# Count pairs with given sum

Last Updated : 13 Apr, 2024

Given an array of N integers, and an integer K, the task is to find the number of pairs of integers in the array whose sum is equal to K.

Examples:

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

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

Input: arr[] = {1, 1, 1, 1}, K = 2
Output:  6
Explanation: Pairs with sum 2 are (1, 1), (1, 1), (1, 1), (1, 1), (1, 1).

Input: arr[] = {10, 12, 10, 15, -1, 7, 6, 5, 4, 2, 1, 1, 1}, K = 11
Output:  9
Explanation: Pairs with sum 11 are (10, 1), (10, 1), (10, 1), (12, -1), (10, 1), (10, 1), (10, 1), (7, 4), (6, 5).

NaÃ¯ve Approach:

A simple solution is to user nested loops, one for traversal of each element and other for checking if there’s another number in the array which can be added to it to give K.

Illustration:

Consider an array arr [ ] = {1 ,5 ,7 ,1} and K = 6

• initialize count = 0
• First iteration
• i = 0
• j = 1
• arr[i]+arr[j] == K
• count = 1
• i = 0
• j = 2
• arr[i] + arr[j] != K
• count = 1
• i = 0
• j = 3
• arr[i] + arr[j] != K
• count = 1
• Second iteration
• i = 1
• j = 2
• arr[i] + arr[j] != K
• count = 1
• i = 1
• j = 3
• arr[i] + arr[j] == K
• count = 2
• Third iteration
• i = 2
• j = 3
• arr[i] + arr[j] != K
• count = 2
• Hence Output is 2 .

Follow the steps below to solve the given problem:

Follow the steps below for implementation:

• Initialize the count variable with 0 which stores the result.
• Use two nested loop and check if arr[i] + arr[j] == K, then increment the count variable.
• Return the count.

Below is the implementation of the above approach.

C++ ```// C++ implementation of simple method to find count of // pairs with given sum K. #include <bits/stdc++.h> using namespace std; // Returns number of pairs in arr[0..n-1] with sum equal // to 'K' int getPairsCount(int arr[], int n, int K) { // Initialize result int count = 0; // 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] == K) count++; return count; } // Driver function to test the above function int main() { int arr[] = { 1, 5, 7, -1 }; int n = sizeof(arr) / sizeof(arr[0]); int K = 6; cout << "Count of pairs is " // Function Call << getPairsCount(arr, n, K); 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 <stdio.h> // Returns number of pairs in arr[0..n-1] with sum equal // to 'sum' int getPairsCount(int arr[], int n, int K) { // Initialize result int count = 0; // 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] == K) count++; return count; } // Driver function to test the above function int main() { int arr[] = { 1, 5, 7, -1 }; int n = sizeof(arr) / sizeof(arr[0]); int K = 6; printf("Count of pairs is %d", // Function Call getPairsCount(arr, n, K)); 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 K = 6; // Function Call getPairsCount(arr, K); } // Prints number of pairs in arr[0..n-1] with sum equal // to 'sum' public static void getPairsCount(int[] arr, int K) { // Initialize result int count = 0; // 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]) == K) count++; System.out.printf("Count of pairs is %d", count); } } // This code is contributed by Aditya Kumar (adityakumar129) ``` 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 ``` Javascript ```<script> // Javascript 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' function getPairsCount(arr, n, sum) { let count = 0; // Initialize result // Consider all possible pairs and check their sums for (let i = 0; i < n; i++) for (let j = i + 1; j < n; j++) if (arr[i] + arr[j] == sum) count++; return count; } // Driver function to test the above function let arr = [ 1, 5, 7, -1, 5 ]; let n = arr.length; let sum = 6; document.write("Count of pairs is " + getPairsCount(arr, n, sum)); // This code is contributed by Mayank Tyagi </script> ``` PHP ```<?php // PHP 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' function getPairsCount(\$arr, \$n, \$sum) { // Initialize result \$count = 0; // Consider all possible pairs // and check their sums for (\$i = 0; \$i < \$n; \$i++) for (\$j = \$i + 1; \$j < \$n; \$j++) if (\$arr[\$i] + \$arr[\$j] == \$sum) \$count++; return \$count; } // Driver Code \$arr = array(1, 5, 7, -1, 5) ; \$n = sizeof(\$arr); \$sum = 6; echo "Count of pairs is " , getPairsCount(\$arr, \$n, \$sum); // This code is contributed by nitin mittal. ?> ``` 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, K): 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] == K: count += 1 return count # Driver function arr = [1, 5, 7, -1] n = len(arr) K = 6 print("Count of pairs is", getPairsCount(arr, n, K)) # This code is contributed by Smitha Dinesh Semwal ```

Output
```Count of pairs is 2

```

Time Complexity: O(n2), traversing the array for each element
Auxiliary Space: O(1)

## Count pairs with given sum using Binary Search.

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

Illustration:

Given arr[ ] = {1, 5, 7, -1} and K = 6

• sort the array = {-1,1,5,7}
• initialize count = 0
• At index = 0:
• val = K – arr[0] = 6 – (-1) = 7
• count = count + upperBound(1, 3, 7) – lowerBound(1, 3, 7)
• count = 1
• At index = 1:
• val = K – arr[1] = 6 – 1 = 5
• count = count + upperBound(2, 3, 5) – lowerBound(2, 3, 5)
• count = 2
• At index = 2:
• val = K – arr[2] = 6 – 5 = 1
• count = count + upperBound(3, 3, 1) – lowerBound(3, 3, 1)
• count = 2
• Number of pairs = 2

Follow the steps below to solve the given problem:

• 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 (K – arr[i]) using lower bound.
• Find the index of the first element having value just greater than (K – arr[i]) using upper bound.
• The gap between these two indices is the number of elements with value same as (K – 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 <bits/stdc++.h> 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 }; int n = sizeof(arr) / sizeof(arr[0]); int k = 6; // Function call cout << "Count of pairs is " << getPairsCount(arr, n, k); return 0; } ``` Java ```// Java code for the above approach import java.io.*; import java.util.*; class GFG { // lowerBound implementation public static int lowerBound(int[] arr, int start, int end, int key) { while (start < end) { int mid = start + (end - start) / 2; if (arr[mid] < key) { start = mid + 1; } else { end = mid; } } return start; } // upperBound implementation public static int upperBound(int[] arr, int start, int end, int key) { while (start < end) { int mid = start + (end - start) / 2; if (arr[mid] <= key) { start = mid + 1; } else { end = mid; } } return start; } // Function to find the count of pairs public static int getPairsCount(int[] arr, int n, int k) { Arrays.sort(arr); int c = 0; for (int i = 0; i < n - 1; i++) { int x = k - arr[i]; int y = lowerBound(arr, i + 1, n, x); int z = upperBound(arr, i + 1, n, x); c = c + z - y; } return c; } public static void main(String[] args) { int[] arr = { 1, 5, 7, -1}; int n = arr.length; int k = 6; // Function call System.out.println("Count of pairs is " + getPairsCount(arr, n, k)); } } // This code is contributed by lokeshmvs21. ``` C# ```// C# code for the above approach using System; using System.Collections; public class GFG { // lowerBound implementation public static int lowerBound(int[] arr, int start, int end, int key) { while (start < end) { int mid = start + (end - start) / 2; if (arr[mid] < key) { start = mid + 1; } else { end = mid; } } return start; } // upperBound implementation public static int upperBound(int[] arr, int start, int end, int key) { while (start < end) { int mid = start + (end - start) / 2; if (arr[mid] <= key) { start = mid + 1; } else { end = mid; } } return start; } // Function to find the count of pairs public static int getPairsCount(int[] arr, int n, int k) { Array.Sort(arr); int c = 0; for (int i = 0; i < n - 1; i++) { int x = k - arr[i]; int y = lowerBound(arr, i + 1, n, x); int z = upperBound(arr, i + 1, n, x); c = c + z - y; } return c; } static public void Main() { // Code int[] arr = { 1, 5, 7, -1}; int n = arr.Length; int k = 6; // Function call Console.WriteLine("Count of pairs is " + getPairsCount(arr, n, k)); } } // This code is contributed by lokesh. ``` Javascript ```// JavaScript code for the above approach // lowerBound implementation function lowerBound(arr, start, end, key) { while (start < end) { var mid = start + Math.floor((end - start) / 2); if (arr[mid] < key) { start = mid + 1; } else { end = mid; } } return start; } // upperBound implementation function upperBound(arr, start, end, key) { while (start < end) { var mid = start + Math.floor((end - start) / 2); if (arr[mid] <= key) { start = mid + 1; } else { end = mid; } } return start; } // Function to find the count of pairs function getPairsCount(arr, n, k) { arr.sort((a, b) => a - b); var c = 0; for (var i = 0; i < n - 1; i++) { var x = k - arr[i]; var y = lowerBound(arr, i + 1, n, x); var z = upperBound(arr, i + 1, n, x); c = c + z - y; } return c; } var arr = [1, 5, 7, -1]; var n = arr.length; var k = 6; // Function call console.log("Count of pairs is " + getPairsCount(arr, n, k)); ``` Python3 ```# Python code to implement the approach import bisect # Function to find the count of pairs def getPairsCount(arr, n, k): arr.sort() x, c = 0, 0 for i in range(n-1): x = k-arr[i] # Lower bound from i+1 y = bisect.bisect_left(arr, x, i+1, n) # Upper bound from i+1 z = bisect.bisect(arr, x, i+1, n) c = c+z-y return c # Driver function arr = [1, 5, 7, -1] n = len(arr) k = 6 # Function call print("Count of pairs is", getPairsCount(arr, n, k)) # This code is contributed by Pushpesh Raj ```

Output
```Count of pairs is 2

```

Time Complexity: O(n * log(n) ), applying binary search on each element
Auxiliary Space: O(1)

## Count pairs with given sum using Hashing

• Check the frequency of K – arr[i] in the arr
• This can be achieved using Hashing.

Illustration:

Given arr[] = {1, 5, 7, -1} and K = 6

• initialize count = 0
• At index = 0:
• freq[K – arr[0]] = freq[6 – 1] = freq[5] = 0
• count = 0
• freq[arr[0]] = freq[1] = 1
• At index = 1:
• freq[K – arr[1]] = freq[6 – 5] = freq[1] = 1
• count = 1
• freq[arr[1]] = freq[5] = 1
• At index = 2:
• freq[K – arr[2]] = freq[6 – 7] = freq[-1] = 0
• count = 1
• freq[arr[2]] = freq[7] = 1
• At index = 3:
• freq[K – arr[3]] = freq[6 – (-1)] = freq[7] = 1
• count = 2
• freq[arr[3]] = freq[-1] = 1
• Number of pairs  = 2

Follow the steps below to solve the given problem:

• Create a map to store the frequency of each number in the array.
• Check if (K – arr[i]) is present in the map, if present then increment the count variable by its frequency.
• After traversal is over, return the count.

Below is the implementation of the above idea :

C++ ```// C++ implementation of simple method to // find count of pairs with given sum. #include <bits/stdc++.h> 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_set<int> s; int count = 0; for (int i = 0; i < n; i++) { if (s.find(k - arr[i]) != s.end()) { count++; } else s.insert(k-arr[i]); } return count; } // Driver code int main() { int arr[] = { 1, 5, 7, -1}; int n = sizeof(arr) / sizeof(arr[0]); int sum = 6; // Function Call 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<Integer, Integer> 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}; int n = arr.length; int sum = 6; System.out.print("Count of pairs is " + getPairsCount(arr, n, sum)); } } // This code is contributed by umadevi9616 ``` 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 }; int n = arr.Length; int sum = 6; Console.Write("Count of pairs is " + getPairsCount(arr, n, sum)); } } // This code is contributed by umadevi9616 ``` Javascript ```<script> // javascript 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' function getPairsCount(arr , n , k) { var m = new Map(); var count = 0; for (var i = 0; i < n; i++) { if (m.has(k - arr[i])) { count += m.get(k - arr[i]); } if (m.has(arr[i])) { m.set(arr[i], m.get(arr[i]) + 1); } else { m.set(arr[i], 1); } } return count; } // Driver function to test the above function var arr = [ 1, 5, 7, -1 ]; var n = arr.length; var sum = 6; document.write("Count of pairs is " + getPairsCount(arr, n, sum)); // This code is contributed by umadevi9616 </script> ``` 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] n = len(arr) sum = 6 print('Count of pairs is', getPairsCount(arr, n, sum)) # This code is contributed by Manish Thapa ```

Output
```Count of pairs is 2

```

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

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