# Count number of distinct pairs whose sum exists in the given array

Given an array of N positive integers. Count the number of pairs whose sum exists in the given array. While repeating pairs will not be counted again. And we can’t make a pair using same position element. Eg : (2, 1) and (1, 2) will be considered as only one pair.

Please read all examples carefully.

**Examples:**

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Input : arr[] = {1, 2, 3, 5, 10} Output : 2 Explanation : Here there are two such pairs: (1 + 2) = 3, (2 + 3) = 5. Note : Here we can't take pair (5, 5) as we can see 5 is not coming twice Input : arr[] = {1, 5, 6, 4, -1, 5} Output : 4 Explanation : (1 + 5) = 6, (1 + 4) = 5, (5 + -1) = 4, (6 + -1) = 5 Note : Here (1, 5) comes twice will be considered as only one pair. Input : arr[] = {5, 5, 5, 5, 10} Output : 1 Explanation : (5 + 5) = 10 Note : Here (5, 5) comes twice will be considered as only one pair.

The idea is to map of pairs to find unique elements. We first store elements and their counts in a map. Then we traverse array elements, for every pair of elements (arr[i], arr[j]), we check if (arr[i] + arr[j]) exists in array. If exists, then we check if it is already counted using map of pairs. If not already counted, then we increment count.

## C++

`// C++ implementation to find count of unique pairs` `// whose sum exists in given array` `#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)` `{` ` ` `// Store counts of all elements in map m` ` ` `// to find pair (arr[i], sum-arr[i])` ` ` `// because (arr[i]) + (sum - arr[i]) = sum` ` ` `map<` `int` `, ` `int` `> m;` ` ` `for` `(` `int` `i = 0; i < n; i++)` ` ` `m[arr[i]]++;` ` ` ` ` `// To remove duplicate items we use result map` ` ` `map<pair<` `int` `, ` `int` `>, ` `int` `> pairs;` ` ` ` ` `int` `count = 0; ` `// Initialize result` ` ` ` ` `// Consider all pairs` ` ` `for` `(` `int` `i = 0; i < n; i++) {` ` ` `for` `(` `int` `j = i + 1; j < n; j++) {` ` ` ` ` `// If sum of current pair exists` ` ` `if` `(m[arr[i] + arr[j]] > 0 && ` ` ` `pairs[{ arr[i], arr[j] }] == 0) {` ` ` `count++;` ` ` `}` ` ` ` ` `// Insert current pair both ways to avoid` ` ` `// duplicates.` ` ` `pairs[{ arr[i], arr[j] }]++;` ` ` `pairs[{ arr[j], arr[i] }]++;` ` ` `}` ` ` `}` ` ` `return` `count;` `}` ` ` `// Driver function to test the above function` `int` `main()` `{` ` ` `int` `arr[] = { 1, 5, 6, 4, -1, 5, 10 };` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` ` ` `cout << getPairsCount(arr, n);` ` ` `return` `0;` `}` |

## Python3

`# Python3 implementation to find count ` `# of unique pairs whose sum exists in` `# given array` ` ` `# Returns number of pairs in arr[0..n-1] ` `# with sum equal to 'sum'` `def` `getPairsCount(arr, n):` ` ` ` ` `# Store counts of all elements in map m` ` ` `# to find pair (arr[i], sum-arr[i])` ` ` `# because (arr[i]) + (sum - arr[i]) = sum` ` ` `m ` `=` `dict` `()` ` ` `for` `i ` `in` `range` `(n):` ` ` `m[arr[i]] ` `=` `m.get(arr[i], ` `0` `) ` `+` `1` ` ` ` ` `# To remove duplicate items ` ` ` `# we use result map` ` ` `pairs1 ` `=` `dict` `()` ` ` ` ` `count ` `=` `0` `# Initialize result` ` ` ` ` `for` `i ` `in` `range` `(n):` ` ` `for` `j ` `in` `range` `(i ` `+` `1` `, n):` ` ` `l ` `=` `arr[i] ` `+` `arr[j]` ` ` `tp ` `=` `(arr[i], arr[j])` ` ` ` ` `if` `l ` `in` `m.keys():` ` ` ` ` `if` `tp ` `not` `in` `pairs1.keys():` ` ` ` ` `count ` `+` `=` `1` ` ` `pairs1[(arr[i], arr[j])] ` `=` `1` ` ` `pairs1[(arr[j], arr[i])] ` `=` `1` ` ` ` ` `return` `count` ` ` `# Driver Code` `arr ` `=` `[` `1` `, ` `5` `, ` `6` `, ` `4` `, ` `-` `1` `, ` `5` `, ` `10` `]` `n ` `=` `len` `(arr)` ` ` `print` `(getPairsCount(arr, n))` ` ` `# This code is contributed by Mohit Kumar` |

**Output:**

6

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