``-``1``, ``5``]` `n ``=` `len``(arr)` `sum` `=` `6`   `print``(``"Count of pairs is"``, getPairsCount(arr,` `                                         ``n, ``sum``))`   `# This code is contributed by` `# Smitha Dinesh Semwal`

## C#

 `// C# implementation of simple method to` `// find count of pairs with given sum` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG {` `    ``public` `static` `int``[] arr = ``new` `int``[] { 1, 5, 7, -1, 5 };`   `    ``// Returns number of pairs in arr[0..n-1]` `    ``// with sum equal to 'sum'` `    ``public` `static` `int` `getPairsCount(``int` `n, ``int` `sum)` `    ``{` `        ``Dictionary<``int``, ``int``> hm` `            ``= ``new` `Dictionary<``int``, ``int``>();`   `        ``// Store counts of all elements` `        ``// in map hm` `        ``for` `(``int` `i = 0; i < n; i++) {`   `            ``// initializing value to 0,` `            ``// if key not found` `            ``if` `(!hm.ContainsKey(arr[i])) {` `                ``hm[arr[i]] = 0;` `            ``}`   `            ``hm[arr[i]] = hm[arr[i]] + 1;` `        ``}` `        ``int` `twice_count = 0;`   `        ``// iterate through each element and` `        ``// increment the count (Notice that` `        ``// every pair is counted twice)` `        ``for` `(``int` `i = 0; i < n; i++) {` `            ``if` `(hm[sum - arr[i]] != 0) {` `                ``twice_count += hm[sum - arr[i]];` `            ``}`   `            ``// if (arr[i], arr[i]) pair satisfies` `            ``// the condition, then we need to ensure` `            ``// that the count is decreased by one` `            ``// such that the (arr[i], arr[i])` `            ``// pair is not considered` `            ``if` `(sum - arr[i] == arr[i]) {` `                ``twice_count--;` `            ``}` `        ``}`   `        ``// return the half of twice_count` `        ``return` `twice_count / 2;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main(``string``[] args)` `    ``{` `        ``int` `sum = 6;` `        ``Console.WriteLine(``"Count of pairs is "` `                          ``+ getPairsCount(arr.Length, sum));` `    ``}` `}`   `// This code is contributed by Shrikant13`

## Javascript

 ``

Output

`Count of pairs is 3`

Time Complexity: O(n), to iterate over the array
Auxiliary Space: O(n), to make a map of size n

More efficient solution in one loop:-

## C++

 `// C++ implementation of simple method to find count of` `// pairs with given sum.` `#include ` `using` `namespace` `std;`   `// Returns number of pairs in arr[0..n-1] with sum equal` `// to 'sum'` `int` `getPairsCount(``int` `arr[], ``int` `n, ``int` `k)` `{` `    ``unordered_map<``int``, ``int``> m;` `    ``int` `count = 0;` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(m.find(k - arr[i]) != m.end()) {` `            ``count += m[k - arr[i]];` `        ``}` `        ``m[arr[i]]++;` `    ``}` `    ``return` `count;` `}`   `// Driver function to test the above function` `int` `main()` `{` `    ``int` `arr[] = { 1, 5, 7, -1, 5};` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``int` `sum = 6;` `    ``cout << ``"Count of pairs is "` `         ``<< getPairsCount(arr, n, sum);` `    ``return` `0;` `}`

## Java

 `// Java implementation of simple method to find count of` `// pairs with given sum.` `import` `java.util.*;`   `class` `GFG{`   `// Returns number of pairs in arr[0..n-1] with sum equal` `// to 'sum'` `static` `int` `getPairsCount(``int` `arr[], ``int` `n, ``int` `k)` `{` `    ``HashMap m = ``new` `HashMap<>();` `    ``int` `count = ``0``;` `    ``for` `(``int` `i = ``0``; i < n; i++) {` `        ``if` `(m.containsKey(k - arr[i])) {` `            ``count += m.get(k - arr[i]);` `        ``}` `        ``if``(m.containsKey(arr[i])){` `            ``m.put(arr[i], m.get(arr[i])+``1``);` `        ``}` `        ``else``{` `            ``m.put(arr[i], ``1``);` `        ``}` `    ``}` `    ``return` `count;` `}`   `// Driver function to test the above function` `public` `static` `void` `main(String[] args)` `{` `    ``int` `arr[] = { ``1``, ``5``, ``7``, -``1``, ``5``};` `    ``int` `n = arr.length;` `    ``int` `sum = ``6``;` `    ``System.out.print(``"Count of pairs is "` `         ``+ getPairsCount(arr, n, sum));` `}` `}`   `// This code is contributed by umadevi9616 `

## Python3

 `# Python implementation of simple method to find count of` `# pairs with given sum.`   `# Returns number of pairs in arr[0..n-1] with sum equal to 'sum'` `def` `getPairsCount(arr, n, ``sum``):` `  ``unordered_map ``=` `{}` `  ``count ``=` `0` `  ``for` `i ``in` `range``(n):` `    ``if` `sum` `-` `arr[i] ``in` `unordered_map:` `      ``count ``+``=` `unordered_map[``sum` `-` `arr[i]]` `    ``if` `arr[i] ``in` `unordered_map:` `      ``unordered_map[arr[i]] ``+``=` `1` `    ``else``:` `      ``unordered_map[arr[i]] ``=` `1` `  ``return` `count`   `# Driver code` `arr ``=` `[``1``, ``5``, ``7``, ``-``1``, ``5``]` `n ``=` `len``(arr)` `sum` `=` `6` `print``(``'Count of pairs is'``, getPairsCount(arr, n, ``sum``))`   `# This code is contributed by Manish Thapa`

## C#

 `// C# implementation of simple method to find count of` `// pairs with given sum.` `using` `System;` `using` `System.Collections.Generic;`   `public` `class` `GFG {`   `    ``// Returns number of pairs in arr[0..n-1] with sum equal` `    ``// to 'sum'` `    ``static` `int` `getPairsCount(``int` `[]arr, ``int` `n, ``int` `k) {` `        ``Dictionary<``int``, ``int``> m = ``new` `Dictionary<``int``, ``int``>();` `        ``int` `count = 0;` `        ``for` `(``int` `i = 0; i < n; i++) {` `            ``if` `(m.ContainsKey(k - arr[i])) {` `                ``count += m[k - arr[i]];` `            ``}` `            ``if` `(m.ContainsKey(arr[i])) {` `                ``m[arr[i]] = m[arr[i]] + 1;` `            ``} ``else` `{` `                ``m.Add(arr[i], 1);` `            ``}` `        ``}` `        ``return` `count;` `    ``}`   `    ``// Driver function to test the above function` `    ``public` `static` `void` `Main(String[] args) {` `        ``int` `[]arr = { 1, 5, 7, -1, 5 };` `        ``int` `n = arr.Length;` `        ``int` `sum = 6;` `        ``Console.Write(``"Count of pairs is "` `+ getPairsCount(arr, n, sum));` `    ``}` `}`   `// This code is contributed by umadevi9616 `

## Javascript

 ``

Output

`Count of pairs is 3`

Time Complexity: O(n), to iterate over the array
Auxiliary Space: O(n), to make a map of size n